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Palanikumar M, Kausar N, Tharaniya P, Stević Ž, Tesgera Tolasa F. Complex Diophantine interval-valued Pythagorean normal set for decision-making processes. Sci Rep 2025; 15:783. [PMID: 39755724 DOI: 10.1038/s41598-024-82532-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2024] [Accepted: 12/05/2024] [Indexed: 01/06/2025] Open
Abstract
A novel method for solving the multiple-attribute decision-making problem is proposed using the complex Diophantine interval-valued Pythagorean normal set (CDIVPNS). This study aims to discuss aggregating operations and how they are interpreted. We discuss the concept of CDIVPN weighted averaging (CDIVPNWA), CDIVPN weighted geometric (CDIVPNWG), generalized CDIVPN weighted averaging (CGDIVPNWA) and generalized CGDIVPN weighted geometric (CGDIVPNWG). This study aimed to examine several aggregation operators using complex Diophantine interval-valued Pythagorean normal sets. We calculated the weighted average and geometric distance based on an aggregating model. We demonstrate that complex Diophantine interval-valued Pythagorean normal sets satisfy algebraic structures such as associative, distributive, idempotent, bounded, commutative and monotonic properties. In this study, we discuss the mathematical properties of the score and accuracy values. We provide an example of how enhanced score and accuracy values are used in the real world. Machine tool technology and computer science play essential roles in robots. To evaluate robotic systems, four factors must be considered such as tasks, precision, speed and completion of the work. Consequently, it is evident that the models are significantly influenced by the natural number ∇. To further demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and applied to a numerical example. Additionally, a comparative study has been carried out to demonstrate the better results that the proposed approach provides when compared to current approaches.
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Affiliation(s)
- Murugan Palanikumar
- Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, 602105, India
| | - Nasreen Kausar
- Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler, 34220, Turkey
| | - Ponnaiah Tharaniya
- Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India
| | - Željko Stević
- School of Industrial Management Engineering, Korea University, 145 Anam-Ro, Seongbuk-Gu, 02841, Seoul, Korea
- Department of Mobile Machinery and Railway Transport, Vilnius Gediminas Technical University, Vilnius, Lithuania
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2
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Abbas F, Ali J, Mashwani WK, Gündüz N, Syam MI. q-Rung orthopair fuzzy 2-tuple linguistic WASPAS algorithm for patients' prioritization based on prioritized Maclaurin symmetric mean aggregation operators. Sci Rep 2024; 14:10659. [PMID: 38724560 PMCID: PMC11538463 DOI: 10.1038/s41598-024-57452-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2024] [Accepted: 03/18/2024] [Indexed: 11/07/2024] Open
Abstract
Due to the fuzziness of the medical field, q-rung orthopair fuzzy 2-tuple linguistic (q-RF2L) set is the privileged way to aid medical professionals in conveying their assessments in the patient prioritization problem. The theme of the present study is to put forward a novel approach centered around the merging of prioritized averaging (PA) and the Maclaurin symmetric mean (MSM) operator within q-RF2L context. According to the prioritization of the professionals and the correlation among the defined criteria, we apply both PA and MSM to assess priority degrees and relationships, respectively. Keeping the pluses of the PA and MSM operators in mind, we introduce two aggregation operators (AOs), namely q-RF2L prioritized Maclaurin symmetric mean and q-RF2L prioritized dual Maclaurin symmetric mean operators. Meanwhile, some essential features and remarks of the proposed AOs are discussed at length. Based on the formulated AOs, we extend the weighted aggregated sum product assessment methodology to cope with q-RF2L decision-making problems. Ultimately, to illustrate the practicality and effectiveness of the stated methodology, a real-world example of patients' prioritization problem is addressed, and an in-depth analysis with prevailing methods is performed.
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Affiliation(s)
- Fatima Abbas
- Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, KPK, Pakistan
| | - Jawad Ali
- Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, KPK, Pakistan
| | - Wali Khan Mashwani
- Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, KPK, Pakistan
| | - Necla Gündüz
- Department of Statistics, Faculty of Science, Gazi University, Ankara, Turkey
| | - Muhammad I Syam
- Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al-Ain, UAE.
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3
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Cao Y, Han X, Wu X, Deveci M, Kadry S, Delen D. Evaluation of food waste treatment techniques using the complex q-rung orthopair fuzzy generalized TODIM method with weighted power geometric operator. JOURNAL OF ENVIRONMENTAL MANAGEMENT 2024; 353:120105. [PMID: 38325282 DOI: 10.1016/j.jenvman.2024.120105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Revised: 12/27/2023] [Accepted: 01/11/2024] [Indexed: 02/09/2024]
Abstract
Food waste has received wide attention due to its hazardous environmental effects, such as soil, water, and air pollution. Evaluating food waste treatment techniques is imperative to realize environmental sustainability. This study proposes an integrated framework, the complex q-rung orthopair fuzzy-generalized TODIM (an acronym in Portuguese for interactive and multi-criteria decision-making) method with weighted power geometric operator, to assess the appropriate technique for food waste. The assessment of food waste treatment techniques can be divided into three phases: information processing, information fusion, and ranking alternatives. Firstly, the complex q-rung orthopair fuzzy set flexibly describes the information with periodic characteristics in the processing process with various parameters q. Then, the weighted power geometric operator is employed to calculate the weight of the expert and form the group evaluation matrix, in which the weight of each input rating depends upon the other input ratings. It can simulate the mutual support, multiplicative preferences, and interrelationship of experts. Next, the generalized TODIM method is employed to rank the food waste treatment techniques, considering experts' psychological characteristics and bounded behavior. Subsequently, a real-world application case examines the practicability of the proposed framework. Furthermore, the sensitivity analysis verifies the validity and stability of the presented framework. The comparative study highlights the effectiveness of this framework using the existing frameworks. According to the result, Anaerobic digestion (0.0043) has the highest priority among the considered alternatives, while Incineration (-0.0009) has the lowest.
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Affiliation(s)
- Yushuo Cao
- School of Economics and Management, Anhui Normal University, Wuhu, 241000, Anhui, China.
| | - Xiao Han
- School of Economics and Management, Anhui Normal University, Wuhu, 241000, Anhui, China.
| | - Xuzhong Wu
- School of Economics and Management, Anhui Normal University, Wuhu, 241000, Anhui, China.
| | - Muhammet Deveci
- Department of Industrial Engineering, Turkish Naval Academy, National Defence University, 34942 Tuzla, Istanbul, Turkey; The Bartlett School of Sustainable Construction, University College London, 1-19 Torrington Place, London, WC1E 7HB, UK; Department of Electrical and Computer Engineering, Lebanese American University, Byblos, Lebanon.
| | - Seifedine Kadry
- Department of Applied Data Science, Noroff University College, Kristiansand, Norway; Artificial Intelligence Research Center (AIRC), Ajman University, Ajman, 346, United Arab Emirates; MEU Research Unit, Middle East University, Amman 11831, Jordan.
| | - Dursun Delen
- Center for Health Systems Innovation, Department of Management Science and Information Systems, Spears School of Business, Oklahoma State University, Stillwater, 74078, Oklahoma, USA; Department of Industrial Engineering, Faculty of Engineering and Natural Sciences, Istinye University, 34396, Sarıyer/İstanbul, Türkiye.
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Ali Z, Emam W, Mahmood T, Wang H. Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems. Heliyon 2024; 10:e24767. [PMID: 38371962 PMCID: PMC10873673 DOI: 10.1016/j.heliyon.2024.e24767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2023] [Revised: 12/29/2023] [Accepted: 01/14/2024] [Indexed: 02/20/2024] Open
Abstract
In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.
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Affiliation(s)
- Zeeshan Ali
- Department of Mathematics and Statistics, Riphah International University Islamabad, Pakistan
| | - Walid Emam
- Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
| | - Tahir Mahmood
- Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan
| | - Haolun Wang
- School of Economics and Management, Nanchang Hangkong University, Nanchang 330063, China
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Rong Y, Yu L. Decision Support System for Prioritization of Offshore Wind Farm Site by Utilizing Picture Fuzzy Combined Compromise Solution Group Decision Method. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1081. [PMID: 37510028 PMCID: PMC10378162 DOI: 10.3390/e25071081] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Revised: 07/12/2023] [Accepted: 07/17/2023] [Indexed: 07/30/2023]
Abstract
The selection of offshore wind farm site (OWFS) has important strategic significance for vigorously developing offshore new energy and is deemed as a complicated uncertain multicriteria decision-making (MCDM) process. To further promote offshore wind power energy planning and provide decision support, this paper proposes a hybrid picture fuzzy (PF) combined compromise solution (CoCoSo) technique for prioritization of OWFSs. To begin with, a fresh PF similarity measure is proffered to estimate the importance of experts. Next, the novel operational rules for PF numbers based upon the generalized Dombi norms are defined, and four novel generalized Dombi operators are propounded. Afterward, the PF preference selection index (PSI) method and PF stepwise weights assessment ratio analysis (SWARA) model are propounded to identify the objective and subjective weight of criteria, separately. In addition, the enhanced CoCoSo method is proffered via the similarity measure and new operators for ranking OWFSs with PF information. Lastly, the applicability and feasibility of the propounded PF-PSI-SWARA-CoCoSo method are adopted to ascertain the optimal OWFS. The comparison and sensibility investigations are also carried out to validate the robustness and superiority of our methodology. Results manifest that the developed methodology can offer powerful decision support for departments and managers to evaluate and choose the satisfying OWFSs.
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Affiliation(s)
- Yuan Rong
- School of Management, Shanghai University, Shanghai 200444, China
| | - Liying Yu
- School of Management, Shanghai University, Shanghai 200444, China
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6
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Wan G, Rong Y, Garg H. An efficient spherical fuzzy MEREC-CoCoSo approach based on novel score function and aggregation operators for group decision making. GRANULAR COMPUTING 2023; 8:1-23. [PMID: 38625159 PMCID: PMC10184975 DOI: 10.1007/s41066-023-00381-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 04/15/2023] [Indexed: 04/17/2024]
Abstract
The major objective of the current investigation is to build an integrated multiple criteria group decision-making (MCGDM) methodology based on combined compromise solution (CoCoSo) and spherical fuzzy set for determining the optimal solar power station. To begin with, an innovative spherical fuzzy score function is brought forward to strengthen the efficiency of the comparison for spherical fuzzy number (SFN). Secondly, several newly operational laws for SFN are defined and some novel aggregation operation based on them are propounded. The corresponding excellent properties of the novel operators are also explored at length. Further, the spherical fuzzy method on the removal effects of criteria (MEREC) technique is presented by the proposed score function to work out the importance of the criteria. Lastly, an MCGDM approach is propounded based on improved spherical fuzzy CoCoSo to obtain the ranking of the solar power station locations. The feasibility and practicability of the proposed SF-MEREC-CoCoSo method are investigated through the comparison study with the extant methods. The sensibility analysis is also executed to discuss the robustness and stability of the propounded methodology.
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Affiliation(s)
- Guorou Wan
- Department of Basic Education, Sichuan College of Architectural Technology, Deyang, 618000 China
| | - Yuan Rong
- School of Management, Shanghai University, Shanghai, 200444 China
| | - Harish Garg
- School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab 147004 India
- Department of Mathematics, Graphics Era Deemed to Be University, Dehradun, Uttarakhand 248002 India
- Applied Science Research Center, Applied Science Private University, Amman, 11931 Jordan
- College of Technical Engineering, The Islamic University, Najaf, Iraq
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7
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q-rung orthopair fuzzy 2-tuple linguistic clustering algorithm and its applications to clustering analysis. Sci Rep 2023; 13:2789. [PMID: 36797313 PMCID: PMC9935624 DOI: 10.1038/s41598-023-29932-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 02/13/2023] [Indexed: 02/18/2023] Open
Abstract
q-ROPFLS, including numeric and linguistic data, has a wide range of applications in handling uncertain information. This article aims to investigate q-ROPFL correlation coefficient based on the proposed information energy and covariance formulas. Moreover, considering that different q-ROPFL elements may have varying criteria weights, the weighted correlation coefficient is further explored. Some desirable characteristics of the presented correlation coefficients are also discussed and proven. In addition, some theoretical development is provided, including the concept of composition matrix, correlation matrix, and equivalent correlation matrix via the proposed correlation coefficients. Then, a clustering algorithm is expanded where data is expressed in q-ROPFL form with unknown weight information and is explained through an illustrative example. Besides, detailed parameter analysis and comparative study are performed with the existing approaches to reveal the effectiveness of the framed algorithm.
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Ali Z, Mahmood T, Gwak J, Jan N. A novel extended Portuguese of Interactive and Multi‐Criteria Decision Making and Archimedean Bonferroni mean operators based on prospect theory to select green supplier with complex q‐rung orthopair fuzzy information. CAAI TRANSACTIONS ON INTELLIGENCE TECHNOLOGY 2023. [DOI: 10.1049/cit2.12185] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Affiliation(s)
- Zeeshan Ali
- Department of Mathematics & Statistics International Islamic University Islamabad Islamabad Pakistan
| | - Tahir Mahmood
- Department of Mathematics & Statistics International Islamic University Islamabad Islamabad Pakistan
| | - Jeonghwan Gwak
- Department of Software Korea National University of Transportation Chungju Korea
- Department of Biomedical Engineering Korea National University of Transportation Chungju Korea
- Department of AI Robotics Engineering Korea National University of Transportation Chungju Korea
- Department of IT & Energy Convergence (BK21 FOUR) Korea National University of Transportation Chungju Korea
| | - Naeem Jan
- Department of Software Korea National University of Transportation Chungju Korea
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9
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Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator. Symmetry (Basel) 2023. [DOI: 10.3390/sym15010251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.
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10
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Group decision-making based on 2-tuple linguistic T-spherical fuzzy COPRAS method. Soft comput 2022. [DOI: 10.1007/s00500-022-07644-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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11
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Mahmood T, Ali Z, Aslam M. Applications of complex picture fuzzy soft power aggregation operators in multi-attribute decision making. Sci Rep 2022; 12:16449. [PMID: 36180458 PMCID: PMC9525635 DOI: 10.1038/s41598-022-20239-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 09/12/2022] [Indexed: 11/09/2022] Open
Abstract
The major theme of this analysis is to suggest a new theory in the form of complex picture fuzzy soft (CPFS) information and to initiate their major algebraic laws, score value, and accuracy values. The mathematical form of the CPFS set includes three main functions, called supporting, abstinence, and supporting against terms with a prominent characteristic that the sum of the triplet will lie in the unit interval. Further, in the consideration of the power aggregation operator using generalized t-norm and t-conorm and CPFS information, we diagnosed the mathematical concept of CPFS power averaging (CPFSPA), CPFS weighted power averaging (CPFSWPA), CPFS ordered weighted power averaging (CPFSOWPA), CPFS power geometric (CPFSPG), CPFS weighted power geometric (CPFSWPG), CPFS ordered weighted power geometric (CPFSOWPG). Moreover, the major results and their particular investigation of the invented approaches are also deliberated. Additionally, in the consideration of diagnosed operators using CPFS information, we illustrated a MADM ("multi-attribute decision-making") tool to find the best option from the family of decisions. Finally, we have shown the supremacy and feasibility of the diagnosed operators with the help of sensitive analysis and geometrical representations.
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Affiliation(s)
- Tahir Mahmood
- Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad, Pakistan.
| | - Zeeshan Ali
- Department of Mathematics & Statistics, International Islamic University Islamabad, Islamabad, Pakistan
| | - Muhammad Aslam
- Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia
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12
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Akram M, Khan A, Ahmad U, Alcantud JCR, Al-Shamiri MMA. A new group decision-making framework based on 2-tuple linguistic complex q-rung picture fuzzy sets. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:11281-11323. [PMID: 36124591 DOI: 10.3934/mbe.2022526] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
The need for multi-attribute decision-making brings more and more complexity, and this type of decision-making extends to an ever wider range of areas of life. A recent model that captures many components of decision-making frameworks is the complex $ q $-rung picture fuzzy set (C$ q $-RPFS), a generalization of complex fuzzy sets and $ q $-rung picture fuzzy sets. From a different standpoint, linguistic terms are very useful to evaluate qualitative information without specialized knowledge. Inspired by the ease of use of the linguistic evaluations by means of 2-tuple linguistic term sets, and the broad scope of applications of C$ q $-RPFSs, in this paper we introduce the novel structure called 2-tuple linguistic complex $ q $-rung picture fuzzy sets (2TLC$ q $-RPFSs). We argue that this model prevails to represent the two-dimensional information over the boundary of C$ q $-RPFSs, thanks to the additional features of 2-tuple linguistic terms. Subsequently, some 2TLC$ q $-RPF aggregation operators are proposed. Fundamental cases include the 2TLC$ q $-RPF weighted averaging/geometric operators. Other sophisticated aggregation operators that we propose are based on the Hamacher operator. In addition, we investigate some essential properties of the new operators. These tools are the building blocks of a multi-attribute decision making strategy for problems posed in the 2TLC$ q $-RPFS setting. Furthermore, a numerical instance that selects an optimal machine is given to guarantee the applicability and effectiveness of the proposed approach. Finally, we conduct a comparison with other existing approaches.
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Affiliation(s)
- Muhammad Akram
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - Ayesha Khan
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - Uzma Ahmad
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - José Carlos R Alcantud
- BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), Universidad de Salamanca, 37007 Salamanca, Spain
| | - Mohammed M Ali Al-Shamiri
- Department of Mathematics, Faculty of Science and Arts, Muhayl Asser, King Khalid University, K.S.A
- Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen
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13
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Multiple attribute decision-making based on maclaurin symmetric mean operators on q-rung orthopair cubic fuzzy sets. Soft comput 2022. [DOI: 10.1007/s00500-022-07363-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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14
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A Hybrid Intuitionistic Fuzzy Group Decision Framework and Its Application in Urban Rail Transit System Selection. MATHEMATICS 2022. [DOI: 10.3390/math10122133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The selection of an urban rail transit system from the perspective of green and low carbon can not only promote the construction of an urban rail transit system but also have a positive impact on urban green development. Considering the uncertainty caused by different conflict criteria and the fuzziness of decision-making experts’ cognition in the selection process of a rail transit system, this paper proposes a hybrid intuitionistic fuzzy MCGDM framework to determine the priority of a rail transit system. To begin with, the weights of experts are determined based on the improved similarity method. Secondly, the subjective weight and objective weight of the criterion are calculated, respectively, according to the DEMATEL and CRITIC methods, and the comprehensive weight is calculated by the linear integration method. Thirdly, considering the regret degree and risk preference of experts, the COPRAS method based on regret theory is propounded to determine the prioritization of urban rail transit system ranking. Finally, urban rail transit system selection of City N is selected for the case study to illustrate the feasibility and effectiveness of the developed method. The results show that a metro system (P1) is the most suitable urban rail transit system for the construction of city N, followed by a municipal railway system (P7). Sensitivity analysis is conducted to illustrate the stability and robustness of the designed decision framework. Comparative analysis is also utilized to validate the efficacy, feasibility and practicability of the propounded methodology.
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Shi X, Lin Z, Zhou L, Bao H. Linguistic q-rung orthopair fuzzy multiple-attribute group decision making based on the grey similarity degree and PROMETHEE II method. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-220579] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are an effective tool for representing fuzzy linguistic information, and they can obtain a wider expression scope than linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers by increasing the value of parameter q. In this paper, we propose a new similarity measure called the grey similarity degree between any two Lq-ROFNs based on the concept of the grey correlation degree. Considering the significance of determining unknown weights, we also propose a grey correlation method to determine each expert’s weight under different alternatives and attributes, and we construct an optimization model to determine incompletely known attribute weights. Furthermore, an approach to linguistic q-rung orthopair fuzzy multiple-attribute group decision making is proposed that combines the grey similarity degree with the PROMETHEE II method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method, and a sensitivity analysis and comparison analysis are also performed.
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Affiliation(s)
- Xuecheng Shi
- School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
| | - Zhichao Lin
- School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
- Anhui University Center for Applied Mathematics, Anhui University, Hefei, Anhui, China
| | - Ligang Zhou
- School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
- Anhui University Center for Applied Mathematics, Anhui University, Hefei, Anhui, China
| | - Hengjia Bao
- School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
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16
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Fermatean Fuzzy Schweizer–Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection. ENTROPY 2022; 24:e24060776. [PMID: 35741498 PMCID: PMC9223001 DOI: 10.3390/e24060776] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2022] [Revised: 05/23/2022] [Accepted: 05/27/2022] [Indexed: 01/27/2023]
Abstract
The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer–Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches.
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17
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Tan J, Liu Y, Senapati T, Garg H, Rong Y. An extended MABAC method based on prospect theory with unknown weight information under Fermatean fuzzy environment for risk investment assessment in B&R. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2022; 14:1-30. [PMID: 35340700 PMCID: PMC8939403 DOI: 10.1007/s12652-022-03769-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/25/2021] [Accepted: 02/09/2022] [Indexed: 06/14/2023]
Abstract
The assessment of investment risk for the countries along the route in Belt and Road (B&R) can be deemed as a multiple criteria group decision making (MCGDM) issue since multiple investment options based on diverse criterions are assessment by experts. Pondering that the complexity and uncertainty of the assessment setting and the cognition fuzziness and psychological behavior of experts bring challenges to risk assessment, this paper designed an integrated MCGDM risk investment evaluation framework by synthesizing MABAC method and prospect theory under Fermatean fuzzy setting. Firstly, a Fermatean fuzzy interactive distance measure is presented to ascertain the weight of evaluation experts and criterions. Next, some Fermatean fuzzy Frank aggregation operators based upon the proposed Frank operations are developed to fuse Fermatean fuzzy information efficiently. In addition, an innovative evaluation framework for risk investment is designed based on improved prospect theory MABAC and CRITIC approaches. Conclusively, an empirical concerning risk investment issues in B&R is employed to confirm the applicability and feasibility of the constructed evaluation framework, involving the simulation experiments on sensitivity analysis and contrast studies. The assessment information provided by investors using the linguistic assessment terms based upon their cognition ability of them. These outcomes obtained by the propounded method and comparison analysis further emphasize the validity and salient merits of the propounded framework and provide several auxiliary suggestions for investors.
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Affiliation(s)
- Jiade Tan
- School of Science, Xihua University, Chengdu, 610039 Sichuan People’s Republic of China
| | - Yi Liu
- School of Mathematics and Information Sciences, Neijiang Normal University, Neijiang, 641100 Sichuan People’s Republic of China
| | - Tapan Senapati
- Department of Mathematics, Padima Janakalyan Banipith, Kukrakhupi, 721517 India
- School of Mathematics and Statistics, Southwest University, Beibei, 400715 Chongqing China
| | - Harish Garg
- School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, 147004 Punjab India
| | - Yuan Rong
- School of Management, Shanghai University, Baoshan District, 200444 Shanghai People’s Republic of China
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18
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Hao D, Zhang R, Bai K. An integrated approach for service quality evaluation of online health communities based on q-rung orthopair fuzzy linguistic aggregation operators. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-211257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Online health communities (OHCs) have emerged as a significant platform for people communicating health information and self-healthcare management. In recent, the researches focusing on its performance measurement and the service quality evaluation have drawn intensive attention. Although some qualitative methods have made evaluation and analyses for the OHCs performance, the studies based on fuzzy multi-attribute decision making theory are rarely developed in the service quality evaluation of OHCs. In view of the complexity and uncertainty of evaluation mission, this paper develops an integrated evaluation approach of the OHC service quality based on the q-rung orthopair fuzzy linguistic aggregation operators. Firstly, we propose the cross-entropy of q-rung orthopair fuzzy numbers, which is applied in solving the optimal weight of indicators by a linear programming model. Next, the q-rung orthopair fuzzy linguistic power average (q-ROFLPA) and q-rung orthopair fuzzy linguistic partitioned dual Maclaurin symmetric mean (q-ROFLPDMSM) operators are developed for aggregating the assessment information and ranking the OHCs. Based on the proposed aggregation operators, the evaluation indicator system and an evaluation framework are constructed to accomplish the service quality evaluation of OHCs. Finally, a practical evaluation case of OHCs is provided to demonstrate the reliability and advantages of the proposed approach.
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Affiliation(s)
- Dong Hao
- School of Economics and Management, BeijingJiaotong University, Beijing, China
| | - Runtong Zhang
- School of Economics and Management, BeijingJiaotong University, Beijing, China
| | - Kaiyuan Bai
- School of Mechanical, Electronic and Control Engineering, Beijing JiaotongUniversity, Beijing, China
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19
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Ali Z, Mahmood T, Ullah K, Chinram R. Confidence levels under complex q-rung orthopair fuzzy aggregation operators and their applications. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-211840] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The major contribution of this analysis is to analyze the confidence complex q-rung orthopair fuzzy weighted averaging (CCQROFWA) operator, confidence complex q-rung orthopair fuzzy ordered weighted averaging (CCQROFOWA) operator, confidence complex q-rung orthopair fuzzy weighted geometric (CCQROFWG) operator, and confidence complex q-rung orthopair fuzzy ordered weighted geometric (CCQROFOWG) operator and invented their feasible properties and related results. Future more, under the invented operators, we diagnosed the best crystalline solid from the family of crystalline solids with the help of the opinion of different experts in the environment of decision-making strategy. Finally, to demonstrate the feasibility and flexibility of the invented works, we explored the sensitivity analysis and graphically shown of the initiated works.
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Affiliation(s)
- Zeeshan Ali
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Tahir Mahmood
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Kifayat Ullah
- Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Lahore, Pakistan
| | - Ronnason Chinram
- Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, Thailand
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20
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Wei D, Rong Y, Garg H. An extended WASPAS approach for teaching quality evaluation based on pythagorean fuzzy reducible weighted Maclaurin symmetric mean. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-210821] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Teaching quality evaluation (TQE) can not only improve teachers’ teaching skills, but also provide an important reference for school teaching management departments to formulate teaching reform measures and strengthen teaching management. TQE is a process of grading and ranking a given teachers based on the comprehensive consideration of multiple evaluation criteria by expert. The Maclaurin symmetric mean (MSM), as a powerful aggregation function, can capture the correlation among multiple input data more efficient. Although multitude weighted MSM operators have been developed to handle the Pythagorean fuzzy decision issues, these above operators do not possess the idempotency and reducibility during the procedure of information fusion. To conquer these defects, we present the Pythagorean fuzzy reducible weighted MSM (PFRWMSM) operator and Pythagorean fuzzy reducible weighted geometric MSM (PFRWGMSM) operator to fuse Pythagorean fuzzy assessment information. Meanwhile, several worthwhile properties and especial cases of the developed operators are explored at length. Afterwards, we develop a novel Pythagorean fuzzy entropy based upon knowledge measure to ascertain the weights of attribute. Furthermore, an extended weighted aggregated sum product assessment (WASPAS) method is developed by combining the PFRWMSM operator, PFRWGMSM operator and entropy to settle the decision problems of unknown weight information. The efficiency of the proffered method is demonstrated by a teaching quality evaluation issue, as well as the discussion of sensitivity analysis for decision outcomes. Consequently, a comparative study of the presented method with the extant Pythagorean fuzzy approaches is conducted to display the superiority of the propounded approach.
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Affiliation(s)
- Dongmei Wei
- School of Computer and Software Engineering, Xihua University, Chengdu, Sichuan, P.R. China
| | - Yuan Rong
- School of Management, Shanghai University, Baoshan District, Shanghai, P.R. China
| | - Harish Garg
- School of Computer and Software Engineering, Xihua University, Chengdu, Sichuan, P.R. China
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21
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Ali Z, Mahmood T, AlSalman H, Alkhamees BF, Rahman SMM. Analysis of medical diagnosis based on variation co-efficient similarity measures under picture hesitant fuzzy sets and their application. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:855-872. [PMID: 34903016 DOI: 10.3934/mbe.2022039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
One of the most dominant and feasible technique is called the PHF setting is exist in the circumstances of fuzzy set theory for handling intricate and vague data in genuine life scenario. The perception of PHF setting is massive universal is compared to these assumptions, who must cope with two or three sorts of data in the shape of singleton element. Under the consideration of the PHF setting, we utilized some SM in the region of the PHF setting are to diagnose the PHFDSM, PHFWDSM, PHFJSM, PHFWJSM, PHFCSM, PHFWCSM, PHFHVSM, PHFWHVSM and demonstrated their flexible parts. Likewise, a lot of examples are exposed under the invented measures based on PHF data in the environment of medical diagnosis to demonstrate the stability and elasticity of the explored works. Finally, the sensitive analysis of the presented works is also implemented and illuminated their graphical structures.
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Affiliation(s)
- Zeeshan Ali
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Tahir Mahmood
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Hussain AlSalman
- Department of Computer Science, College of Computer and Information Sciences, King Saud University, Riyadh, 11543, Saudi Arabia
| | - Bader Fahad Alkhamees
- Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia
| | - Sk Md Mizanur Rahman
- Information and Communication Engineering Technology, School of Engineering Technology and Applied Science, Centennial College, Toronto, Canada
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22
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Garg H, Gandomi AH, Ali Z, Mahmood T. Neutrality aggregation operators based on complex q‐rung orthopair fuzzy sets and their applications in multiattribute decision‐making problems. INT J INTELL SYST 2022. [DOI: 10.1002/int.22657] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Harish Garg
- School of Mathematics, Thapar Institute of Engineering and Technology Deemed University Patiala Punjab India
| | - Amir H. Gandomi
- Data Science Institute, Faculty of Engineering & Information Technology University of Technology Sydney Ultimo New South Wales Australia
| | - Zeeshan Ali
- Department of Mathematics and Statistics International Islamic University Islamabad Islamabad Pakistan
| | - Tahir Mahmood
- Department of Mathematics and Statistics International Islamic University Islamabad Islamabad Pakistan
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23
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Xu Y, Liu S, Wang J. Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions. PLoS One 2021; 16:e0258772. [PMID: 34673796 PMCID: PMC8530323 DOI: 10.1371/journal.pone.0258772] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 10/06/2021] [Indexed: 11/23/2022] Open
Abstract
Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.
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Affiliation(s)
- Yuan Xu
- School of Economics and Management, Beijing Jiaotong University, Beijing, China
| | - Shifeng Liu
- School of Economics and Management, Beijing Jiaotong University, Beijing, China
| | - Jun Wang
- School of Economics and Management, Beijing University of Chemical Technology, Beijing, China
- * E-mail:
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24
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A novel picture fuzzy linguistic Muirhead Mean aggregation operators and their application to multiple attribute decision making. Soft comput 2021; 25:14741-14756. [PMID: 34429713 PMCID: PMC8376630 DOI: 10.1007/s00500-021-06121-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/04/2021] [Indexed: 02/07/2023]
Abstract
The Picture fuzzy linguistic set (PFLS) is an extension of the intuitionistic fuzzy set (IFS) and linguistic variables (LVs), which has been applied successfully in the process of decision making. Considering the lack of closeness of extant PFLS operations and the interrelationship among input attributes do not consider. In this paper, for the sake of addressing those limitations, we firstly redefine some novel operational laws for PFLS by introducing linguistic scale functions and the related properties are studied. Then, a novel score function and accuracy function are also defined to compare PFLSs. Subsequently, in consideration of the superiority of the Muirhead Mean (MM) operator in capturing the interaction relationship between the input parameters, we extend the MM operator to the Picture fuzzy linguistic context and then propose Picture fuzzy linguistic weighted MM operator and its dual form in a new light. After that, these operators have adopted to build two novel models to solve multiple attribute decision-making (MADM) problems. Finally, a practical example for the selection of the innovative “Mobike” sharing bike design is provided to illustrate the practicality and effectiveness of proposed approaches.
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25
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Garg H, Ali Z, Yang Z, Mahmood T, Aljahdali S. Multi-criteria decision-making algorithm based on aggregation operators under the complex interval-valued q-rung orthopair uncertain linguistic information. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-210442] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The paper aims to present a concept of a Complex interval-valued q-rung orthopair uncertain linguistic set (CIVQROULS) and investigated their properties. In the presented set, the membership grades are considered in terms of the interval numbers under the complex domain while the linguistic features are added to address the uncertainties in the data. To further discuss more, we have presented the operation laws and score function for CIVQROULS. In addition to them, we present some averaging and geometric operators to aggregate the different pairs of the CIVQROULS. Some fundamental properties of the proposed operators are stated. Afterward, an algorithm for solving the decision-making problems is addressed based on the proposed operator using the CIVQROULS features. The applicability of the algorithm is demonstrated through a case study related to brain tumors and their effectiveness is compared with the existing studies.
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Affiliation(s)
- Harish Garg
- School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, Punjab, India
| | - Zeeshan Ali
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Zaoli Yang
- College of Economics and Management, Bejing University of Technology, Beijing, China
| | - Tahir Mahmood
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Sultan Aljahdali
- Department of Computer Science, College of Computers and Information Technology, Taif University, Taif, Saudi Arabia
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26
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Lin M, Li X, Chen R, Fujita H, Lin J. Picture fuzzy interactional partitioned Heronian mean aggregation operators: an application to MADM process. Artif Intell Rev 2021. [DOI: 10.1007/s10462-021-09953-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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27
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A novel multiple attribute decision-making approach for evaluation of emergency management schemes under picture fuzzy environment. INT J MACH LEARN CYB 2021. [DOI: 10.1007/s13042-021-01280-1] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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28
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Liu R, Mou X, Liu HC. Occupational Health and Safety Risk Assessment based on Combination Weighting and Uncertain Linguistic Information: Method Development and Application to a Construction Project. IISE Trans Occup Ergon Hum Factors 2021; 8:175-186. [PMID: 33448249 DOI: 10.1080/24725838.2021.1875519] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
OCCUPATIONAL APPLICATIONSOccupational hazards and work-related accidents are a substantial problem in countries around the world. Therefore, it is of great importance to develop appropriate techniques to assess and reduce the risk of occupational hazards. In many situations, however, exact data are inadequate to model real-life scenarios, because of the complexity of occupational health and safety (OHS) risk assessment problems. We present a new OHS risk assessment model to assess and rank the risk of occupational hazards based on combination weighting and uncertain linguistic information. Moreover, a practical example of a shopping mall construction project is given to illustrate the effectiveness of the proposed model. The new model was found to provide a useful, practical, and flexible way for risk evaluation in OHS. In particular, it offered a new method for capturing domain expert opinions and prioritizing potential occupational hazards to improve the health and safety of workers.
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Affiliation(s)
- Ran Liu
- School of Management, Shanghai University, Shanghai, China
| | - Xun Mou
- School of Management, Shanghai University, Shanghai, China
| | - Hu-Chen Liu
- School of Economics and Management, Tongji University, Shanghai, China
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