Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

An integrated CRITIC and EDAS model using linguistic T spherical fuzzy Hamacher aggregation operators and its application to group decision making

Green technologies are defined as the utilization of advanced scientific and technological methodologies to fabricate products that minimize environmental impact. The assessment of green technology alternatives necessitates a comprehensive analysis incorporating a multitude of criteria, many of which may be conflicting. Optimal selections must encompass technical performance, economic feasibility, environmental sustainability, and societal implications. Additionally, the data gaps and vague information typical when dealing with emerging technologies make traditional techniques unproductive. This work thus proposes a dynamic multi-criteria group decision making (MCGDM) model by integrating the Criteria Importance Through Intercriteria Correlation (CRITIC) method with the Evaluation based on Distance from Average Solution (EDAS) technique under the linguistic T-spherical fuzzy (LT-SF) environment. Initially, we define some Hamacher operations for LT-SF numbers (LT-SFNs) and then use them to develop some Hamacher aggregation operators (HAOs) synthesizing expert assessments. Meanwhile, some prominent features of these newly developed operators are also discussed. Next, we introduce a novel LT-SF-CRITIC-EDAS model, where LT-SF-CRITIC determines criteria weights, and LT-SF-EDAS evaluates the ranking of available alternatives. To illustrate the designed model's applicability, we apply it to a real-world scenario of selecting the most appropriate green technology from available options. Finally, a sensitivity analysis and comparative evaluation against existing methods demonstrate our proposed approach's superior feasibility and reliability. This research contributes to advancing decision making methodologies for assessing green technologies under complex and uncertain conditions.

An extension of the best-worst method based on the spherical fuzzy sets for multi-criteria decision-making

The ambiguous information in multi-criteria decision-making (MCDM) and the vagueness of decision-makers for qualitative judgments necessitate accurate tools to overcome uncertainties and generate reliable solutions. As one of the latest and most powerful MCDM methods for obtaining criteria weight, the best-worst method (BWM) has been developed. Compared to other MCDM methods, such as the analytic hierarchy process, the BWM requires fewer pairwise comparisons and produces more consistent results. Consequently, the main objective of this study is to develop an extension of BWM using spherical fuzzy sets (SFS) to address MCDM problems under uncertain conditions. Hesitancy, non-membership, and membership degrees are three-dimensional functions included in the SFS. The presence of three defined degrees allows decision-makers to express their judgments more accurately. An optimization model based on nonlinear constraints is used to determine optimal spherical fuzzy weight coefficients (SF-BWM). Additionally, a consistency ratio is proposed for the SF-BWM to assess the reliability of the proposed method in comparison to other versions of BWM. SF-BWM is examined using two numerical decision-making problems. The results show that the proposed method based on the SF-BWM provided the criteria weights with the same priority as the BWM and fuzzy BWM. However, there are differences in the criteria weight values based on the SF-BWM that indicate the accuracy and reliability of the obtained results. The main advantage of using SF-BWM is providing a better consistency ratio. Based on the comparative analysis, the consistency ratio obtained for SF-BWM is threefold better than the BWM and fuzzy BWM methods, which leads to more accurate results than BWM and fuzzy BWM.

A new multi-objective optimization ratio analysis plus full multiplication form method for the selection of an appropriate mining method based on 2-tuple spherical fuzzy linguistic sets

The selection of an appropriate mining method is considered as an important tool in the mining design process. The adoption of a mining method can be regarded as a complex multi-attribute group decision-making (MAGDM) problem as it may contain uncertainty and vagueness. The main goal of this paper is to propose an extended multi-objective optimization ratio analysis plus full multiplication form (MULTIMOORA) method that is based on a 2-tuple spherical fuzzy linguistic set (2TSFLS). The MULTIMOORA method under 2TSFL conditinos has been developled as a novel approach to deal with uncertainty in decision-making problems. The proposed work shows that 2TSFLSs contain collaborated features of spherical fuzzy sets (SFSs) and 2-tuple linguistic term sets (2TLTSs) and, hence, can be considered as a rapid and efficient tool to represent the experts' judgments. Thus, the broader structure of SFSs, the ability of 2TLTSs to represent linguistic assessments, and the efficiency of the MULTIMOORA approach have motivated us to present this work. To attain our desired results, we built a normalized Hamming distance measure and score function for 2TSFLSs. We demonstrate the applicability and realism of the proposed method with the help of a numerical example, that is, the selection of a suitable mining method for the Kaiyang phosphate mine. Then, the results of the proposed work are compared with the results of existing methods to better reflect the strength and effectiveness of the proposed work. Finally, we conclude that the proposed MULTIMOORA method within a 2TSFLS framework is quite efficient and comprehensive to deal with the arising MAGDM problems.

A new group decision-making framework based on 2-tuple linguistic complex q-rung picture fuzzy sets

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.

Sustainable Circular Supplier Selection in the Power Battery Industry Using a Linguistic T-Spherical Fuzzy MAGDM Model Based on the Improved ARAS Method

In the power battery industry, the selection of an appropriate sustainable recycling supplier (SCS) is a significant topic in circular supply chain management. Evaluating and selecting a SCS for spent power batteries is considered a complex multi-attribute group decision-making (MAGDM) problem closely related to the environment, economy, and society. The linguistic T-spherical fuzzy (Lt-SF) set (Lt-SFS) is a combination of a linguistic term set and a T-spherical fuzzy set (T-SFS), which can accurately describe vague cognition of human and uncertain environments. Therefore, this article proposes a group decision-making methodology for a SCS selection based on the improved additive ratio assessment (ARAS) in the Lt-SFS context. This paper extends the Lt-SF generalized distance measure and defines the Lt-SF similarity measure. The Lt-SF Heronian mean (Lt-SFHM) operator and its weighted form (i.e., Lt-SFWHM) were developed. Subsequently, a new Lt-SF MAGDM model was constructed by integrating the LT-SFWHM operator, generalized distance measure, and ARAS method. In it, the expert weight on the attribute was determined based on the similarity measure, using the generalized distance measure to obtain the objective attribute weight and then the combined attribute weight. Finally, a real case of SCS selection in the power battery industry is presented for demonstration. The effectiveness and practicability of this method were verified through a sensitivity analysis and a comparative study with the existing methods.

A novel group decision making method for interval-valued pythagorean fuzzy preference relations

Interval-valued Pythagorean fuzzy preference relation (IVPFPR) plays an important role in representing the complex and uncertain information. The application of IVPFPRs gives better solutions in group decision making (GDM). In this paper, we investigate a new method to solve GDM problems with IVPFPRs. Firstly, novel multiplicative consistency and consensus measures are proposed. Subsequently, the procedure for improving consistency and consensus levels are put forward to ensure that every individual IVPFPR is of acceptable multiplicative consistency and consensus simultaneously. In the context of minimizing the deviations between the individual and collective IVPFPRs, the objective experts’ weights are decided according to the optimization model and the aggregated IVPFPR is derived. Afterwards, a programming model is built to derive the normalized Pythagorean fuzzy priority weights, then the priority weights of alternatives are identified as well. An algorithm for GDM method with IVPFPRs is completed. Finally, an example is cited and comparative analyses with previous approaches are conducted to illustrate the applicability and effectiveness of the proposed method.

Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment

In this article, we have introduced a new linguistic generalized spherical fuzzy set by combining the idea of generalized spherical fuzzy set and linguistic fuzzy set. Linguistic generalized spherical fuzzy set is described by linguistic positive, linguistic neutral and linguistic negative membership degrees with the condition that the square sum of its linguistic membership degrees is less than or equal to 3 which deal with the uncertain and imprecise information in decision making in a much more suitable way. We have discussed some basic operations of linguistic generalized spherical fuzzy sets and introduced new score and accuracy functions to compare any two linguistic generalized spherical fuzzy numbers. We have developed various types of aggregation operators based on the newly defined linguistic generalized spherical fuzzy set, which have been manifested to construct a new multi-criteria group decision-making technique. Numerical example has been presented to demonstrate the proposed model. Finally, sensitivity and comparative analysis is performed to show the reliability and efficiency of the new multi-criteria group decision-making technique.

A state-of-the-art survey on spherical fuzzy sets1

In addition to the well-known fuzzy sets, a novel type of fuzzy set called spherical fuzzy set (SFS) is recently introduced in the literature. SFS is the generalized structure over existing structures of fuzzy sets (intuitionistic fuzzy sets-IFS, Pythagorean fuzzy sets-PFS, and neutrosophic fuzzy sets-NFS) based on three dimensions (truth, falsehood, and indeterminacy) to provide a wider choice for decision-makers (DMs). Although the SFS has been introduced recently, the topic attracts the attention of academicians at a remarkable rate. This study is the expanded version of the authors’ earlier study by Ozceylan et al. [1]. A comprehensive literature review of recent and state-of-the-art papers is studied to draw a framework of the past and to shed light on future directions. Therefore, a systematic review methodology that contains bibliometric and descriptive analysis is followed in this study. 104 scientific papers including SFS in their titles, abstracts and keywords are reviewed. The papers are then analyzed and categorized based on titles, abstracts, and keywords to construct a useful foundation of past research. Finally, trends and gaps in the literature are identified to clarify and to suggest future research opportunities in the fuzzy logic area.

Evaluation of the product quality of the online shopping platform using t-spherical fuzzy preference relations

As a generalization of Pythagorean fuzzy sets and picture fuzzy sets, spherical fuzzy sets provide decision makers more flexible space in expressing their opinions. Preference relations have received widespread acceptance as an efficient tool in representing decision makers’ preference over alternatives in the decision-making process. In this paper, some new preference relations are investigated based on the spherical fuzzy sets. Firstly, the deficiency of the existing operating laws is elaborated in detail and three cases are described to identify the accuracy of the proposed operating laws in the context of t-spherical fuzzy environment. Also, a novel score function is proposed to obtain the consistent value in ranking of the alternatives. The backbone of this research, t-spherical fuzzy preference relation, consistent t-spherical fuzzy preference relations, incomplete t-spherical fuzzy preference relations, consistent incomplete t-spherical fuzzy preference relations, and acceptable incomplete t-spherical fuzzy preference relations are established. Additionally, some ranking and selection algorithms are established using the proposed novel score function and preference relations to tackle the uncertainty in real-life decision-making problems. Finally, evaluation of the product quality of the online shopping platform problem is demonstrated to show the applicability and reliability of proposed technique.

Convergence or Divergence among Business Models of Public Bus Transport Authorities across the Globe: A Fuzzy Approach

Building on the debate about global convergence or divergence of practices, this study aims to query the viability of a new strategic action tool specifically geared to the interests of public bus transportation authorities (PBTA) around the globe and explore the degree of homogeneity in their responses as well as the possible drivers of them. To answer its research question, the study first offers a generic business model design for a PBTA, which integrates an extended version of the business model canvas with external environmental factors in order to enhance its sustainability. Subsequently, the importance attributions of international transportation experts to different model components are evaluated by using the Spherical Fuzzy AHP method. The model is developed in three hierarchical layers and evaluated by experts from four continents: America, Asia, Australia, and Europe. The results indicate that the expert opinions tend to converge more on the internal components of the model and diverge on the external components, especially regarding economic and technological factors. A strategic response action set is also designed to facilitate the adoption of the model by PBTA. The study not only extends the research on the strategic management of the public bus transportation domain but also contributes to the convergence and divergence debate by offering a reconciliatory duality perspective.

Emergency decision support modeling under generalized spherical fuzzy Einstein aggregation information

Dominant emergency action should be adopted in the case of an emergency situation. Emergency is interpreted as limited time and information, harmfulness and uncertainty, and decision-makers are often critically bound by uncertainty and risk. This framework implements an emergency decision-making approach to address the emergency situation of COVID-19 in a spherical fuzzy environment. As the spherical fuzzy set (SFS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision-making problems (DMPs). Keeping in view the features of the SFSs, the purpose of this paper is to present some robust generalized operating laws in accordance with the Einstein norms. In addition, list of propose aggregation operators using Einstein operational laws under spherical fuzzy environment are developed. Furthermore, we design the algorithm based on the proposed aggregation operators to tackle the uncertainty in emergency decision making problems. Finally, numerical case study of COVID-19 as an emergency decision making is presented to demonstrate the applicability and validity of the proposed technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

Hamacher heronian mean operators for multi-critria decision-making under multi-valued picture fuzzy uncertain lingsuitic environment

Picture fuzzy set (PFS) and linguistic term set (LTS) are two significant notions in multi-criteria decision-making (MCDM). In practice, decision-makers sometimes need utilize the multiple probable membership degrees for an uncertain linguistic term to express evaluation information. Motivated by these, to better convey the vagueness and uncertainty of cognitive information, multi-valued picture fuzzy uncertain linguistic set combining picture hesitant fuzzy set with uncertain linguistic term set is proposed. We firstly define the concepts of multi-valued picture fuzzy uncertain linguistic set and multi-valued picture fuzzy uncertain linguistic number. Hamacher operations are more general and flexible in information fusion, thus, Hamacher operations and comparison method are developed at the same time. Improved generalized Heronian Mean operator can simultaneously reflect correlations between values and prevent the redundant calculation. Then, two operators of improved generalized weighted Heronian mean and improved generalized geometric weighted Heronian mean in view of Hamacher operations are proposed. Meanwhile, some distinguished properties and instances of two operators are explored as well. Moreover, a novel MCDM approach applying the developed operators is constructed. Ultimately, an illustrative example on vendor selection is performed, and sensitivity analysis and comparison analysis are provided to verify the powerfulness of the proposed method.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

A Decision Support Model for Hotel Recommendation Based on the Online Consumer Reviews Using Logarithmic Spherical Hesitant Fuzzy Information

Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.

Multi-attribute group decision making based on sine trigonometric spherical fuzzy aggregation operators

Spherical fuzzy set (SFS) is also one of the fundamental concepts for address more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi parameters. Taking this feature and the significance of the SFSs into the consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the Spherical fuzzy numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with an application for the selection of an authentic COVID-19 laboratory. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

Emergency decision support modeling for COVID-19 based on spherical fuzzy information

Significant emergency measures should be taken until an emergency event occurs. It is understood that the emergency is characterized by limited time and information, harmfulness and uncertainty, and decision-makers are always critically bound by uncertainty and risk. This paper introduces many novel approaches to addressing the emergency situation of COVID-19 under spherical fuzzy environment. Fundamentally, the paper includes six main sections to achieve appropriate and accurate measures to address the situation of emergency decision-making. As the spherical fuzzy set (FS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision-making problems (DMPs). First, we discuss basic algebraic operational laws (AOLs) under spherical FS. In addition, elaborate on the deficiency of existing AOLs and present three cases to address the validity of the proposed novel AOLs under spherical fuzzy settings. Second, we present a list of Einstein aggregation operators (AgOp) based on the Einstein norm to aggregate uncertain information in DMPs. Thirdly, we are introducing two techniques to demonstrate the unknown weight of the criteria. Fourthly, we develop extended TOPSIS and Gray relational analysis approaches based on AgOp with unknown weight information of the criteria. In fifth, we design three algorithms to address the uncertainty and ambiguity information in emergency DMPs. Finally, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed three algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.

A new emergency response of spherical intelligent fuzzy decision process to diagnose of COVID19

The control of spreading of COVID-19 in emergency situation the entire world is a challenge, and therefore, the aim of this study was to propose a spherical intelligent fuzzy decision model for control and diagnosis of COVID-19. The emergency event is known to have aspects of short time and data, harmfulness, and ambiguity, and policy makers are often rationally bounded under uncertainty and threat. There are some classic approaches for representing and explaining the complexity and vagueness of the information. The effective tool to describe and reduce the uncertainty in data information is fuzzy set and their extension. Therefore, we used fuzzy logic to develop fuzzy mathematical model for control of transmission and spreading of COVID19. The fuzzy control of early transmission and spreading of coronavirus by fuzzy mathematical model will be very effective. The proposed research work is on fuzzy mathematical model of intelligent decision systems under the spherical fuzzy information. In the proposed work, we will develop a newly and generalized technique for COVID19 based on the technique for order of preference by similarity to ideal solution (TOPSIS) and complex proportional assessment (COPRAS) methods under spherical fuzzy environment. Finally, an illustrative the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested method, along with a sensitivity analysis and comparative analysis, showing the feasibility and reliability of its results.

Novel similarity measures in spherical fuzzy environment and their applications

Spherical fuzzy sets (SFSs) have gained great attention from researchers in various fields. The spherical fuzzy set is characterized by three membership functions expressing the degrees of membership, non-membership and the indeterminacy to provide a larger preference domain. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and vagueness information. The similarity measure is one of the essential and advantageous tools to determine the degree of similarity between items. Several studies on similarity measures have been developed due to the importance of similarity measure and application in decision making, data mining, medical diagnosis, and pattern recognition in the literature. The contribution of this study is to present some novel spherical fuzzy similarity measures. We develop the Jaccard, exponential, and square root cosine similarity measures under spherical fuzzy environment. Each of these similarity measures is analyzed with respect to decision-makers' optimistic or pessimistic point of views. Then, we apply these similarity measures to medical diagnose and green supplier selection problems. These similarity measures can be computed easily and they can express the dependability similarity relation apparently.

Evaluation of the COVID-19 Pandemic Intervention Strategies with Hesitant F-AHP

In this study, a hesitant fuzzy AHP method is presented to help decision makers (DMs), especially policymakers, governors, and physicians, evaluate the importance of intervention strategy alternatives applied by various countries for the COVID-19 pandemic. In this research, a hesitant fuzzy multicriteria decision making (MCDM) method, hesitant fuzzy Analytic Hierarchy Process (hesitant F-AHP), is implemented to make pairwise comparison of COVID-19 country-level intervention strategies applied by various countries and determine relative importance scores. An illustrative study is presented where fifteen intervention strategies applied by various countries in the world during the COVID-19 pandemic are evaluated by seven physicians (a professor of infectious diseases and clinical microbiology, an infectious disease physician, a clinical microbiology physician, two internal medicine physicians, an anesthesiology and reanimation physician, and a family physician) in Turkey who act as DMs in the process.

Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment

With the rapid outbreak of COVID-19, most people are facing antivirus mask shortages. Therefore, it is necessary to reasonably select antivirus masks and optimize the use of them for everyone. However, the uncertainty of the effects of COVID-19 and limits of human cognition add to the difficulty for decision makers to perfectly realize the purpose. To maximize the utility of the antivirus mask, we proposed a decision support algorithm based on the novel concept of the spherical normal fuzzy (SpNoF) set. In it, firstly, we analyzed the new score and accuracy function, improved operational rules, and their properties. Then, in line with these operations, we developed the SpNoF Bonferroni mean operator and the weighted Bonferroni mean operator, some properties of which are also examined. Furthermore, we established a multi-criteria decision-making method, based on the proposed operators, with SpNoF information. Finally, a numerical example on antivirus mask selection over the COVID-19 pandemic was given to verify the practicability of the proposed method, which the sensitive and comparative analysis was based on and was conducted to demonstrate the availability and superiority of our method.

Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products

A single-valued neutrosophic linguistic set (SVNLS) is a popular fuzzy tool for describing deviation information in uncertain complex situations. The aim of this paper is to study some logarithmic distance measures and study their usefulness in multiple attribute group decision making (MAGDM) problems within single-valued neutrosophic linguistic (SVNL) environments. For achieving the purpose, SVNL weighted logarithmic averaging distance (SVNLWLAD) and SVNL ordered weighted logarithmic averaging distance (SVNLOWLAD) measures are firstly developed based on the logarithmic aggregation method. Then, the SVNL combined weighted logarithmic averaging distance (SVNLCWLAD) measure is presented by unifying the advantages of the previous SVNLWLAD and SVNLOWLAD measures. Moreover, a new MAGDM model by utilizing the SVNLCWLAD measure is presented under SVNL environments. Finally, a supplier selection for fresh aquatic products is taken as a case to illustrate the performance of the proposed framework.

Fuzzy Decision Support Modeling for Hydrogen Power Plant Selection Based on Single Valued Neutrosophic Sine Trigonometric Aggregation Operators

In recent decades, there has been a massive growth towards the prime interest of the hydrogen energy industry in automobile transportation fuel. Hydrogen is the most plentiful component and a perfect carrier of energy. Generally, evaluating a suitable hydrogen power plant site is a complex selection of multi-criteria decision-making (MCDM) problem concerning proper location assessment based on numerous essential criteria, the decision-makers expert opinion, and other qualitative/quantitative aspects. This paper presents the novel single-valued neutrosophic (SVN) multi-attribute decision-making method to help decision-makers choose the optimal hydrogen power plant site. At first, novel operating laws based on sine trigonometric function for single-valued neutrosophic sets (SVNSs) are introduced. The well-known sine trigonometry function preserves the periodicity and symmetric in nature about the origin, and therefore it satisfies the decision-maker preferences over the multi-time phase parameters. In conjunction with these properties and laws, we define several new aggregation operators (AOs), called SVN weighted averaging and geometric operators, to aggregate SVNSs. Subsequently, on the basis of the proposed AOs, we introduce decision-making technique for addressing multi-attribute decision-making (MADM) problems and provide a numerical illustration of the hydrogen power plant selection problem for validation. A detailed comparative analysis, including a sensitivity analysis, was carried out to improve the understanding and clarity of the proposed methodologies in view of the existing literature on MADM problems.

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems.

Child Development Influence Environmental Factors Determined Using Spherical Fuzzy Distance Measures

This paper aims to resolve the issue of the ranking of the fuzzy numbers in decision analysis, artificial intelligence, and optimization. In the literature, many ideas have been established for the ranking of the fuzzy numbers, and those ideas have some restrictions and limitations. We propose a method based on spherical fuzzy numbers (SFNs) for ranking to overcome the existing restrictions. Further, we investigate the basic properties of SFNs, compare the idea of spherical fuzzy set with the picture fuzzy set, and establish some distance operators, namely spherical fuzzy distance-weighted averaging (SFDWA), spherical fuzzy distance order-weighted averaging (SFDOWA), and spherical fuzzy distance order-weighted average weighted averaging (SFDOWA WA) operators with the attribute weights’ information incompletely described. Further, we design an algorithm to solve decision analysis problems. Finally, to validate the usage and applicability of the established procedure, we assume the child development influence environmental factors problem as a practical application.