COPRAS method based on interval-valued hesitant Fermatean fuzzy sets and its application in selecting desalination technology

A new approach to MADM problem using interval-valued hesitant Fermatean fuzzy Hamacher operators and statistical variance

Water ecological civilization construction (WECC) is regarded as the core and cornerstone of ecological civilization construction. However, a lot of uncertainty is involved in assessing the WECC level, which presents serious and intricate difficulties for the related multiple- attribute decision-making (MADM) processes. The interval-valued hesitant Fermatean fuzzy set (IVHFFS) is a powerful tool for handling uncertainty in MADM issues. However, in the existing MADM approaches, attribute weight calculation involves high data redundancy and low computational efficiency. The existing aggregation operators ignore the importance of the attributes and their ordered positions. In order to solve these problems, in this paper, we propose a novel MADM model using interval-valued hesitant Fermatean fuzzy (IVHFF) Hamacher aggregation operator (AO) and statistical variance (SV) weight calculation. Firstly, the SV weight calculation method is given under IVHFFSs, aiming to computing objective weights of attributes. This greatly reduces data redundancy and improves the computational complexity. Secondly, we propose some IVHFF Hamacher AOs, such as IVHFF Hamacher (ordered) weighted averaging operator, IVHFF Hamacher (ordered) weighted geometric operator, IVHFF Hamacher hybrid averaging operator and geometric operator which consider the significance of the attributes and their ordered positions. Thirdly, a new MADM model based on the above information AOs and SV weight calculation is proposed. Finally, a comparative study on the real-world application for WECC and randomly generated data sets is also carried out to further demonstrate that our method outperforms the existing methods.

A bipolar fuzzy decision-making system for assessing high-risk coexisting tuberculosis disease in pregnant women

Tuberculosis (TB) diagnosis poses a formidable challenge in global healthcare, particularly impacting older individuals and pregnant women. Diagnosing TB disease during pregnancy and in comorbid patients is more challenging due to overlapping symptoms with normal pregnancy conditions and existing treatments for other diseases, necessitating careful assessment to differentiate TB symptoms from those of other underlying conditions. To address this issue, this study designs a novel bipolar fuzzy decision-support system by integrating the concept of complex proportional assessment (COPRAS) and a technique for order preference by similarity to the ideal solution (TOPSIS) approaches using bipolar heptagonal fuzzy numbers. The approach is utilized to assess the high-risk of TB coinfection disease in pregnant women. The bipolar fuzzy set provides positive and negative membership degrees of an element, which divulge a balanced perspective by both the presence and absence of the disease. Additionally, a defuzzification algorithm is proposed for bipolar heptagonal fuzzy numbers, converting bipolar heptagonal fuzzy into a bipolar crisp score (CBHpFBCS). The bipolar fuzzy entropy measure is utilized to weight the criteria. The findings highlight that TB+HIV ( G 3 ) coinfection is more severe in pregnant women compared to other TB comorbidities. Finally, sensitivity and comparative analyses are executed across diverse criteria weight scenarios and with existing fuzzy multi-criteria decision-making (MCDM) methods to validate the robustness of the proposed method and its outcomes.

Stochastic MCDM with normal approximation of the uniformly distributed variables for assessing sustainable insulation materials

The sustainability-related decision-making oftentimes involves uncertain information. One of the key solutions in representing the interval information is the use of the interval information (numbers). This paper proposes a multi-criteria decision-making approach that relies on the algebra of random variables in handling the interval information. The interval information is provided in the form of the uniform distributions that are represented by mean and variance parameters. Following the central limit theorem, the normal approximation is involved. Then, the pair-wise comparisons are facilitated to establish the probabilities of dominance and rank the alternatives accordingly. The proposed approach allows for effectively handling the uncertainty and is user-friendly. The empirical application dealing with selection of the sustainable insulation materials is presented to validate the proposed approach. The technological, economic, environmental, and social facets of sustainability are considered when comparing the insulation materials. Sensitivity of the results is then checked via the Monte Carlo simulation.

A New Approach to the Viable Ranking of Zero-Carbon Construction Materials with Generalized Fuzzy Information

This paper aims to put forward an integrated decision approach, with generalized fuzzy information for the viable selection of zero- and low-carbon materials for construction. In countries such as India, the construction sector accounts for high pollution levels and high carbon emissions. To restore sustainability and eco-friendliness, the adoption of low-carbon materials for construction is essential and, owing to the multiple attributes associated with the selection, the problem is viewed as a multi-criteria decision-making problem. Earlier studies on material selection have faced certain issues, such as the following: (i) the modeling of uncertainty is an ordeal task; (ii) the flexibility given to experts during preference elicitation is lacking; (iii) the interactions among the criteria are not well captured; and (iv) a consideration of the criteria type is crucial for ranking. To alleviate these issues, the primary objective of this paper was to develop an integrated framework, with decision approaches for material selection in the construction sector that promote sustainability. To this end, generalized fuzzy information (GFI) was adopted as the preference style as it is both flexible and has the ability to model uncertainty from the following three dimensions: membership, non-membership, and hesitancy grades. Furthermore, the CRITIC approach was extended to the GFI context for calculating criteria weights objectively, by effectively capturing criteria interactions. Furthermore, the COPRAS technique was put forward with the GFI rating for ranking zero- and low-carbon construction materials, based on diverse attributes. The usefulness of the framework was demonstrated via a case example from India and the results showed that the design cost, the financial risk, safety, water pollution, and land contamination were the top five criteria, with blended cement, mud bricks, and bamboo as the top three material alternatives for zero- and low-carbon construction. Finally, a sensitivity analysis and a comparison with other methods revealed the theoretical positives of this framework’s robustness and consistency–but it also revealed some limitations of the proposed framework.

Reverse triple I method based on the Pythagorean fuzzy inference model and its application

This paper is devoted to discussing the reverse triple I method based on the Pythagorean fuzzy set (PFS). We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO) and Pythagorean fuzzy biresiduum. The reverse triple I methods for Pythagorean fuzzy modus ponens (PFMP) and Pythagorean fuzzy modus tollens (PFMT) are also established. In addition, some interesting properties of the reverse triple I method of PFMP and PFMT inference models are analysed, including the robustness, continuity and reversibility. Finally, a practical problem is provided to illustrate the effectiveness of the reverse triple I method for PFMP in decision-making problems. The advantages of the new method over existing methods are also expounded. Overall, compared with the existing methods, the proposed methods are based on logical reasoning rather than using aggregation operators, so the novel methods are more logical, can better deal with the uncertain problems in complex decision-making environments and can completely reflect the decision-making opinions of decision-makers.

Fermatean Fuzzy Schweizer–Sklar Operators and BWM-Entropy-Based Combined Compromise Solution Approach: An Application to Green Supplier Selection

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.

Interval-Valued Pythagorean Fuzzy Similarity Measure-Based Complex Proportional Assessment Method for Waste-to-Energy Technology Selection

This study introduces an integrated decision-making methodology to choose the best “waste-to-energy (WTE)” technology for “municipal solid waste (MSW)” treatment under the “interval-valued Pythagorean fuzzy sets (IPFSs)”. In this line, first, a new similarity measure is developed for IPFSs. To show the utility of the developed similarity measure, a comparison is presented with some extant similarity measures. Next, a weighting procedure based on the presented similarity measures is proposed to obtain the criteria weight. Second, an integrated approach called the “interval-valued Pythagorean fuzzy-complex proportional assessment (IPF-COPRAS)” is introduced using the similarity measure, linear programming model and the “complex proportional assessment (COPRAS)” method. Furthermore, a case study of WTE technologies selection for MSW treatment is taken to illustrate the applicability and usefulness of the presented IPF-COPRAS method. The comparative study is made to show the strength and stability of the presented methodology. Based on the results, the most important criteria are “greenhouse gas (GHG)” emissions (P3), microbial inactivation efficacy (P7), air emissions avoidance (P9) and public acceptance (P10) with the weight/significance degrees of 0.200, 0.100, 0.100 and 0.100, respectively. The evaluation results show that the most appropriate WTE technology for MSW treatment is plasma arc gasification (H4) with a maximum utility degree of 0.717 followed by anaerobic digestion (H7) with a utility degree of 0.656 over various considered criteria, which will assist with reducing the amount of waste and GHG emissions and also minimize and maintain the costs of landfills.

A Fuzzy Multi-Criteria Method for Sustainable Ferry Operator Selection: A Case Study

This study is motivated by the Zhuhai municipal government, which needs to select a sustainable ferry operator. Previous research has ignored the evaluation and selection of ferry operators. In addition, since ferry operator evaluation involves conflicting qualitative and quantitative criteria, and there may be uncertainty and ambiguity in the evaluation of criteria by experts, a fuzzy multi-criteria decision-making (MCDM) approach is required to address this challenge. To this end, this paper proposes an integrated MCDM framework model to evaluate and select the best ferry operator. First, a ferry operator evaluation index system with 15 sub-criteria is constructed according to literature and expert opinions; then the fuzzy analytic hierarchy process (FAHP) is used to determine the subjective weight of the criteria, and the entropy weight (EW) method is used to calculate the objective weight of the criteria. We use the linear weighting method to obtain the comprehensive weights of the criteria; finally, the fuzzy technique for order preference by similarity to ideal solution (FTOPSIS) method is adapted to determine the best ranking of the alternatives. This paper takes the Wanshan Islands in Zhuhai as a real case study to verify the proposed FAHP-EW-FTOPSIS method. The results show that the proposed method can be effectively applied to the evaluation and selection of ferry operators. Sensitivity analysis of criteria weights demonstrates the effectiveness and robustness of the proposed framework model. Key findings based on the research provide management insights that can benefit relevant stakeholders. This is the first paper to study the evaluation and selection of ferry operators. Hence, the evaluation index system and integrated framework model proposed in this paper can make important contributions to the evaluation of ferry operators.

Fault Diagnosis in Regenerative Braking System of Hybrid Electric Vehicles by Using Semigroup of Finite-State Deterministic Fully Intuitionistic Fuzzy Automata

Regenerative braking is one of the most promising and ecologically friendly solutions for improving energy efficiency and vehicle stability in electric and hybrid electric cars. This research describes a data-driven method for detecting and diagnosing issues in hybrid electric vehicle regenerative braking systems. Early fault identification can help enhance system performance and health. This study is centered on the construction of an inference system for fault diagnosis in a generalized fuzzy environment. For such an inference system, finite-state deterministic fully intuitionistic fuzzy automata (FDFIFA) are established. Semigroup of FDFIFA and its algebraic properties including substructures and structure-preserving maps are investigated. The inference system uses FDFIFA semigroups as variables, and FDFIFA semigroup homomorphisms are employed to illustrate the relationship between variables. The newly established model is then applied to diagnose the possible fault and their nature in the regenerative braking systems of hybrid electric vehicles by modeling the performance of superchargers and air coolers. The method may be used to evaluate faults in a wide range of systems, including autos and aerospace systems.