Pythagorean Fuzzy Bonferroni Mean with Weighted Interaction Operator and Its Application in Fusion of Online Multidimensional Ratings

Aiming at the aggregation problem of online multi-attribute interactive ratings, a decision-making method based on Pythagorean Fuzzy Bonferroni mean with weighted interaction (PFWIBM) operator is developed by mining the advantages of ratings driven decision-making and the quantitative advantages of Pythagorean fuzzy sets on linguistic ratings. First, the shortcomings of existing operators in criterion interactive representation are analyzed, and the improved Bonferroni mean with weighted interaction and its dual operator are defined, which are used to aggregate the membership information and non-membership information under the Pythagorean fuzzy environment, respectively, and then the PFWIBM operator is constructed. Second, a generation method of interaction coefficients embedded in the PFWIBM operator is designed by combining expert knowledge and user ratings to overcome the limitations of the method of relying on subjective setting parameter values. Third, based on the proposed operator and the transformation relationship between Pythagorean fuzzy sets and linguistic ratings, an online multi-dimensional rating aggregation decision-making approach for solving product raking problems is developed. Finally, the proposed method is applied to a passenger car ranking example to show the feasibility of the method, and through some comparative analysis, the advantages of the proposed operator are clarified, and the influence of operator parameters on the decision-making results is analyzed.

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.

T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the T-spherical fuzzy interaction geometric Bonferroni mean operator are first defined. Then, the T-spherical fuzzy interaction weighted Bonferroni mean operator and the T-spherical fuzzy weighted interaction geometric Bonferroni mean operator are defined. Based on the Dombi mean and the Bonferroni mean operator, some T-Spherical fuzzy Dombi Bonferroni mean operators are proposed, including the T-spherical fuzzy Dombi Bonferroni mean operator, T-spherical fuzzy geometric Dombi Bonferroni mean operator, T-spherical fuzzy weighted Dombi Bonferroni mean operator and the T-spherical fuzzy weighted geometric Dombi Bonferroni mean operator. The properties of these proposed operators are studied. An attribute weight determining method based on the T-spherical fuzzy entropy and symmetric T-spherical fuzzy cross-entropy is developed. A new decision making method based on the proposed T-Spherical fuzzy Bonferroni mean operators is proposed for partly known or completely unknown attribute weight situations. The furniture procurement problem is presented to illustrate the new algorithm, and some comparisons are made.

Group decision-making for the selection of an antivirus mask under fermatean fuzzy soft information

With the rapid increase of COVID-19, mostly people are facing antivirus mask shortages. It is necessary to select a good antivirus mask and make it useful for everyone. For maximize the efficacy of the antivirus masks, we propose a decision support algorithm based on the concept of Fermatean fuzzy soft set (FFSfS). The basic purpose of this article is to introduce the notion of FFSfS to deal with problems involving uncertainty and complexity corresponding to various parameters. Here, the valuable properties of FFSfS are merged with the Yager operator to propose four new operators, namely, Fermatean fuzzy soft Yager weighted average (FFSfYWA), Fermatean fuzzy soft Yager ordered weighted average (FFSfYOWA), Fermatean fuzzy soft Yager weighted geometric (FFSfYWG) and Fermatean fuzzy soft Yager ordered weighted geometric (FFSfYOWG) operators. The fundamental properties of proposed operators are discussed. For the importance of proposed operators, a multi-attribute group decision-making (MAGDM) strategy is presented along with an application for the selection of an antivirus mask over the COVID-19 pandemic. The comparison with existing operators shows that existing operators cannot deal with data involving parametric study but developed operators have the ability to deal decision-making problems using parameterized information.

Picture Fuzzy Linear Assignment Method and Its Application to Selection of Pest House Location

The theory of picture fuzzy sets is useful for handling uncertainty in multiple attribute decision making problems by considering membership, non-membership and indeterminacy degrees independently for each element. In this paper, by extending the classical linear assignment method, we propose a novel method which is called picture fuzzy linear assignment method (PF-LAM) for solving multiple criteria group decision-making problems with picture fuzzy sets. A ranking procedure consisting of aggregation functions, score functions, accuracy functions, and weighted rank frequency and a binary mathematical model are presented to determine the priority order of various alternatives. The applicability and validity of the proposed method is shown through the selection of pest house locations. The proposed method helps managers to find the best location to construct the pest house based on the determined criteria.