Some q-rung orthopair fuzzy hybrid aggregation operators and TOPSIS method for multi-attribute decision-making

A new approach to sustainable logistic processes with q-rung orthopair fuzzy soft information aggregation

In recent years, as corporate consciousness of environmental preservation and sustainable growth has increased, the importance of sustainability marketing in the logistic process has grown. Both academics and business have increased their focus on sustainable logistics procedures. As the body of literature expands, expanding the field's knowledge requires establishing new avenues by analyzing past research critically and identifying future prospects. The concept of "q-rung orthopair fuzzy soft set" (q-ROFSS) is a new hybrid model of a q-rung orthopair fuzzy set (q-ROFS) and soft set (SS). A q-ROFSS is a novel approach to address uncertain information in terms of generalized membership grades in a broader space. The basic alluring characteristic of q-ROFS is that they provide a broader space for membership and non-membership grades whereas SS is a robust approach to address uncertain information. These models play a vital role in various fields such as decision analysis, information analysis, computational intelligence, and artificial intelligence. The main objective of this article is to construct new aggregation operators (AOs) named "q-rung orthopair fuzzy soft prioritized weighted averaging" (q-ROFSPWA) operator and "q-rung orthopair fuzzy soft prioritized weighted geometric" (q-ROFSPWG) operator for the fusion of a group of q-rung orthopair fuzzy soft numbers and to tackle complexities and difficulties in existing operators. These AOs provide more effective information fusion tools for uncertain multi-attribute decision-making problems. Additionally, it was shown that the proposed AOs have a higher power of discriminating and are less sensitive to noise when it comes to evaluating the performances of sustainable logistic providers.

Confidence Levels Complex q-Rung Orthopair Fuzzy Aggregation Operators and Its Application in Decision Making Problem

The theory investigated in this analysis is substantially more suitable for evaluating the dilemmas in real life to manage complicated, risk-illustrating, and asymmetric information. The complex Pythagorean fuzzy set is expanded upon by the complex q-rung orthopair fuzzy set (Cq-ROFS). They stand out by having a qth power of the real part of the complex-valued membership degree and a qth power of the real part and imaginary part of the complex-valued non-membership degree that is equal to or less than 1. We define the comparison method for two complex q-rung orthopair fuzzy numbers as well as the score and accuracy functions (Cq-ROFNs). Some averaging and geometric aggregation operators are examined using the Cq-ROFSs operational rules. Additionally, their main characteristics have been fully illustrated. Based on the suggested operators, we give a novel approach to solve the multi-attribute group decision-making issues that arise in environmental contexts. Making the best choice when there are asymmetric types of information offered by different specialists is the major goal of this work. Finally, we used real data to choose an ideal extinguisher from a variety of options in order to show the effectiveness of our decision-making technique. The effectiveness of the experimental outcomes compared to earlier research efforts is then shown by comparing them to other methods.

Green Recycling Supplier Selection of Shared Bicycles: Interval-Valued Pythagorean Fuzzy Hybrid Weighted Methods Based on Self-Confidence Level

In the face of practical problems such as the increasing demand for shared bicycles and the number of faulty vehicles which are hard to handle and repair in time, shared bicycles operators tend to outsource recycling services to suppliers. To solve the problem of recycling supplier selection, this paper constructs a novel evaluation index system involving the three traditional dimensions and introduces an interval-valued Pythagorean fuzzy (IVPF) hybrid weighted decision-making model based on the self-confidence level. Subsequently, the self-confidence IVPF hybrid weighted average geometric operator and self-confidence IVPF ordered hybrid weighted average geometric operator are proposed by integrating the self-confidence level of experts, the superiority of the weighted and geometric average rules. The significant merit of the developed operators is that they can incorporate the self-confidence level of the expert as well as effectively combine the characteristics of the weighted and geometric average mechanism. A multi-attribute decision-making (MADM) framework is then constructed by using the proposed aggregation approach. Finally, on the basis of the established evaluation index system, a case concerning the green recycling supplier selection of shared bicycles is applied to display the superiority and practicability of the presented method.

TOPSIS method for spherical fuzzy MAGDM based on cumulative prospect theory and combined weights and its application to residential location

Nowadays, how to choose a comfortable and relatively satisfactory residence is one of the multiple attribute group decision making (MAGDM) issues which people are paying more and more attention. However, since the inaccuracy and fuzziness of the information are given by decision makers (DMs) in practical decision-making and psychological factors of DMs should be considered in the decision-making process, this paper presents TOPSIS approach based on cumulative prospect theory (CPT) to deal with the MAGDM issues under the spherical fuzzy environment. Furthermore, considering the objective relationship between the attributes, the combined weights are used to get attribute weights in spherical fuzzy sets (SFSs). Finally, an example of residential location is introduced to prove the validity of our proposed approach by comparing with spherical fuzzy TOPSIS(SF-TOPSIS) method and spherical fuzzy WASPAS (SF-WASPAS) method.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts’ weight determining model

How to select the optimal strategy to compete with rivals is one of the hottest issues in the multi-attribute decision-making (MADM) field. However, most of MADM methods not only neglect the characteristics of competitors’ behaviors but also just obtain a simple strategy ranking result cannot reflect the feasibility of each strategy. To overcome these drawbacks, a two-person non-cooperative matrix game method based on a hybrid dynamic expert weight determination model is proposed for coping with intricate competitive strategy group decision-making problems within q-rung orthopair fuzzy environment. At the beginning, a novel dynamic expert weight calculation model, considering objective individual and subjective evaluation information simultaneously, is devised by integrating the superiorities of a credibility analysis scale and a Hausdorff distance measure for q-rung orthopair fuzzy sets (q-ROFSs). The expert weights obtained by the above model can vary with subjective evaluation information provided by experts, which are closer to the actual practices. Subsequently, a two-person non-cooperative fuzzy matrix game is formulated to determine the optimal mixed strategies for competitors, which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally, an illustrative example, several comparative analyses and sensitivity analyses are conducted to validate the reasonability and effectiveness of the proposed approach. The experimental results demonstrate that the proposed approach as a CSGDM method with high efficiency, low computation complexity and little calculation burden.

A consensus reaching process based on the concordance correlation measure of intuitionistic fuzzy sets in multi-criteria decision making

Although some correlation measure of intuitionistic fuzzy sets(IFSs) have been proposed, some of them cannot express the consistency of information or satisfy the axioms of similarity measure. In this paper, we present a consensus reaching process based on the concordance correlation measure of IFSs in multi-criteria decision making problems. Firstly, we define an innovative concordance correlation measure of IFSs, which not only takes the average information deviation of IFSs into account but also overcomes the disadvantages of previous correlation measures. In addition, its properties and the relationship between the defined new concordance correlation measure and Pearson correlation coefficient of IFSs are discussed. Secondly, considering that the classical TOPSIS method cannot be applied to the correlation measure with negative values, we continue to introduce the concept of relative concordance correlation measure and propose a consensus reaching process with minimum adjustment for an innovative behavioral TOPSIS method. Furthermore, a detailed numerical example and the comparison analyses are provided to verify the advantages of the proposed method. At last, we discuss the sensitivity and stability of the method.

Novel q-rung orthopair fuzzy interaction aggregation operators and their application to low-carbon green supply chain management

The low-carbon supply chain management is big a challenge for the researchers due to the rapid increase in global warming and environmental concerns. With the advancement of the environmental concerns and social economy, it is an unavoidable choice for a business to achieve sustainable growth for low-carbon supply chain management. Since the root of the chain depends upon the supplier selection and choosing an excellent low-carbon supply. Green supplier selection is one of the most crucial activities in low-carbon supply chain management, it is critical to develop rigorous requirements and a system for selection in low-carbon green supply chain management (LCGSCM). A q-rung orthopair fuzzy number (q-ROFN) is pair of membership degree (MD) and non-membership degrees (NMD) which is reliable to address uncertainties in the various real-life problems. This article sets out a decision analysis approach for interactions between MDs and NMDs with the help of q-ROFNs. For this objective, we develop new aggregation operators (AOs) named as, q-rung orthopair fuzzy interaction weighted averaging (q-ROFIWA) operator, q-rung orthopair fuzzy interaction ordered weighted averaging (q-ROFIOWA) operator, q-rung orthopair fuzzy interaction hybrid averaging (q-ROFIHA) operator, q-rung orthopair fuzzy interaction weighted geometric (q-ROFIWG) operator, q-rung orthopair fuzzy interaction ordered weighted geometric (q-ROFIOWG) operator and q-rung orthopair fuzzy interaction hybrid geometric (q-ROFIHG) operator. These AOs define an advanced approach for information fusion and modeling uncertainties in multi-criteria decision-making (MCDM). At the end, a robust MCDM approach based on newly developed AOs is developed. Some significant properties of these AOS are analyzed and the efficiency of the developed approach is assessed with a practical application towards sustainable low-carbon green supply chain management.

Improved cosine and cotangent function-based similarity measures for q-rung orthopair fuzzy sets and TOPSIS method

Despite the importance of cosine and cotangent function- based similarity measures, the literature has not provided a satisfactory formulation for the case of q-rung orthopair fuzzy set (qROFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a similarity measure and strict inclusion relation. In addition, the maximum operator-based similarity measures are criticized. Then, new improved, axiomatically supported cosine and cotangent function-based similarity measures for qROFSs are proposed. Additional properties of the new similarity measures are discussed to guarantee their good performance. Two algorithmic procedures of TOPSIS method that based on fixed and relative ideal solutions are discussed. The numerical examples are provided to support the findings

Novel Approach for Third-Party Reverse Logistic Provider Selection Process under Linear Diophantine Fuzzy Prioritized Aggregation Operators

Aggregation operators are fundamental concept for information fusion in real-life problems. Many researchers developed aggregation operators for multi-criteria decision-making (MCDM) under uncertainty. Unfortunately, the existing operators can be utilized under strict limitations and constraints. In this manuscript, we focused on new prioritized aggregation operators which remove the strict limitations of the existing operators. The addition of reference parameters associated with membership and non-membership grades in the linear Diophantine Fuzzy sets provide a robust modeling for MCDM problems. The primary objective of this manuscript is to introduce new aggregation operators for modeling uncertainty by using linear Diophantine Fuzzy information. For this objective we develop aggregation operators (AO) namely, "linear Diophantine Fuzzy prioritized weighted average" (LDFPWA) operator and "linear Diophantine Fuzzy prioritized weighted geometric" (LDFPWG) operator. Certain essential properties of new prioritized AOs are also proposed. A secondary objective is to discuss a practical application of third party reverse logistic provider (3PRLP) optimization problem. The efficiency, superiority, and rationality of the proposed approach is analyzed by a numerical example to discuss 3PRLP. The symmetry of optimal decision and ranking of feasible alternatives is followed by a comparative analysis.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management

The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in which degree of truthness and degree of falsity meet the condition 0≤Θ˘2(x)+K2(x)≤1. Another extension of PFS is a q´-rung orthopair fuzzy set (q´-ROFS), in which truthness degree and falsity degree meet the condition 0≤Θ˘q´(x)+Kq´(x)≤1,(q´≥1), so they can characterize the scope of imprecise information in more comprehensive way. q´-ROFS theory is superior to FS, IFS, and PFS theory with distinguished characteristics. This study develops a few aggregation operators (AOs) for the fusion of q´-ROF information and introduces a new approach to decision-making based on the proposed operators. In the framework of this investigation, the idea of a generalized parameter is integrated into the q´-ROFS theory and different generalized q´-ROF geometric aggregation operators are presented. Subsequently, the AOs are extended to a “group-based generalized parameter”, with the perception of different specialists/decision makers. We developed q´-ROF geometric aggregation operator under generalized parameter and q´-ROF geometric aggregation operator under group-based generalized parameter. Increased water requirements, in parallel with water scarcity, force water utilities in developing countries to follow complex operating techniques for the distribution of the available amounts of water. Reducing water losses from water supply systems can help to bridge the gap between supply and demand. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the q´-ROF environment. An illustrative example related to water loss management has been given to show the validity of the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the liability and dominance of proposed techniques to the existing one is also considered.