Some q-rung orthopair fuzzy Muirhead means with their application to multi-attribute group decision making

Recently proposed q-rung orthopair fuzzy set (q-ROFS) is a powerful and effective tool to describe fuzziness, uncertainty and vagueness. The prominent feature of q-ROFS is that the sum and square sum of membership and non-membership degrees are allowed to be greater than one with the sum of qth power of the membership degree and qth power of the non-membership degree is less than or equal to one. This characteristic makes q-ROFS more powerful and useful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS). The aim of this paper is to develop some aggregation operators for fusing q-rung orthopair fuzzy information. As the Muirhead mean (MM) is considered as a useful aggregation technology which can capture interrelationships among all aggregated arguments, we extend the MM to q-rung orthopair fuzzy environment and propose a family of q-rung orthopair fuzzy Muirhead mean operators. Moreover, we investigate some desirable properties and special cases of the proposed operators. Further, we apply the proposed operators to solve multi-attribute group decision making (MAGDM) problems. Finally, a numerical instance as well as some comparative analysis are provided to demonstrate the validity and superiorities of the proposed method

On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.<br /

Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers\u27 preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.<br /

A method to multi-attribute decision making with picture fuzzy information based on Muirhead mean

The recently proposed picture fuzzy set (PFS) is a powerful tool for handling fuzziness and uncertainty. PFS is character-ized by a positive membership degree, a neutral membership degree, and a negative membership degree, making it more suitable and useful than the intuitionistic fuzzy set (IFS) when dealing with multi-attribute decision making (MADM). The aim of this paper is to develop some aggregation operators for fusing picture fuzzy information. Considering the Muirhead mean (MM) is an aggregation technology which can consider the interrelationship among all aggregated ar-guments, we extend MM to picture fuzzy context and propose a family of picture fuzzy Muirhead mean operators. In addition, we investigate some properties and special cases of the proposed operators. Further, we develop a novel meth-od to MADM in which the attribute values take the form of picture fuzzy numbers (PFNs). Finally, a numerical example is provided to illustrate the validity of the proposed method

Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness

Using linear programming for weights identification of generalized bonferroni means in R

The generalized Bonferroni mean is able to capture some interaction effects between variables and model mandatory requirements. We present a number of weights identification algorithms we have developed in the R programming language in order to model data using the generalized Bonferroni mean subject to various preferences. We then compare its accuracy when fitting to the journal ranks dataset

A generalization of the Bonferroni mean based on partitions

The mean defined by Bonferroni in 1950 (known by the same name) averages all non-identical product pairs of the inputs. Its generalizations to date have been able to capture unique behavior that may be desired in some decision-making contexts such as the ability to model mandatory requirements. In this paper, we propose a composition that averages conjunctions between the respective means of a designated subset-size partition. We investigate the behavior of such a function and note the relationship within a given family as the subset size is changed. We found that the proposed function is able to more intuitively handle multiple mandatory requirements or mandatory input sets

Fuzzy decision making in complex frameworks with generalized aggregation operators

[EN] This article presents a new aggregation system applied to fuzzy decision making. The fuzzy generalized unified aggregation operator (FGUAO) is a system that integrates many operators by adding a new aggregation process that considers the relevance that each operator has in the analysis. It also deals with an uncertain environment where the information is studied with fuzzy numbers. A wide range of particular cases and properties are studied. This approach is further extended by using quasi-arithmetic means. The paper ends studying the applicability in decision making problems regarding the European Union decisions. For doing so, the work uses a multi-person aggregation process obtaining the multi-person - FGUAO operator. An example concerning the fixation of the interest rate by the European Central Bank is presented. (C) 2018 Elsevier B.V. All rights reserved.We would like to thank the associate editor and the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Chilean Government through the Fondecyt Regular program (project number 1160286), the University of Chile, the project PIEF-GA-2011-300062 of the European Commission and the Distinguished Scientist Fellowship Program of the King Saud University (Saudi Arabia), is gratefully acknowledged.Merigó -Lindahl, JM.; Gil-Lafuente, AM.; Yu, D.; Llopis Albert, C. (2018). Fuzzy decision making in complex frameworks with generalized aggregation operators. Applied Soft Computing. 68:314-321. https://doi.org/10.1016/j.asoc.2018.04.002S3143216

Pythagorean 2-tuple linguistic power aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problems with Pythagorean 2-tuple linguistic information. Then, we utilize power average and power geometric operations to develop some Pythagorean 2-tuple linguistic power aggregation operators: Pythagorean 2-tuple linguistic power weighted average (P2TLPWA) operator, Pythagorean 2-tuple linguistic power weighted geometric (P2TLPWG) operator, Pythagorean 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, Pythagorean 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, Pythagorean 2-tuple linguistic power hybrid average (P2TLPHA) operator and Pythagorean 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness