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

A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power Muirhead mean

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method

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

Improved Knowledge Measures for q-Rung Orthopair Fuzzy Sets

The q-rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFSs). In this paper, we define the knowledge measure for qROFS by using the cosine inverse function. The information precision and information content are two facets of knowledge measure. Both facets of knowledge measure are considered. The properties of knowledge measure and their graphical explanations are discussed. An application of the knowledge measure in multi-attribute group decision-making (MAGDM) problem under the confidence level approach is given. A numerical example of the selection of renewable energy sources is discussed

Group Decision Algorithm for Aged Healthcare Product Purchase Under q-Rung Picture Normal Fuzzy Environment Using Heronian Mean Operator

With the intensification of the aging, the health issue of the elderly is arousing public concern increasingly. Various healthcare products for the elderly are emerging from the market, thus how to select suitable aged healthcare product is critical to the well-being of the elderly. In the literature, nonetheless, a comprehensive and standardized evaluation framework to support healthcare product purchase decision for the aged is currently lacking. This paper proposes a novel group decision-making method to aid the decision-making of aged healthcare product purchase based on q-rung picture normal fuzzy Heronian mean (q-RPtNoFHM) operators. In it, firstly, a new fuzzy variable called the q-rung picture normal fuzzy set (q-RPtNoFS) is defined to reasonably describe different responses to healthcare product evaluation, for which, some definitions including operational laws, a score function, and an accuracy function of q-RPtNoFSs are introduced. Then, two q-RPtNoFHM operators are presented to aggregate group decision information. In addition, some properties of q-RPtNoFHM operators, such as monotonicity, commutativity, and idempotency, are discussed. Finally, an example on antihypertensive drugs purchase is gave to illustrate the practicality of the proposed method, and conduct sensitivity analysis to analyze the effectiveness and flexibility of proposed methods

Identification and classification of digital green innovation based on interaction Maclaurin symmetric mean operators by using T-spherical fuzzy information

The digital green concept refers to the devotion to digital technology, i.e., techniques of procedures in the area of ecological or sustainable conservation. It contains leveraging digital techniques, procedures, and new tools to evaluate environmental problems and promote sustainable development. The major influence of this article is to evaluate the selection of the best digital green technology. For this, we aim to propose the idea of Maclaurin symmetric mean (MSM) operators based on interaction operational laws for T-spherical fuzzy (TSF) information, such as TSF interaction weighted averaging (TSFIWA), generalized TSF interaction weighted averaging (GTSFIWA), TSF interaction weighted geometric averaging (TSFIWGA), TSF interaction MSM (TSFIMSM), TSF interaction Bonferroni mean (TSFIBM), and TSF interaction weighted Maclaurin symmetric mean (TSFIWMSM) operators. Some dominant and reliable properties are also invented for evaluation. Moreover, to address the best digital green innovation (DGI) among the top five DGIs, we illustrate the procedure of the multi-attribute decision-making (MADM) technique under the presence of the derived operators. Finally, we demonstrate a numerical example for evaluating the comparative study between the proposed and existing or prevailing operators to enhance the worth of the derived theory

EDAS method for multiple attribute group decision making under q-rung orthopair fuzzy environment

Extended q-rung orthopair fuzzy sets (q-ROFSs) is an excellent tool to depict the qualitative assessing information in multiple attribute group decision making (MAGDM) environments. The EDAS method is very effective especially when the conflicting attributes exist in the MAGDM issues in which the optimal alternative should have the biggest value of PDAS and the smallest value of NDAS. In this paper, we put forward the EDAS method for MAGDM issues under q-ROFSs, which makes use of average solution (AS) for assessing the chosen alternatives. The positive distance from AS (PDAS) and negative distance from AS (NDAS) is derived through the score of q-ROFSs. Then, the sorting order or the optimal alternative can be acquired by computing integrative appraisal score. Finally, a numerical example for buying a refrigerator is given to testify our developed EDAS method and some comparative analysis are also raised to further show the precious merits of this method. First published online 27 November 201

VIKOR method for multiple criteria group decision making under 2-tuple linguistic neutrosophic environment

In this article, the VIKOR method is proposed to solve the multiple criteria group decision making (MCGDM) with 2-tuple linguistic neutrosophic numbers (2TLNNs). Firstly, the fundamental concepts, operation formulas and distance calculating method of 2TLNNs are introduced. Then some aggregation operators of 2TLNNs are reviewed. Thereafter, the original VIKOR method is extended to 2TLNNs and the calculating steps of VIKOR method with 2TLNNs are proposed. In the proposed method, it’s more reasonable and scientific for considering the conflicting criteria. Furthermore, the VIKOR are extended to interval-valued 2-tuple linguistic neutrosophic numbers (IV2TLNNs). Moreover, a numerical example for green supplier selection has been given to illustrate the new method and some comparisons are also conducted to further illustrate advantages of the new method

Some Cosine Similarity Measures and Distance Measures between Complex q-Rung Orthopair Fuzzy Sets and Their Applications

As a modification of the q-rung orthopair fuzzy sets (QROFSs), complex QROFSs (CQROFSs) can describe the inaccurate information by complex-valued truth grades with an additional term, named as phase term. Cosine similarity measures (CSMs) and distance measures (DMs) are important tools to verify the grades of discrimination between the two sets. In this manuscript, we develop some CSMs and DMs for CQROFSs. Firstly, the CSMs and Euclidean DMs (EDMs) for CQROFSs and their properties are investigated. Because the CSMs do not keep the axiom of similarity measure (SM), we investigate a technique to develop other SMs based on CQROFSs, and they meet the axiom of the SMs. Moreover, we propose a cosine DM (CDM) based on CQROFSs by considering the interrelationship among the SMs and DMs, then we propose an extended TOPSIS method to solve the multi-attribute decision-making problems. Finally, we provide some sensible examples to demonstrate the practicality and efficiency of the suggested procedure, at the same time, the graphical representations of the developed measures are also utilized in this manuscript