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

Xu, Yan; Shang, Xiaopu; Wang, Jun; Zhang, Runtong; Li, Weizi; Xing, Yuping

doi:10.3233/jifs-172130

Cited by 31 publications

(36 citation statements)

References 43 publications

(38 reference statements)

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“…Wang et al [29] proposed Muirhead mean operators of picture fuzzy sets and applied them to assessment of financial investment risk. Xu et al [30] propose a family of picture fuzzy Muirhead mean operators and applied them to multi-attribute decision making. Although picture fuzzy aggregation operators have been widely use in many ares, there are some drawbacks.…”

Section: The Development State For Picture Fuzzy Aggregation Operatorsmentioning

confidence: 99%

Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

Luo

Long

2021

Symmetry

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The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

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Section: The Development State For Picture Fuzzy Aggregation Operatorsmentioning

confidence: 99%

Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

Luo

Long

2021

Symmetry

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“…Jana et al [52] established PiF-Dombi's AOs and its applications to MADM problems. Xu et al [53] established a method to picture fuzzy MADM by using Muirhead mean operators. Wang et al [54] developed diverse methods for picture fuzzy Muirhead mean operators to solve DM-complication.…”

Section: Introduction An Literature Reviewmentioning

confidence: 99%

Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Hashmi

Tehrim

Riaz

et al. 2021

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Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in [0,1]. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach.

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“…Because of this, PFSs and their application in MADM have also received a lot of attention. A variety of related research topics, such as correlation coefficients of PFSs (Singh 2015), distance measure of PFSs (Son 2016), picture fuzzy clustering (Thong 2016), application of PFSs in decision making Ju et al 2019), AOs of picture fuzzy numbers (PFNs) for MADM (Garg 2017b;Wei 2017Wei , 2018Wei et al 2018a;Jana et al 2019;Xu et al 2019), MADM methods based on PFSs (Wang et al 2018a;Liang et al 2018), and extensions of PFSs (Wei et al 2018b;Mahmood et al 2019;Khalil et al 2019) are gaining importance.…”

Section: Introductionmentioning

confidence: 99%

Multiple-attribute decision-making based on picture fuzzy Archimedean power Maclaurin symmetric mean operators

et al. 2020

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In this paper, a novel multiple attribute decision making method based on a set of Archimedean power Maclaurin symmetric mean operators of picture fuzzy numbers is proposed. The Maclaurin symmetric mean operator, power average operator, and operational rules based on Archimedean T-norm and T-conorm are introduced into picture fuzzy environment to construct the aggregation operators. The formal definitions of the aggregation operators are presented. Their general and specific expressions are established. The properties and special cases of the aggregation operators are respectively explored and discussed. Using the presented aggregation operators, a method for solving the multiple attribute decision making problems based on picture fuzzy numbers is designed. The method is illustrated through example and experiments and validated by comparisons. The results of the comparisons show that the proposed method is feasible and effective that can provide the generality and flexibility in aggregation of values of attributes and consideration of interactions among attributes and the capability to lower the negative effect of biased attribute values on the result of aggregation.

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

Cited by 31 publications

References 43 publications

Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Multiple-attribute decision-making based on picture fuzzy Archimedean power Maclaurin symmetric mean operators

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