Abstract
For the dynamic multi-attribute decision-making problem, the decision information is usually given in the form of the interval-valued picture fuzzy number (IVPFN), and the attributes are also usually related to each other, a decision method based on the interval-valued picture fuzzy geometric weighted Heronian average mean (IVPFGWHM) operator is proposed. First, the algorithms of IVPFN are defined by combining the picture fuzzy number (PFN) with the algorithms of the interval-valued intuitionistic fuzzy number (IVIFN). Then, using the algorithms of IVPFN and geometric Heronian average mean operators, four Heronian mean operators for IVPFN are proposed: the interval-valued picture fuzzy geometric Heronian average mean (IVPFGHM) operator, the interval-valued picture fuzzy geometric weighted Heronian average mean (IVPFGWHM) operator, and the dynamic interval-valued picture fuzzy geometric weighted Heronian average mean (DIVPFGWHM) operator. Then some properties of these operators are studied. Furthermore, a multi-attribute decision-making process based on DIVPFGWHM is proposed. At the same time, with the aid of the best-worst method (BWM), we obtained the attribute weights. Finally, by analyzing the current situation of logistics industry and using the proposed method to select logistics companies, and by comparing with the other methods to illustrate the effectiveness and advantages of the developed method.
Highlights
Since Zadeh proposed fuzzy sets [1], it has been widely used to describe fuzzy and uncertain decision information
This paper presents a weighted geometric Heronian mean (GHM) operator based on IVPF to deal with dynamic multi-attribute decision making problems, extends the real number GWHM operator to the field of IVPF, and defines the IVPFGWHM operator that can handle dynamic multi-attribute decision-making problems
PRELIMINARIES we briefly introduced the preliminary knowledge of interval-valued picture fuzzy number (IVPFN) and GHM operators, and defined the algorithms of IVPFNs
Summary
Since Zadeh proposed fuzzy sets [1], it has been widely used to describe fuzzy and uncertain decision information. In dealing with multi-attribute decision-making problems, the aggregation operator is a very effective method, Wang and Garg [28] define some Pythagorean fuzzy interaction aggregation operators with the aid of Archimedean t-conorm and t-norm (ATT), but the above aggregation operator only considers the independence of the attributes, in actual situations, different attributes will have different degrees of connection Such as complementarity, redundancy, preference relations, etc. Zhou et al [34] proposed a decision-making method based on interval-valued intuitionistic fuzzy geometric weighted Heronian average operator for the multi-attribute group decisionmaking problem where the decision information is IVIFNs and the attributes are related to each other.
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