Research On Multiple-attribute Decision Making Method Based On Interval-valued Complex Fuzzy Soft Sets

In multi-attribute decision making environments,accurate decision-making is particularly important,but it is difficult for decision makers to give accurate evaluation values.To this end,scholars have successively proposed fuzzy set theories such as intuitionistic fuzzy sets,interval valued fuzzy sets,hesitant fuzzy sets,Pythagoras fuzzy sets,neutrosophic sets,orthogonality fuzzy sets and so on.However,these fuzzy set theories are used to describe one-dimensional information,which cannot capture the periodic and seasonal changes of the information.The interval-valued complex fuzzy soft sets(IV-CFSSs)overcomes this disadvantage and can be used to describe periodic information.At the same time,the IV-CFSSs have the following characteristics in describing information:(1)The evaluation value can be extended from the precise value to the interval value to reduce the subjective bias of the decision makers to a certain extent;(2)IV-CFSSs extend membership values from real numbers to complex numbers,and the description information expands from one dimension to two dimensions;(3)IV-CFSSs also have the advantages of soft sets,which can make parameterization unlimited and facilitate the classification of decision objects.This paper studies the multi-attribute decision making methods based on IV-CFSSs.The main content of this article is as follows:In part one,this paper defines the addition operation,multiplication operation,partial membership operation and partial non-membership operation of IV-CFSSs.The operations and comparison method of interval-valued complex fuzzy soft numbers(IV-CFSNs)are defined.In part two,this paper defines distance measure of IV-CFSSs and various formulas for calculating distance measures of IV-CFSSs,including the normalized Hamming distance,the normalized Euclidean distance,the generalized Euclidean distance,and the generalized weighted Euclidean Distance,the weighted Hamming distance,the weighted Euclidean distance.A TOPSIS method based on distance measure for IV-CFSSs is constructed,and it is applied to economic analysis to verify the feasibility of the TOPSIS method.In part three,this paper defines similarity measure and entropy of IV-CFSSs and define the formulas used to calculate similarity measures,generalized similarity measures,generalized weighted similarity measures,standard entropy,generalized entropy,and generalized weighted entropy.The relationships between similarity measure and entropy of IV-CFSSs are also studied.A MABAC method based on the similarity measure and entropy for IV-CFSSs is constructed,and a numerical example of attendance device selection is given to illustrate the feasibility of the proposed algorithm.In part four,this paper defines interval-valued complex fuzzy soft weighted arithmetic average(IV-CFSWAA)operator and interval-valued complex fuzzy soft weighted geometric average(IV-CFSWGA)operator.And this paper studies the relevant properties of these operators.Based on these two operators,two interval-valued complex fuzzy soft EDAS methods in multi-attribute group decision-making environment areproposed.Finally,a numerical example of an economic problem is provided to verify the feasibility and applicability of the proposed method.