The Research And Application Of The Ranking Problem Of Multi-attribute Decision Making Method For Interval-valued Fuzzy Number

As an extension of fuzzy number,the interval-valued fuzzy number comprehensively considers the multi-dimensional information.However,until now,few studies have been carried out from the perspective of interval-valued fuzzy Numbers.Therefore,this paper studies the ranking method of multi-attribute decision making of interval-valued fuzzy number from the perspective of structured elements.For the measurement of interval-valued fuzzy numbers,the corresponding relationship between interval-valued fuzzy number and vector is studied in the phase plane of fuzzy numbers.By introducing the measure function and combining the geometric characteristics of interval-valued fuzzy number,this paper defines two methods for calculating the distance between interval-valued fuzzy numbers and transforms them into judging the order relations between them.The rationality of the proposed definition is analyzed theoretically.For the sorting probability of interval-valued fuzzy number,two kinds of sorting probability formulae,SPFA and SPFFD,are defined respectively from the area of the graph enclosed by the interval-valued fuzzy number and the fuzziness of the interval-valued fuzzy number.The homomorphism of fuzzy real number space and continuous random variable space is proved.Through the joint probability density of the random variable corresponding to the interval value fuzzy number,based on the spatial position relationship between the two interval-value fuzzy numbers,the third sorting probability formula,SPFPD is defined.An example shows that SPFPD method is scientific and effective.To solve the problem of multi-attribute decision making model for interval-valued fuzzy number,the principle of triple mean square error is adopted to determine the attribute value of interval-valued fuzzy number.The attribute weight is determined by introducing the column entropy and taking all experts' opinions into consideration.The sequencing of schemes is determined by sequence relations and sequence probability respectively.The latter can provide risk reference for decision makers and assist the formulation of early-warning measures in the later stage.Compared with the scheme scores in the form of interval number and fuzzy number,the interval value fuzzy number depicts the score range and uncertainty,introduces changes,and comprehensively depicts the actual situation from a higher dimension.This paper has 38 figures,6 tables and 58 references.