Research On The Construction Method Of Interval-valued Intuitionistic Fuzzy Set Information Measure Based On Geometric Images

Fuzzy set theory,founded by Zadeh in 1965,is a method of describing fuzzy phenomena.In the following decades,the fuzzy set theory has gradually been expanded and strengthened.During this period,Atanassov proposed interval-valued intuitionistic fuzzy set(IVIFS)in 1989,because of its membership and non-membership of each element are both closed sub-intervals of[0,1],which becomes an effective form of establishing a model for solving fuzzy decision-making problems.Since the things in real life are vague,uncertain,and may be affected by the subjectivity of decision makers,in most fuzzy multi-criteria decision making(MCDM)problems,the preference for alternatives provided by the decision makers is usually insufficient to satisfy the clear membership and non-membership values.In addition,information measures are important tool for processing fuzzy data,which mainly includes distance measure,similarity measure,entropy measure and knowledge measure.Based on the above background,this paper mainly does the following work:1.From the image representation analysis of IVIFS,the membership and nonmembership of a single-element IVIFS can be seen as two parts,that is,an IVIFS is decomposed into two interval fuzzy sets(IVFSs).From this,we study the construction methods of distance measure and similarity measure respectively.Moreover,we show that the proposed distance measures and similarity measures constructed in new methods can cover part of existing measures in the content of IVIFS.2.A new axiomatic definition of the hesitancy entropy on IVIFS is given,and the distance function is introduced in the construction.The relationship between distance function and distance measure is illustrated.Based on various distance functions,a large number of new entropy measures can be constructed.Next,a comparative example is used to illustrate the proposed hesitancy entropy is superior to some existing entropy measures in some cases.Another example shows the application of entropy measure in multi-criteria decision making(MCDM)problem,which proves the feasibility of hesitancy entropy construction method.