| Intuitionistic fuzzy sets are an extension of traditional fuzzy sets,which are represented by three functions:membership degree,non-membership degree,and hesitancy degree.Therefore,intuitionistic fuzzy sets are more flexible and practical than traditional fuzzy sets in dealing with fuzziness and uncertainty.Subsequently,according to the needs of practical problems,various generalizations of intuitionistic fuzzy sets have been posed one after another.One of the generalization forms is interval-valued intuitionistic fuzzy sets,which express the membership degree and non-membership degree of each element as intervals instead of real numbers.In addition,type-2 intuitionistic fuzzy sets are also an important promotion form of intuitionistic fuzzy sets.It has the ability to reflect the high uncertainty related to the membership degree,and provides additional degrees of freedom from the decision-maker's decision-making process.Compared with simple intuitionistic fuzzy sets,these two types of fuzzy sets can deal with uncertainty more accurately,so as to contain more uncertainty information.This paper mainly studies the fuzzy measures and their applications on interval-valued intuitionistic fuzzy sets and type2 intuitionistic fuzzy sets.The main work of the paper are as follows:1.A new distance measure on interval-valued intuitionistic fuzzy sets that takes into account the width of the interval have been introduced,so that the uncertainty of the outputs is closely related to the uncertainty of the inputs.In addition,we define a new quaternary function on interval-valued intuitionistic fuzzy sets to construct the above-mentioned distance measures,which called interval-valued intuitionistic fuzzy dissimilarity function.Two specific methods for constructing the quaternary functions are also given.Besides,we also analyzed the degradation of the distance measure in this paper,and found that our measures can perfectly cover the measures on a simpler set.Finally,the width-based distance measure proposed in this paper is applied to pattern recognition and medical diagnosis problems,verified by examples,and compared with distance measure on other literatures to prove its superiority to other formulas.2.A new similarity measure on type-2 intuitionistic fuzzy sets is given.Unlike other methods that use the duality of distance measures to construct similarity measures,the similarity measure in this article is obtained based on the Jaccard coefficient,which is more flexible.Moreover,we apply this similarity measure to a multi-attribute group decision-making problem to rank alternatives,and provide an example to illustrate the feasibility of the method. |
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