A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns

A New Approach to Intuitionistic Fuzzy Decision Making Based on Projection Technology and Cosine Similarity Measure

For a multi-attribute decision making (MADM) problem, the information of alternatives under different attributes is given in the form of intuitionistic fuzzy number(IFN). Intuitionistic fuzzy set (IFS) plays an important role in dealing with un-certain and incomplete information. The similarity measure of intuitionistic fuzzy sets (IFSs) has always been a research hotspot. A new similarity measure of IFSs based on the projection technology and cosine similarity measure, which con-siders the direction and length of IFSs at the same time, is first proposed in this paper. The objective of the presented pa-per is to develop a MADM method and medical diagnosis method under IFS using the projection technology and cosine similarity measure. Some examples are used to illustrate the comparison results of the proposed algorithm and some exist-ing methods. The comparison result shows that the proposed algorithm is effective and can identify the optimal scheme accurately. In medical diagnosis area, it can be used to quickly diagnose disease. The proposed method enriches the exist-ing similarity measure methods and it can be applied to not only IFSs, but also other interval-valued intuitionistic fuzzy sets(IVIFSs) as well

New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

In this paper we propose a new approach to construct similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop new approach for solving problems of pattern recognition and multi-criteria fuzzy decision making

Similarity Measure: An Intuitionistic Fuzzy Rough Set Approach

‎In fuzzy set theory‎, ‎the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets‎. ‎It is also to be noted that the intuitionistic fuzzy set is reflected as an extension of the fuzzy set accommodating both membership and non-membership functions together with a hesitation margin‎. ‎In the intuitionistic fuzzy set theory‎, ‎the sum of the membership function and the non-membership function is a value between 0 and 1‎. ‎In recent times‎, ‎intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory‎. ‎Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in real-life problems and that is why many researchers paid more attention to this concept‎. ‎Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties‎. ‎In this paper‎, ‎we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a set-theoretic approach‎. ‎The proposed measure is able to give an exact result‎. ‎In the application part‎, ‎we consider a real-life problem for selecting a fair play award-winning team in a cricket tournament and describe the algorithm‎