Many belief revision applications require a measure of similarity. We have described a simple, yet powerful, operational measure of similarity based on change. The advantages of this measure are that it: (i) is nonprobabilistical, (ii) is quantitative in character, (iii) not set theoretical, (iv) takes the internal structure of the information state into consideration, (v) is not necessarily sy...

Measuring similarity between nodes has been an issue of extensive research in the social network analysis literature. In this paper, we construct a new measure of similarity between nodes based on the game-theoretic interaction index (Grabisch and Roubens, 1997). Despite the fact that, in general, this index is computationally challenging, we show that in our network application it can be compu...

Memory-based collaborative filtering is the most popular approach to build recommender systems. Despite its success in many applications, it still suffers from several major limitations, including data sparsity. Sparse data affect the quality of the user similarity measurement and consequently the quality of the recommender system. In this paper, we propose a novel user similarity measure based...

Because of its inherently asymmetric nature, set-theoretic analysis offers many interesting contrasts with analysis based on correlations. Until recently, however, social scientists have been slow to embrace set-theoretic approaches. The perception was that this type of analysis is restricted to primitive, binary variables and that it has little or no tolerance for error. With the advent of ‘‘f...

Negation in information processing is an important notion, especially in fuzzy information processing. How to cognize and deal with various negations of fuzzy information, a new fuzzy set FSCOM with contradictory negation, opposite negation and medium negation was presented in [1]. This paper defines fuzzy degree and similarity measure of fuzzy set FSCOM, gives some properties and calculation f...

Neutrosophic sets was defined by Smarandache, which is a generalized of fuzzy sets and intuitionistic fuzzy sets. A single valued neutrosophic set is an instance of neutrosophic sets defined by Wang et al. (2005). In this study, we introduce similarity measure on two single valued neutrosophic sets. We develop an entropy of single valued neutrosophic sets. Finally, we give an example which demo...

Similarity measure plays an important role in medical diagnosis. In this paper, a new rough cotangent similarity measure between two rough neutrosophic sets is proposed. The notion of rough neutrosophic set is used as vector representations in 3D-vector space. The rating of all elements in rough neutrosophic set is expressed with the upper and lower approximation operator and the pair of neutro...

In this paper, we research the relationship between entropy and similarity of interval valued intuitionistic fuzzy sets in detail and prove eight theorems that entropy and similarity of interval valued intuitionistic fuzzy sets can be transformed to each other based on their axiomatic definitions. Finally, we propose some formulaes to calculate entropy and similarity of interval valued intuitio...

Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering confl...

In this paper, we introduce an axiomatic definition of the similarity measure of intuitionistic fuzzy sets (IFS) that differs from the definition of Li [15]. The relationship between the similarity measure and the entropy of IFS is investigated in detail. Six theorems on how the similarity measure could be transformed into the entropy for IFS and vice versa are proposed based on their axiomatic...