Journal of Intelligent & Fuzzy Systems - Volume 37, issue 2

Authors: Shi, Zhan-Hong | Zhang, Ding-Hai

Article Type: Research Article

Abstract: Measuring the similarity between images is an essential problem in various image processing and pattern recognition applications. In pattern recognition problems, it is indispensable to give formulas for calculating similarity between different patterns. But it is very difficult to find a certain measure that can be successfully applied to all kinds of pattern recognition problems. Intuitionistic fuzzy sets have been successfully applied to various areas such as pattern recognition and medical diagnostics. In intuitionistic fuzzy sets theory, the calculation of the similarity between intuitionistic fuzzy sets is a significant technique for distinguishing the similarity degree between intuitionistic fuzzy sets. The …existing similarity measures almost are obtained in the sense of distance. In this paper, we present a novel way to obtain the similarity measure between intuitionistic fuzzy sets from a new perspective. Our main purpose is to show that according to the membership and non-membership functions of intuitionistic fuzzy sets, a triangular norm can induce an inclusion degree. Using this triangular norm and the induced inclusion degree, a similarity measure of intuitionistic fuzzy sets can be obtained. We also prove some properties of the proposed similarity measure between intuitionistic fuzzy sets. As the applications of similarity degree proposed in this paper, we first present an intuitionistic fuzzy clustering algorithm based on similarity degree. Then, the similarity degree proposed in this paper is applied to pattern recognition. At the same time, the numerical examples are employed to illustrate the effectiveness of proposed method. Show more

Keywords: Intuitionistic fuzzy sets, Similarity measure, Triangular norm, Fuzzy clustering, Pattern recognition

DOI: 10.3233/JIFS-190102

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 2, pp. 3041-3051, 2019

Authors: She, Yanhong | Wang, Wei | He, Xiaoli | Du, Yan | Liu, Yaoyao

Article Type: Research Article

Abstract: Formal concept analysis, originally proposed by Wille, is a mathematical tool to analyse and represent data in the form of complete formal context. However, in situations with incomplete information, one only has partial knowledge about a concept, recently, a common conceptual framework of the notions of interval sets and incomplete formal contexts for representing partially-known concepts were presented. In this study, we examine and reinterpret the existing studies on partially known concepts by means of three-valued logics. By treating an incomplete formal context as a three-valued formal context and considering the one-to-one correspondence between interval sets and three-valued mappings, we …investigate the condition under which the four types of partially known concepts can be generated by using three-valued implication operators. Moreover, we also evaluate the role of three-valued logic in characterizing attribute implications. A sufficient and necessary condition for computing the true value of an implication correctly in the sense of Kriple semantics is provided. Show more

Keywords: Formal context, partially-known concept, three-valued logic, attribute implication

DOI: 10.3233/JIFS-190111

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 2, pp. 3053-3064, 2019