TAILIEUCHUNG - Rough picture fuzzy set and picture fuzzy topologies

Approximation of a picture fuzzy set on a crisp approximation space gives a rough picture fuzzy set. In this paper, the concept of a rough picture set is introduced, besides we also investigate some topological structures of a rough picture fuzzy set are investigated, such are lower and upper rough picture fuzzy approximation operators. | Journal of Computer Science and Cybernetics, , (2015), 245– 253 DOI: ROUGH PICTURE FUZZY SET AND PICTURE FUZZY TOPOLOGIES NGUYEN XUAN THAO† AND NGUYEN VAN DINH‡ Faculty of Information Technology, Vietnam National University of Agriculture, † thaonx281082@; ‡ nvdinh2000@ Abstract. Approximation of a picture fuzzy set on a crisp approximation space gives a rough picture fuzzy set. In this paper, the concept of a rough picture set is introduced, besides we also investigate some topological structures of a rough picture fuzzy set are investigated, such are lower and upper rough picture fuzzy approximation operators. Keywords. Rough set, picture fuzzy set, rough picture fuzzy set, approximation operators, picture fuzzy topological space. 1. INTRODUCTION Rough set theory was introduced by Z. Pawlak in 1980s [1]. It becomes a usefully mathematical tool for data mining, especially for redundant and uncertain data. At first, the establishment of the rough set theory is based on equivalence relation. The set of equivalence classes of the universal set, obtained by an equivalence relation, is the basis for the construction of upper and lower approximation of the subset of the universal set. Fuzzy set theory was introduced by L. Zadeh since 1965 [2]. Immediately, it became a useful method to study the problems of imprecision and uncertainty. After that, there are some extensions of fuzzy set, which also widely used. Intuitionistic fuzzy sets were introduced in 1986, by K. Atanassov [3], which is a generalization of the notion of a fuzzy set. In 2013, B. C. Cuong and V. Kreinovich introduced the concept of picture fuzzy set [4], in which a given set were to be in with three memberships: a degree of positive membership, a degree of negative membership, and a degree of neutral membership of an element in this set. After that, L. H. Son gives an application of picture fuzzy set in the problems of clustering [5]. In .

• Kỹ thuật lập trình
• Rough picture fuzzy set
• Picture fuzzy topologies
• Rough set
• Picture fuzzy set
• Rough picture fuzzy set
• Approximation operators
• Picture fuzzy topological space