TAILIEUCHUNG - Some new de morgan picture operator triples in picture fuzzy logic

Some basic operators of fuzzy logic as negation, t-norms, t-conorms for picture fuzzy sets firstly are defined and studied in [6, 9]. This paper is devoted to some classes of representable picture fuzzy t-norms and representable picture fuzzy t-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic De Morgan triples of picture operators. | Journal of Computer Science and Cybernetics, , (2017), 143–164 DOI SOME NEW DE MORGAN PICTURE OPERATOR TRIPLES IN PICTURE FUZZY LOGIC BUI CONG CUONG1 , ROAN THI NGAN2 , LE BA LONG3 1 Institute 2 Basic of Mathematics; 1 bccuong@ Science Faculty, Ha Noi University of Natural Resources and Environment 3 Post and Telecommunication Institute of Technology Abstract. A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are direct extensions of the fuzzy sets and the intuitionistic fuzzy sets. Then some operations on PFS with some properties are considered in [7, 5]. Some basic operators of fuzzy logic as negation, t-norms, t-conorms for picture fuzzy sets firstly are defined and studied in [6, 9]. This paper is devoted to some classes of representable picture fuzzy t-norms and representable picture fuzzy t-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic De Morgan triples of picture operators. Keywords. Picture fuzzy sets, Picture fuzzy t-norms, Picture fuzzy t-conorm, De Morgan picture operator triple. 1. INTRODUCTION Recently, Bui Cong Cuong and Kreinovich (2013) first defined “picture fuzzy sets” [7, 5], which are a generalization of the Zadeh’s fuzzy sets [27, 28] and the Antanassov’s intuitionistic fuzzy sets [2, 1]. This concept is particularly effective in approaching the practical problems in relation to the synthesis of ideas, such as decisions making problems, voting analysis, fuzzy clustering, financial forecasting. The basic definitions and basic operators in the picture fuzzy sets theory were given in [3, 4, 7, 5]. The new basic logic connectives on the PFS firstly were presented in [6, 9]. These new concepts are supporting to new computing procedures in computational intelligence problems and in other applications (see [14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26]). In this paper we study some algebraic properties of the picture fuzzy t-norms and the picture

• Kỹ thuật lập trình
• Journal of Computer Science and Cybernetics
• Picture fuzzy sets
• Picture fuzzy t norms
• Picture fuzzy t conorm
• De Morgan picture operator triple
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