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Picture fuzzy set (2013) is a generalization of the Zadeh’ fuzzy set (1965) and the Antanassov’ intuitionistic fuzzy set. The new concept could be useful for many computational intelligent problems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10, 11]. New concept –Pythagorean picture fuzzy set (PPFS) is a combination of Picture fuzzy set with the Yager’s Pythagorean fuzzy set [12, 13, 14]. First, in the Part 1 of this paper, we consider basic notions on PPFS as set operators of PPFS’s, Pythagorean picture relation, Pythagorean picture fuzzy soft set. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picture negation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS. As a result we will have a new branch of the picture fuzzy set theory. | Journal of Computer Science and Cybernetics V.35 N.4 2019 293-304 DOI 10.15625 1813-9663 35 4 13898 PYTHAGOREAN PICTURE FUZZY SETS PART 1- BASIC NOTIONS BUI CONG CUONG Institute of Mathematics VAST bccuong@math.ac.vn Crossref Similarity Check Powered w ITheritlMte Abstract. Picture fuzzy set 2013 is a generalization of the Zadeh fuzzy set 1965 and the Anta-nassov intuitionistic fuzzy set. The new concept could be useful for many computational intelligent problems. Basic operators of the picture fuzzy logic were studied by Cuong Ngan 10 11 . New concept -Pythagorean picture fuzzy set PPFS is a combination of Picture fuzzy set with the Yager s Pythagorean fuzzy set 12 13 14 . First in the Part 1 of this paper we consider basic notions on PPFS as set operators of PPFS s Pythagorean picture relation Pythagorean picture fuzzy soft set. Next the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS picture negation operator picture t-norm picture t-conorm picture implication operators on PPFS. As a result we will have a new branch of the picture fuzzy set theory. Keywords. Picture Fuzzy Set Pythagorean Picture Fuzzy Set. 1. INTRODUCTION Recently Bui Cong Cuong and Kreinovich 2013 first defined picture fuzzy sets PFS 8 which are a generalization of the Zadeh fuzzy sets 1 and the Antanassov s intuitionistic fuzzy sets 3 . 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 notions in the picture fuzzy sets theory were given in 9 10 . The new basic connectives in picture fuzzy logic on PFS firstly were presented in 11 25 . These new concepts are supporting to new computing procedures in computational intelligence problems and in other applications see 17 18 19 20 21 22 23 24 . In 2013 Yager introduced new concept - Pythagorean fuzzy set PFS with some new applications in decision making problems .
