Intuitionistic fuzzy numbers and intuitionistic distribution numbers (Q2710042)

The concepts of an intuitionistic fuzzy set (an extension of the concept of an ordinary fuzzy set [see \textit{K. T. Atanassov}, Fuzzy Sets Syst. 20, 87-96 (1986; Zbl 0631.03040), Intuitionistic fuzzy sets, Physcia-Verlag, Heidelberg (1999; Zbl 0939.03057)]) and of intuitionistic fuzzy number are discussed and some of their properties are given. For the set \(\text{IDN}(R)\) of all intuitionistic fuzzy distribution numbers on the universe \(R\) several theorems are proved, e.g.:NEWLINENEWLINENEWLINETheorem 3.1: Let be \(A, B\in \text{IND}(R)\). Then \(A+ B\in\text{IND}(R)\). Especially, if \(A, B\in \text{IND}^+(R)\), then \(A+B\in \text{IND}^+(R)\), where \(\text{IND}^+(R)\) is the set of all positive intuitionistic fuzzy distribution numbers on \(R\).NEWLINENEWLINENEWLINEPseudo-metrics and pseudo-metric spaces are introduced and studied.