One of the methods of studying on two sets is to calculate the similarity of two sets. Triangular norms and conorms generalize the basic connectives between fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets. In this paper we used triangular conorms (S-norm). The advantage of using S-norm is that the similarity order does not change using different norms. In fact, we are looking for a new definition for calculating the similarity of two Pythagorean fuzzy sets. To achieve this goal, using an S-norm, we first present a formula for calculating the similarity of two Pythagorean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Pythagorean fuzzy sets which prove truthful in similarity conditions. Finally, we give some examples of this method.
A generalized intuitionistic fuzzy set (GIF SB) is proposed. It is shown that Atanassov's intuitionistic fuzzy set, intuitionistic fuzzy sets of root type and intuitionistic fuzzy sets of second type are special cases of this new one. Some important notions, basic algebraic properties of GIF SB, three operators and their relationship are discussed. The algebraic properties include being closed under union, being closed under intersection, being closed under a necessity measure, being closed under a possibility measure and de Morgan type identities.Keywords: Generalized intuitionistic fuzzy set, Intuitionistic fuzzy set, Intuitionistic fuzzy sets of root type, Intuitionistic fuzzy sets of second type.
AMS Classification:47S40.
This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (OC) curves of the plan are like a band having high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the OC bands of using of binomial with the OC bands of using of Poisson distribution.
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