Lano, K., The intuitionistic alternative set theory, Annals of Pure and Applied Logic 59 (1993) 141-156. The Alternative Set Theory, as defined in Vopenka and Sochor, demonstrates how a set theory which avoids actually infinite sets can serve as a framework for much of classical mathematics. This paper defines a theory which can serve as an intuitionistic analogue of AST, and examines motivatio...

A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational la...

Intuitionistic permeable values in BCK/BCI-algebras are introduced, and several properties are investigated. A relation between an intuitionistic permeable S-value and an intuitionistic permeable I-value is discussed. Conditions for the intuitionistic lower (upper) level set to be S-energetic and I-energetic are considered. Conditions for a couple of numbers to be an intuitionistic permeable S-...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. Using the notion of intuitionistic fuzzy sets, Çoker [5] introduced the notion of intuitionistic fuzzy topological spaces. In this paper, we define the notion of intuitionistic fuzzy semiopen (r...

Generalized intuitionistic fuzzy soft set theory, proposed by Park et al. [Journal of Korean Institute of Intelligent Systems 21(3) (2011) 389-394], has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we prove that certain De Margan’s law hold in generalized intuitionistic fuzzy soft set theory with respect to union and intersection operations on gener...

In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβopen sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the charact...