This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X,R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approxima...

With the arrival of the information age, information acquisition and communication have become more and more important in the field of information technology. This paper uses the concept of homomorphism as a basic tool to study the communication between fuzzy information systems. The concepts of consistent and compatible mappings with respect to fuzzy sets are firstly defined and their basic pr...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

In 1965 L. A Zadeh [11] introduced fuzzy sets as a generalization of ordinary sets. After that C. L. Chang [2] introduced fuzzy topology and that led to the discussion of various aspects of L-topology by many authors. The Čech closure spaces introduced by Čech E. [1] is a generalization of the topological spaces. The theory of fuzzy closure spaces has been established by Mashhour and Ghanim [4]...

The extension of rough set model is an important research direction in rough set theory. The aim of this paper is to present a new extension. At the first, we introduce a pair of dual intuitionistic fuzzy operators (Θ,Φ). And some important properties are examined about these these operators. Moreover, θ-lower and φ-upper approximation operators are defined, by using the operators, and a novel ...

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

In this paper, we investigate the properties of join preserving maps in complete residuated lattices. We define join approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between join preserving operators and Alexandrov fuzzy topologies. We give their examples. AMS Subject Classification: 03E72, 03G10, 06A15, 06F07

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to ...