In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...

The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces.

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

The purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

the purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

the main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. we develop the theory of t-bestsimultaneous approximation in quotient spaces. then, we discuss the relationshipin t-proximinality and t-chebyshevity of a given space and its quotientspace.

7 In this paper, we show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusin’s theorem, which is well-known in classical measure theory, is generalized to fuzzy measure space by using the 9 regularity and weakly null-additivity. A version of Egoro2’s theorem for the fuzzy measure de3ned on metric spaces is given. An application of Lusin’s theorem to approximation...