Fuzzy set theory is a useful tool to describe situations in which the data are imprecise or vague. Fuzzy sets handle such situation by attributing a degree to which a certain object belongs to a set. The idea of fuzzy norm was initiated by Katsaras in [1984]. Felbin [1992] defined a fuzzy norm on a linear space whose associated fuzzy metric is of Kaleva and Seikkala type [1984]. Cheng and Morde...

We present some properties regarding Darboux property, non-atomicity, regular fuzziness of multimeasures taking values in the family of all closed nonvoid subsets of a real normed space. Key–words: Darboux property, fuzzy multimeasure, atom, non-atomic, regular, diffused.

in this paper, we investigate the generalizedhyers--ulam stability of the functional equation

The purpose of this paper is to introduce and discuss the concept of orthogonality in the fuzzy metric spaces. At last we introduce and discuss the concept of orthogonality in the fuzzy normed spaces, and obtain some results on orthogonality in fuzzy normed spaces similar to orthogonality in normed spaces.

In this paper, we define and study Cheng-Mordeson L-fuzzy normed spaces. Further, we consider the finite dimensional Cheng-Mordeson L-fuzzy normed spaces and prove some theorems about completeness, compactness and weak convergence in these spaces. As application, we get a stability result in the setting of Cheng-Mordeson L-fuzzy normed spaces.

In the paper [7] C. Huang and C. Moraga suggested a new method to extract fuzzy if-then rules from training data based on information matrix technique with Gaussian membership function. In this paper, we extend this method to the Archimedean t-normed space of quasitriangular fuzzy numbers.

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space. Mathematics Subject Classification 39B55, 39B52, 39B82

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.

The object of this paper is to determine Hyers–Ulam–Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS.

In this paper, we study lacunary statistical convergence in intuition-istic fuzzy normed space. We also introduce here a new concept, that is, statistical completeness and show that IFNS is statistically complete but not complete.