No abstract

In this paper, at first, we define the notion of general fuzzy automaton over a field; we call this automaton vector general fuzzy automaton (VGFA). Moreover, we present the concept of max-min vector general fuzzy automaton. We show that if two max-min VGFA are similar, they constitute an isomorphism. After that, we prove that if two VGFA constitute an isomorphism with threshold α, they are equivalent with threshold α, where $\alpha \in [0,1]$. Also, some examples are given to clarify these new notions.

In this paper, we recall the notion of intuitionistic fuzzy 2-normed space introduced by Mursaleen and Lohani [26] and using the direct method, we investigate the Hyers Ulam-Rassias stability of the following quadratic functional equation f (ax + by) + f (ax − by) − a 2 f (x + y) = a 2 f (x − y) − (2a 2 − a) f (x) − (2b 2 − a) f (y) in this space.

In this paper , using the fixed point alternative approach , we investigate the Hyers Ulam-Rassias

The aim of this paper is to investigate fuzzy Hyers-Ulam-Rassias stability of the general case of quadratic functional equation where and fixed integers with . These functional equations are equivalent. This has been proven by Ulam, 1964.