Properties of Compact fuzzy Normed Space

Abstract

In this paper we recall the definition of fuzzy norm then basic properties of fuzzy
 normed space is recalled after that we introduced the definition of compact fuzzy
 normed space. Then basic properties of compact fuzzy normed space is proved.

Fuzzy Norm on Fuzzy <img src=image/13427754_01.gif>-Normed Space

“…Various concepts related to fuzzy set are developed based on this definition 2.1. Among other are the development of fuzzy point that is discussed in [1], [13][14][15][16][17][18], [22][23][24] and [32]. The concept of fuzzy point is as follows.…”

“…For any vector space Y over a field L and B  be a fuzzy set in Y, it is defined function , : The next, the definition of Fn-NS that is approached using fuzzy point is given as discussed on [22]. Clearly, it is not the same from definition in [4], [18] and [37][38]. (1)…”

“…Likewise with fuzzy 2-normed space (F2-NS) to fuzzy n-normed space (Fn-NS). One of them is intuitionistic approach which uses the concept of the continuous t-norm and the continuous t-conorm [2,4,5,11,12,18,20], [25][26][27][28][29][30][31][32][33]. However, the concept of FNS which uses the fuzzy point approach of the fuzzy set is also used by many authors [1], [14][15][16][17], [22][23][24].…”

Some Properties of Fuzzy Inner Product Space

“…Kider [14], introduced the notion of fuzzy absolute value and studied properties of finite dimensional fuzzy normed space. The concept of general fuzzy normed space was presented by Kider and Gheeab in 2019 [15]. They proved basic properties of this space and the general fuzzy normed space GFB(V, U) [16].…”

The Hausdorff Algebra Fuzzy Distance and its Basic Properties

“…The concept of general fuzzy normed space were presented by Kider and Gheeab in 2019, [9] [10] also they proved basic properties of this space and the general fuzzy normed space GFB (V, U). Kider and Kadhum in 2019, [11] introduce the notion fuzzy compact linear operator and proved its basic properties.…”