in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

In this note, we study an approximation property of regular fuzzy neural network(RFNN). It is shown that any fuzzy-valued measurable function can be approximated by the four-layer RFNN in the sense of fuzzy integral norm for the finite sub-additive fuzzy measure on R.

Though the transitive closure of a reflexive and symmetric fuzzy relation R is unique and there are several algorithms to calculate it, there can be many transitive openings (maximal T -indistinguishability operators among the ones smaller than or equal to R). This paper presents a method to calculate transitive openings of a reflexive and symmetric fuzzy relation R. It is worth noticing that a...

In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

Using s-norm S, we introduce the notion of sensible fuzzy R-subgroups in near-rings, and some related properties are investigated. Mathematics Subject Classification: 06F35, 03G25, 03E72.

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

We introduce and  study  fuzzy (co-)inner product and fuzzy(co-)norm of hyperspaces. In this regard by considering  the notionof hyperspaces, as a generalization of vector spaces, first we willintroduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions offuzzy (co-)norm and fuzzy (co-)orthogonality  in hyperspaces. Inparticular, we will prove that ...