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.

We consider the problem of computing a restricted nonnegative matrix factorization (NMF) of an m × n matrix X . Specifically, we seek a factorization X ≈ BC, where the k columns of B are a subset of those from X and C ∈ Rk×n ≥0 . Equivalently, given the matrix X , consider the problem of finding a small subset, S, of the columns of X such that the conic hull of S ε-approximates the conic hull o...

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in...

fuzzy segmentation is an effective way of segmenting out objects in images containing both random noise and varying illumination. in this paper, a modified method based on the comprehensive learning particle swarm optimization (clpso) is proposed for pixel classification in hsi color space by selecting a fuzzy classification system with minimum number of fuzzy rules and minimum number of incorr...

The Shapley-Folkman theorem and its corollaries [ 1, 2, 3, 4, 5, 6, 81 provide strong bounds on the distance between the sum of a family of nonconvex sets and the convex hull of the sum. Proofs of the theorem are nonconstructive, and require moderately advanced analysis. The proof developed below is based on elementary considerations. It provides an approximation sequentially with the successiv...

The concept of fuzzy segment was introduced in [2]. In this paper we suggest a notion of strict fuzzy segment and provide a linear algorithm for recognizing it thanks to a simple property of convex hull. A linear method to decompose a thick curve into strict fuzzy segments is also given. The quality of decomposition can be easily controlled by setting two threshold values: the maximum order and...

The concept of space underlying geographic information systems is basically Euclideazl, requiring all subjects to adhere to the same view of space. This makes most attempts to deal with intprecise or uncertain geographic information difficult or sometimes even impossible. In this paper, we describe a way of incorporating imprecise qualitative spatial reasoning with quantitative reasoning in geo...

A measure of nonspecificity is proposed for fuzzy sets with continuous membership functions defined, in general, on the n-dimensional Euclidean space R". The proposed measure is restricted to fuzzy sets that are convex. The measure is justified in terms of the usual axiomatic requirements.

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and  fuzzy gener...