we obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. also weconsider relations kadec-klee property and shur property with this objects.these theorems are extend of papers mohebi and narayana.

Multiplicative operations for fuzzy numbers raise several problems both from the theoretical and practical point of view in fuzzy arithmetic. The multiplication based on Zadeh's extension principle and its triangular and trapezoidal approximation is used in several recent works in applications in geology. Recently, new product-type operation are introduced and studied, as e.g. the cross product...

— Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computerimplementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the most well known is an application to fuzzy control. In some cases, fuzzy methodology is applied e...

The present work is concerned with the uniqueness problem of best simultaneous approximation. An n-dimensional l1or l∞-simultaneous unicity space is characterized in terms of Property A. c © 2007 Elsevier Ltd. All rights reserved.

There are many papers in the literature that deal with the problem of the design of a fuzzy system from a set of given training examples. Those who get the best approximation accuracy are based on TSK fuzzy rules, which have the problem of not being as interpretable as Mamdany-type Fuzzy Systems. A question now is posed: How can the interpretability of the generated fuzzy rule-table base be inc...

There are many papers in the literature that deal with the problem of the design of a fuzzy system from a set of given training examples. Those who get the best approximation accuracy are based on TSK fuzzy rules, which have the problem of not being as interpretable as Mamdany-type Fuzzy Systems. A question now is posed: How can the interpretability of the generated fuzzy rule-table base be inc...

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

This article describes a Hopfield-Tank model of the Euclidean traveling salesman problem (using Aiyer’s subspace approach) that incorporates a “fuzzy” interpretation of the rows of the activation array. This fuzzy approach is used to explain the network’s behavior. The fuzzy interpretation consists of computing the center of mass of the positive activations in each row. This produces real numbe...

In this paper, we prove some results concerning the existence of invariant best approximation in Banach spaces. Our main result improves the corresponding results of Jungck and Hussain, Hussain et.al. In the sequel, we discuss some results on best simultaneous approximation in ordered semi-convex structure.

We obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. Also weconsider relations Kadec-Klee property and shur property with this objects.These theorems are extend of papers mohebi and Narayana.