in this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-lukasiewicz operator. in fact lukasiewicz t-norm is one of the four basic t-norms. a new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on ...

This papers aims at clarifying the meaning of diierent interpretations of the Max-Min or, more generally, the Max-t-norm rule in fuzzy systems. It turns out that basically two distinct approaches play an important role in fuzzy logic and its applications: fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information .

Using Generalized Modus Ponens reasoning, we examine the values of inferred conclusion when the premise of the rule and the observed fact have a partial overlapping. We work with fuzzy if-then rules with a single input single output and the t-norm t(x, y) = max((1+λ)(x+y−1)−λxy, 0), λ ≥ −1, for composition operation. This t-norm is important to use because for λ = −1 and λ = 0 it gives the very...

Complete pre-orders can be characterized in terms of the transitivity of the corresponding strict preference and indifference relations. In this paper, we investigate this characterization in a fuzzy setting. We consider two types of completeness (weak completeness and strong completeness) and decompose a fuzzy pre-order by means of an indifference generator, in particular a Frank t-norm. In th...

It is well known that each bounded ultraquasi-metric on a set induces, in a natural way, an [0,1]-fuzzy poset. On the other hand, each [0,1]-fuzzy poset can be seen as a stationary fuzzy ultraquasi-metric space for the continuous t-norm Min. By extending this construction to any continuous t-norm, a stationary fuzzy quasi-metric space is obtained. Motivated by these facts, we present several co...

This paper aims to fuzzify the width problem of classical approximation theory. New concepts fuzzy Kolmogorov n-width and linear are introduced on basis α-fuzzy distance which is induced by norm. Furthermore, relationship between widths in normed space discussed. Finally, exact asymptotic orders corresponding a given norm finite-dimensional Sobolev estimated.

Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial solution of Ulam’s problem for the case of...

In the recent past Kernelized Fuzzy C-Means clustering technique has earned popularity especially in the machine learning community. This technique has been derived from the conventional Fuzzy C-Means clustering technique of Bezdek by defining the vector norm with the Gaussian Radial Basic Function instead of a Euclidean distance. Subsequently the fuzzy cluster centroids and the partition matri...

Originally, fuzzy logic was proposed to describe human reasoning. Lately, it turned out that fuzzy logic is also a convenient approximation tool, and that moreover, sometimes a better approximation can be obtained if we use real values outside the interval 0; 1]; it is therefore necessary to describe possible extension of t-norms and t-conorms to such new values. It is reasonable to require tha...