In the literature on social choice with fuzzy preferences, a central question is how to represent the transitivity of a fuzzy binary relation. Arguably the most general way of doing this is to assume a form of transitivity called max-star transitivity. The star operator in this formulation is commonly taken to be a triangular norm. The familiar max-min transitivity condition is a member of this...

This paper presents an approach to a system based on fuzzy logic for the design of interpolative curves and surfaces in the context of Computer Aided Geometric Design (CAGD). Some problems arising from a previous model are studied by using a similarity approach. Keywords— Fuzzy interpolation, indistinguishability operator, fuzzy number, Computer Aided Geometric Design,approximate reasoning, t-n...

We define a 2-category whose objects are fuzzy sets and whose maps are relations subject to certain natural conditions. We enrich this category with additional monoidal and involutive structure coming from t-norms and negations on the unit interval. We develop the basic properties of this category and consider its relation to other familiar categories. A discussion is made of extending these re...

The notion of filter is established in fuzzy class theory. Graded properties of filters, prime filters and related concepts are investigated. In particular we study properties of filters relativized with respect to the basic three t-norms: Gödel, product, and Lukasiewicz. It is shown that our approach gives rise to a broad class of models including probability and necessity measures on fuzzy se...

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.