International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The most common ways used to generate indistinguishability operators, namely as transitive closure of reflexive and symmetric fuzzy relation, via the Representation Theorem and as decomposable relations, are related for archimedean t-norms introducing the notion of length of indistinguishability operators.

In his paper "Probabilistic Theories of Relations", Menger showed that, in some cases, Prod-Indistinguishabilities are the same as the antilogarithms of distances; later, Ovchinikov obtained a characterization for Prod-Indistinguishabilities.

In this note, Menger's result is included in a larger frame to obtain more Prod-Indistinguishabilities from distances, and Ovchinnikov's characterization is translated to distances in order to reach a larger class of them.

The purpose of this paper is to analyze the operators induced by relations and conversely the relations induced by operators in fuzzy logic. Given a t-norm * and given a non-empty universal set X, it is well known that if R is a fuzzy *-preorder on X then the operator induced by R, , is a fuzzy consequence operator (FCO). In fact, is a *-coherent FCO. It is also known that if C is a *-coherent FCO then the relation induced by C, R_C, is a fuzzy *-preorder. We explore the *-coherence axiom because we do not know in the literature any example of non-coherent operator. Then, several families of these operators will be shown. Moreover we prove that the equivalence between fuzzy preorders and fuzzy consequence operators is held in only one way. As a result, a characterization of the *-preorder concept using the induced operator is given. Also some characterizations which show when an operator induces a *-preorder are proved. Finally, we will show that the characterization of the operators induced by relations given for finite universes cannot be generalized for infinite universes.

We introduce the concept of locally internal aggregation function with domain ℝⁿ and values in ℝ, and demonstrate some results which lead to the characterization of such functions.

We take as a setting point the Fuzzy Temporal Profile (FTP) model, which is used to describe the temporal evolution of a certain physical parameter. This model defines the approximation of an evolution curve by means of a set of linear sections between a series of significant points (X₀, X₁, …, X_N), and in which each section is defined by means of an imprecise constraint on the duration, the increase in value and the slope between the points connected by the section. Following the FTP model we present a language for the representation of trends, the semantics of which is projected onto a fuzzy definition of each one of the constraints of a profile of interest.

A very important problem associated with the use of learning algorithms consists of fixing the correct assignment of the initial domains for the predictive variables. In the fuzzy case, this problem is equivalent of define the fuzzy labels for each variable. In this work, we propose the inclusion in a learning algorithm, called SLAVE, of a particular kind of linguistic hedges as a way to modify the intial semantic of the labels. These linguistic hedges allow us both to learn and to tune fuzzy rules.

Let us consider a classical problem of decision-making with fuzzy rewards. In order to choose the alternative which corresponds to the best fuzzy reward, we need to use a total order for the fuzzy numbers involved in the problem. In this paper, we consider a definition of such a total order, which is based upon two subjective aspects: the degree of optimism/pessimism and the liking for risk/safety. We also use the graded numbers which are analogous to the fuzzy numbers. However, the operations with graded numbers are carried out as a simple extension of operations with real intervals.

This paper presents a new procedure for handling fuzzy algorithm. It consists of transforming the steps of a fuzzy algorithm into production rules of a fuzzy grammar, executing it using the dynamic of this grammar and adjusting its execution by means of the learning capability of the fuzzy formal languages. With this method, some flexible criterial about the goodness of the execution of a fuzzy algorithm are only necessary for adjusting it. Finally, this procedure is applied for executing and adjusting a fuzzy rule-based system.

This section is maintained by Vladik Kreinovich. Please send you abstract (or copies of papers that you want to see reviewed here) to vladik@cs.utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.