In this paper, new definitions of a fuzzy basis and a fuzzy dimension for a fuzzy vector space are presented. A fuzzy basis for a fuzzy vector space (E, μ) is a fuzzy set β on E. The cardinality of a fuzzy basis β is called the fuzzy dimension of (E, μ). The fuzzy dimension of a finite dimensional fuzzy vector space is a fuzzy natural number. For a fuzzy vector space, any two fuzzy bases have t...

The main goal of this work is to study the performance of CARFIR (Automatic Construction of Rules in Fuzzy Inductive Reasoning) methodology for the modelling and prediction of the human central nervous system (CNS). The CNS controls the hemodynamical system by generating the regulating signals for the blood vessels and the heart.CARFIR is able to automatically construct fuzzy rules starting fro...

Introducing fuzzy predicates in inductive logic programming may serve two different purposes: allowing for more adaptability when learning classical rules or getting more expressivity by learning fuzzy rules. This latter concern is the topic of this paper. Indeed, introducing fuzzy predicates in the antecedent and in the consequent of rules may convey different non-classical meanings. The paper...

This communication recalls some of the Bobylev’s definitions of support function of a fuzzy set and distance between fuzzy sets. Their equivalence with the generalized Hausdorff metric and the support function defined by of Puri and Ralescu is analyzed.

Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek’s sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasipseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric. We investigate several properties of this struc...

We introduce the notion of the Gromov-Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov-Hausdorff distance on metric spaces can be deduced from our approach.

In this paper we study the behavior of the (transfinite) small inductive dimension (trind) ind on finite products of topological spaces. In particular we essentially improve Toulmin’s estimation [T] of trind for Cartesian products.

For simplicity, we adopt the following rules: T , T1, T2 denote topological spaces, A, B denote subsets of T , F denotes a subset of T A, G, G1, G2 denote families of subsets of T , U , W denote open subsets of T A, p denotes a point of T A, n denotes a natural number, and I denotes an integer. One can prove the following propositions: (1) Fr(B ∩A) ⊆ FrB ∩A. (2) T is a T4 space if and only if f...

We propose a model of a middleware system enabling personalized web search for users with different preferences. We integrate both inductive and deductive tasks to find user preferences and consequently best objects. The model is based on modeling preferences by fuzzy sets and fuzzy logic. We present the model-theoretic semantic for fuzzy description logic f-EL which is the motivation of creati...