the aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. in this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. in particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. finally, dimension of a fuzzy hypervector space isdefined and the basi...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

In [4], D. Osipov and A. Parshin developed an approach to harmonic analysis on higher dimensional local fields through categories of filtered vector spaces as in [3]. In the present paper we give a variant of this approach that behaves nicely for inductive arguments. We establish Pontryagin duality, the Fourier inversion formula, and a Plancherel formula for all dimensions. ∗This paper was writ...

We show that the proximity inductive dimension defined by Isbell agrees with Brouwer originally described (for Polish spaces without isolated points) on class of compact Hausdorff spaces. This shows Fedorchuk?s example a space whose exceeds its Lebesgue covering is an as Smirnov. answers Isbell?s question whether or not and coincide.

The starting point of this paper is the classical well-known theorem due to G. BIRKHOFF, P. HALL, and J. SCHMIDT which establishes a one-to-one correspondence between compact closure operators, inductive closure operators, inductive closure systems, and closure operators generated in universal algebras (and generated in deductive systems, respectively). In the paper presented we make first step...

A variety of methods exist for inductive learning of classification rules using crisp sets. In this paper we illustrate an inductive learner that uses fuzzy sets, where the membership functions of the linguistic terms are given in advance. We also show how the induction of conjunctive rules fit into a fuzzy set covering framework (FuzzyBexa) that we introduced before.

The aim of this research is to develop a strat­ egy of reasoning under uncertainty in the context of the Fuzzy Inductive Reasoning methodology. This methodology allows the prediction of systems behavior by means of two different schemes. The first one corre­ sponds to a pattern prediction scheme, based exclusively on pattern rules. The second one corresponds to a purely Sugeno infer­ ence syste...