## Volume 7, No. 1, 2012

- Bronevich A.G., Rozenberg I.N.

**«Conditional Fuzzy Measures, Functional Mappings, and Fuzzy Variables in the Framework of Probabilistic Approach»**

In the paper we consider basic principles of the fuzzy measure theory in the framework of probabilistic approach. As a result we introduce notions of conditional fuzzy measures, fuzzy variables and its numerical characteristics.Keywords: fuzzy measure, lower and upper probabilities, fuzzy variables.

Resources: title page of the article, elibrary.ru.

- Ionin V.K.

**«Fuzzy Metric Spaces»**

We show how the set Ã of all partial functions that are compressions of real line, generates a structure on an arbitrary set called Ã-structure. It is proved that the specification of this Ã-structure is equivalent to defining some usual metric on the set. This new definition of metric spaces is naturally extended to fuzzy sets.Keywords: fuzzy sets, metric spaces, fuzzy metric spaces, categories, morphisms.

Resources: title page of the article, elibrary.ru.

- Plesniewicz G.S.

**«Queries to Fuzzy Boolean Ontologies»**

Fuzzy Boolean ontologies are considered. Their concepts are propositional variables and links between concepts are represented by formulas of Zadeh’s fuzzy propositonal logic LZ. The base of facts for such ontology consists of a finite set of expressions in the form r <= varphi <= s, where varphi in LZ and 0 <= r <= s <= 1. The problem of query answering for bases of facts is solved.Keywords: fuzzy logic, ontologies, fuzzy Boolean ontologies, queries.

Resources: title page of the article, elibrary.ru.