Fuzzy Description Logics are logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In this work, we start addressing the problem of incorporating Multi-Criteria Decision Making (MCDM) into fuzzy Descripti...

Various expanded rough set models based on tolerance relations enlarge the application fields of rough set theory. Through generating tolerance relations to fuzzy tolerance relations and combining with dominance relations, a tolerance class of a fuzzy tolerance relation is further decomposed into a positive fuzzy tolerance class, a negative fuzzy tolerance class and a purely fuzzy tolerance cla...

The need for fuzzy knowledge bases arises from many application fields, such as trust management. To represent fuzzy data, a syntactic and semantic extension of RDF is proposed. The syntax adds to each triple a truth value. The semantic for Fuzzy RDF and Fuzzy RDF Schema allows to derive truth values for derived statements as well. Fuzzy RDF/RDFS does not aim to become a standard extension to p...

After introducing and developing fuzzy set theory, a lot of studies have been done to combine statistical methods and fuzzy set theory. This works, called fuzzy statistics, have been developed in some branches. In this article we review essential works on fuzzy estimation, fuzzy hypotheses testing, fuzzy regression, fuzzy Bayesian statistics, and some relevant fields. Zusammenfassung: Nach Entw...

Quadratic programming can be seen both as a general approach to linear programming and a special class of nonlinear programming. Moreover, Quadratic Programming problems are of utmost importance in a variety of relevant practical fields, such as, portfolio selection. This work presents and develops a novel fuzzy-sets-based method that solves a class of quadratic programming problems with vaguen...

Fuzzy Description Logics (Fuzzy DLs) are logics that allow to deal with structured knowledge affected by fuzziness. Fuzzy DLs are at the heart of Fuzzy OWL 2, a fuzzy version of the standard ontology language OWL 2. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In particu...

Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differen...

Over the last decade or so, significant advances have been made in two distinct technological areas: fuzzy logic and computational neutral networks. The theory of fuzzy logic provides a mathematical framework to capture the uncertainties associated with human cognitive processes, such as thinking and reasoning. Also, it provides a mathematical morphology to emulate certain perceptual and lingui...

Multi-dimensional Fuzzy differential equations driven by multi-dimensional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differ...