Conceptual design and implementation of the fuzzy semantic model

FSM is one of few database models that support fuzziness, uncertainty and impreciseness of real-world at the class definition level. FSM authorizes an entity to be partially member of its class according to a given degree of membership that reflects the level to which the entity verifies the extent properties of this class. This paper deals with the conceptual design of FSM and adresses some implementation issues.ou

On fuzzy reasoning schemes

In this work we provide a short survey of the most frequently used fuzzy reasoning schemes. The paper is organized as follows: in the first section we introduce the basic notations and definitions needed for fuzzy inference systems; in the second section we explain how the GMP works under Mamdani, Larsen and G¨odel implications, furthermore we discuss the properties of compositional rule of inference with several fuzzy implications; and in the third section we describe Tsukamoto’s, Sugeno’s and the simplified fuzzy inference mechanisms in multi-input-single-output fuzzy systems

Preassociative aggregation functions

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730

"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60