Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. As a solution we will combine fuzzy Description Logics with a possibilistic layer. Then, we will show how to perform reasoning by relying on classical existing reasoners. Description Logics (DLs for short) are a family of logics for representing structured knowledge which have proved to be very use...

Machina and Schmeidler [Machina, M., Schmeidler, D., 1992. A more robust definition of subjective probability. Econometrica 60, 745–780] show that probabilistic sophistication can be obtained in a Savage setting without imposing expected utility by dropping Savage's axiom P2 (sure-thing principle) and strengthening his axiom P4 (weak comparative probability). Their stronger axiom, however, embo...

To a fuzzy choice function C we assign the indicators of revealed preference WAFRP (C), SAFRP (C) and the indicators of congruence WFCA(C), SFCA(C). These indicators measure the degree to which the fuzzy choice function C verifies the axioms of revealed preference WAFRP , SAFRP and of congruenceWFCA and SFCA, respectively.

the objective of this paper is to deal with the fuzzy conic program- ming problems. the aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. toward this end, the convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. un- der this setting, duality t...

A hierarchy of weak variants of Martin’s Axiom is extended and shown to be strict.

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

In this paper, the new kind of parameter strong (weak) domination number in a bipolar fuzzy graph is defined and established the parametric conditions. Another new kind of parameter a totalstrong (weak) bipolar domination number is defined and established the parametric conditions. The properties of strong (weak) bipolar domination number and totalstrong (weak) bipolar domination numbersare dis...

For certain weak versions of the Axiom of Choice (most notably, the Boolean Prime Ideal theorem), we obtain equivalent formulations in terms of partial orders, and filter-like objects within them intersecting certain dense sets or antichains. This allows us to prove some consequences of the Boolean Prime Ideal theorem using arguments in the style of those that use Zorn’s Lemma, or Martin’s Axiom.

We develop the commutator theory for fuzzy congruence relations of general universal algebras. In particular, algebras in modular varieties, we characterize congruences using Day’s terms.

In this paper we introduce a new direction in the investigations of the open problem of the representation of algebraic lattices by the weak congruence lattices. In some cases the representability of some lattice follows from the representability of another lattice. We give some results. AMS Mathematics Subject Classification (2010): 08A30