The notion of fuzzy function based on many-valued equivalence relations (many-valued similarity relations (equalities) [17, 18, 19], fuzzy equivalence relations [4, 6, 7, 21, 22, 26], similarity relations [1, 2, 3, 15, 28], indistinguishability operators [27], etc.) has been introduced by several authors, and applied to category theory [5], approximate reasoning and fuzzy control theory [8, 10,...

The aim of this chapter is to revisit an experiment of Kahneman and Tversky (1992) to arrive at conclusions about Prospect theory and the ways of human thinking, but using a fuzzy approach, especially the compensatory one. New results shall be proved and others well-known shall be changed or confirmed. The study comprises the examination of logical predicates like those expressed by the followi...

This paper deals with some dependencies between fuzzy conjunctions and fuzzy implications. More precisely, a fuzzy implication generated from a fuzzy conjunction and a fuzzy conjunction induced by a fuzzy implication is considered. In the case of a fuzzy conjunction only border conditions and monotonicity are assumed. The results are illustrated by examples of weak fuzzy connectives.

At AAAI'93, Elkan has claimed to have a result trivializing fuzzy logic. This trivialization is based on too strong a view of equivalence in fuzzy logic and relates to a fully compositional treatment of uncertainty. Such a treatment is shown to be impossible in this paper. We emphasize the distinction between i) degrees of partial truth which are allowed to be truth functional and which pertain...

Simulations and bisimulations are known to be useful for abstracting and comparing formal systems, and they have recently been introduced into fuzzy systems. In this study, we provide sound and complete logical characterizations for simulation and bisimulation, which are defined over fuzzy labeled transition systems via two variants of the Hennessy-Milner Logic. The logic for characterizing fuz...

Very recently, a (fuzzy modal) logic to reason about coherent conditional probability, in the sense of de Finetti, has been introduced by the authors. Under this approach, a conditional probability ð j Þ is taken as a primitive notion defined over conditional events of the form ‘‘’ given ’’, ’j for short, where is not the impossible event. The logic, called FCP(L ), exploits an idea already use...

This paper is intended to introduce the subtractive derivations and study some of their algebraic properties on R l -monoids. Also, we give characterizations Gödel center. Moreover, algebras are characterized by a fixed set derivations. Finally, discuss relationship between other for id="M3"> These r...

Modus ponens provides the central theme. There are laws, of the form A → C. A logic (or other theory) L collects such laws. Any datum A (or theory T incorporating such data) provides input to the laws of L. The central ternary relation R relates theories L; T and U , where U consists of all of the outputs C got by applying modus ponens to major premises from L and minor premises from T . Underl...

Proof-functional logical connectives allow reasoning about the structure of logical proofs, in this way giving to the latter the status of first-class objects. This is in contrast to classical truth-functional connectives where the meaning of a compound formula is dependent only on the truth value of its subformulas. In this paper we present a typed lambda calculus, enriched with strong product...

An often raised objection to fuzzy logic can be articulated as follows. Fuzzy sets are intended to represent vague collections of objects. On the one hand, boundaries of such collections are inherently imprecise. On the other hand, fuzzy sets are defined by membership degrees which are precise. There is, therefore, an obvious discrepancy between the imprecision of a collection and the precision...