In this paper we present some Boolean algebras in the form of lattice by using the fuzzy implication. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature. KeywordsFuzzy logic connectives, Fuzzy implication, Algebras, Lattice.

Witold Pedrycz, Giancarlo Succi, and Ofer Shai Owing to the immense size of the search space in the SAT problem, evolutionary computing arises as a viable and attractive option. The objective of this study is to formulate the SAT problem in the evolutionary setting and carry out comprehensive xperimental studies. The approach relies on the embedding principle: we generalize the Boolean problem ...

We introduce the stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. Combining the advantages of both formalisms, the introduced language allows highly configurable default reasoning involving fuzzy truth values. We show that several properties of Boolean stable models are n...

Metaset is a new concept of set with partial membership relation. It is designed to represent and process vague, imprecise data – similarly to fuzzy sets. Metasets are based on the classical set theory primitive notions. At the same time they are directed towards efficient computer implementations and applications. The degrees of membership for metasets are expressed as finite binary sequences,...

What is fuzzy logic? Fuzzy logic is an extension of Boolean logic which allows intermediate values between True and False. As in Boolean logic, a true statement is expressed by the value “1” and a false statement by the value “0”. However, unlike in probability theory, the value must not be interpreted as a confidence level but rather as a Membership Function (MF). Therefore, every statement is...

We propose an extension principle for fuzzy logic to obtain a Boolean logic able to manage incomplete and partially inconsistent information. Such a logic is strictly related with an extended notion of belief measure. The aim is to give suitable tools to design expert systems able to manage information probabilistic in nature.

This paper shows, by examples, that Lemma 2.1, Lemma 3.1, Corollary 3.1, Corollary 3.2, Theorem 3.1, Corollary 3.3, Theorem 3.3 and Lemma 4.1 in [Y. Luo, Resolution of fuzzy relation equation (I) based on Boolean-type implications, Comput. Math. Appl. 52 (2006) 421–428] about resolution of fuzzy relation equations based on Boolean-type implications, are false. We also point out that the solutio...

We introduce a framework within which reasoning according to à Lukasiewicz logic can be represented. We consider a separable Boolean algebra B endowed with a (certain type of) group G of automorphisms; the pair (B, G) will be called a Boolean ambiguity algebra. B is meant to model a system of crisp properties; G is meant to express uncertainty about these properties. We define fuzzy proposition...