Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming to find logics that can handle inconsistency and graded truth at once, in this paper we explore the notion of paraconsistent fuzzy logic. We show that degree-preserving fuzzy logics have paraconsistency features and study them as logics of formal inc...

Paraconsistent logics are specially tailored to deal with inconsistency, while fuzzy logics primarily deal with graded truth and vagueness. Aiming to find logics that can handle inconsistency and graded truth at once, in this paper we explore the notion of paraconsistent fuzzy logic. We show that degree-preserving fuzzy logics have paraconsistency features and study them as logics of formal inc...

Gilles CHAMPENOIS Collège Saint-André, Saint-Maur, France [email protected] ABSTRACT. Grainy numbers are defined as tuples of bits. They form a lattice where the meet and the join operations are an addition and a multiplication. They may be substituted for the real numbers in the definition of fuzzy sets. The aim is to propose an alternative negation for the complement that we’ll call ...

The satisfiability problem for monadic infinite-valued Gödel logic is known to be undecidable. We identify a fragment of this logic extended with strong negation whose satisfiability is not only decidable but it is decidable within classical logic. We use this fragment to formalize the rules of CADIAG-2, a well performing fuzzy expert system assisting in the differential diagnosis in internal m...

In science and engineering, there are “paradoxical” cases when we have some arguments in favor of some statement A (so, the degree to which A is known to be true is positive (non-zero)), and we also have some arguments in favor of its negation ¬A, and we do not have enough information to tell which of these two statements is correct. Traditional fuzzy logic, in which “truth values” are describe...

—Many authors have emphasized the similarity between quantum logic and fuzzy logic. In this paper, we show that, in spite of this similarity, these logics are not identical. Speci cally, we show that while quantum logic has a special “square root of not” operation which is very useful in quantum computing, fuzzy logic lacks such an operation. I. SIMILARITY BETWEEN QUANTUM LOGIC AND FUZZY LOGIC ...

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i. e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, B...

Fuzzy logic in narrow sense: A summary on t-norm-based logics In the seventies and eighties operations over [0,1] corresponding to connectives of a multi-valued logic has been studied and used to define Fuzzy Set operations. From then t-norms, t-conorms, negation and implication functions have been widely studied and applied. The nineties were the start point of the study of the kernel of fuzzy...

In this study, ?-interval valued set is defined whose elements are closed sub-intervals including ? of unit interval that I = [0, 1]. With different order relation on set, the properties examined. By help relation, it shown complete lattice. Negation function given in to study theoretical set. means discussions fundamental features studied. fuzzy sets defined. The algebraic these level subsets ...

fuzzy logic, 67algebraic semantics, 53approximate reasoning, 6axiomatic extensions of MTL, 56 Bellman, R., 21bipolar possibilistic logic, 93BL logic, 51 canonical chain, 66canonical completeness, 66canonical extension, 83Carnap, R., 3comparative truth, 63compositionality, 29computational complexity, 73core fuzzy logic, 58 De Finetti B., 3degre...