In this paper, extension of the EQ-logic by the ∆connective is introduced. The former is a new kind of many-valued logic which based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra by the ∆ operation and then introduce axioms and inference rules of EQ∆-logic. We also prove th...

This paper develops the recursive model for connective rules (as proposed in V. Cutello, E. Molina, J. Montero, Associativeness versus recursiveness, in: Proceedings of the 26th IEEE International Symposium on Multiple-valued Logic, Santiago de Compostela, Spain, 29±31 May, 1996, pp. 154±159; V. Cutello, E. Molina, J. Montero, Binary operators and connective rules, in: M.H. Smith, M.A. Lee, J. ...

In [1, 2] we studied various concepts of bipolar queries (cf. Dubois and Prade [3]). We advocated there the use of a fuzzified version of the original crisp definition introduced by Lacroix and Lavency [4]. However, the fuzzification proposed, as general as it was, leaves open the choice of a representation of logical entities, notably the logical connectives and quantifiers. In the present pap...

The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like ”antitone” or ”isotone” concepts constructed from fuzzy binary relations, but also to allow the two universes (of objects and attributes) to be equipped each with its own truth structur...

We are interested in generalizations of the concepts of t-norm and t-conorm. In a companion chapter in this volume [14] we have presented a family of hypert-norms ∧q and a family of hyper-t-conorms ∨p. The prefix hyper is used to indicate multi-valued operations, also known as hyperoperations (see [5, 14]), i.e. operations which map pairs of elements to sets of elements. See [14] for the constr...

In this paper we propose computationally simple, pointwise formulas for extended t-norms and t-conorms on fuzzy truth values. The complex convolutions of the extended operations are shown to be equivalent to simple pointwise expressions for several special cases. Linear fuzzy truth values are defined and it is shown that the extended Łukasiewicz operations preserve linearity. Since linear fuzzy...

To avoid self-contradictions in Fuzzy Set Theory, it is needed to consider only fuzzy sets that are not selfcontradictory and whose complements are also not selfcontradictory. This paper deals with a subset Fnc(E) in [0, 1] , where the above conditions are satisfied. A particular Fuzzy Set Theory is defined in Fnc(E) with adequate logical connectives. Finally, which classical properties hold in...

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of...

In this paper, we extend research done in max-min fuzzy neural networks in several important ways. We replace max and min operations used in the fuzzy operations by more general t-norms and co-norms, respectively. In addition, instead of the Łukasiewicz equivalence connective used in network of ReyesGarcia and Bandler, we employ in our hybridization a variety of equivalence connectives. We expl...

The paper outlines the rationale for using Fuzzy Logic, and Granular Computing, to emulate compositional decision making processes. Significant features of this Fuzzy Logic framework are that ambiguity in the music is maintained, while allowing the evolution of unfolding processes which reflects the temporal nature of music as performed. Granular Computing and Fuzzy Logic have been designed for...