Fuzzy logics based on triangular norms and their corresponding conorms are investigated. An aarmative answer to the question whether in such logics a speciic level of satissability of a set of formulas can be characterized by the same level of satissability of its nite subsets is given. Tautologies, contradictions and contingencies with respect to such fuzzy logics are studied, in particular fo...

This paper deals with the simplest fuzzy PI controllers under various defuzzification methods. The various simplest fuzzy PI controllers consist of two triangular input fuzzy sets and three triangular output fuzzy sets on the universe of discourse of input and output variables, respectively, linear control rules, intersection T-norm, Lukasiewicz and Zadeh OR T-conorms, and any valid inference m...

We adopt the coding/decoding method of image processing based on the direct and inverse fuzzy transforms defined in previous papers. We have considered 100 images of sizes 256 × 256 (pixels) extracted from the wellknown database Corel Galery (Arizona Directory). A comparison with the coding/decoding method based on the fuzzy relation equations with the Lukasiewicz triangular norm is also presen...

Rule-driven processing is a proven way of achieving high-speed in fuzzy processing. Up to now, ruledriven architectures where designed to work with minimum or product as T-norm. Nevertheless, a Lukasiewicz T-norm is typically used with the compositional rule of inference in expert systems applications that are based on a fuzzy inference engine. This paper presents a rule-driven processing archi...

Ontology consistency has been shown to be undecidable for a wide variety of fairly inexpressive fuzzy Description Logics (DLs). In particular, for any t-norm “starting with” the Lukasiewicz t-norm, consistency of crisp ontologies (w.r.t. witnessed models) is undecidable in any fuzzy DL with conjunction, existential restrictions, and (residual) negation. In this paper we show that for any t-norm...

in this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-lukasiewicz operator. in fact lukasiewicz t-norm is one of the four basic t-norms. a new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on ...

in the present paper, a partial order on a non- archimedean fuzzymetric space under the  lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

In the present paper, a partial order on a non- Archimedean fuzzymetric space under the  Lukasiewicz t-norm is introduced and fixed point theoremsfor single and multivalued mappings are proved.

We study the transitivity of fuzzy preference relations, often considered as a fundamental property providing coherence to a decision process. We consider the transitivity of fuzzy relations w.r.t. conjunctors, a general class of binary operations on the unit interval encompassing the class of triangular norms usually considered for this purpose. Having fixed the transitivity of a large prefere...

Continuing to pursue a research direction that we already explored in connection with Gödel-Dummett logic and Ruspini partitions, we show here that Lukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis. En route to our main result we obtain an elementary, logic-independent characterisation of triangu...