On fuzzy implication in De Morgan algebras

Istituto di Matematica, Facoltà di Architettura, Università di Napoli, Via Monteoliveto 3, 80134 Napoli, Italy
Fuzzy Sets and Systems (Impact Factor: 1.75). 11/1989; DOI: 10.1016/0165-0114(89)90238-8

ABSTRACT The behaviour of some fuzzy implications with respect to measure of fuzziness and their deductive power is studied in a lattice framework. The point of view of Bandler and Kohout [1] and Willmott [7] is followed.

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    ABSTRACT: Fourteen properties and their interdependencies contributed to the analysis of six classes implication operators–S-implications, R-implications, QL-implications, Force implication, f- generated implication operator and g- generated implication operator– are explored in this paper. It is found that all the properties can be inferred from three mutually independent properties. Then, the proven concerning which properties are true, false or satisfied for each of the six classes of implication operators is given. Based on which, the author get the property I(x(n(x)) = n (x) for all x ∈[0,1] that does not hold for force implication, f-generated implication operator and g-generated implication operator.
    Computational Intelligence, International Conference on Intelligent Computing, ICIC 2006, Kunming, China, August 16-19, 2006. Proceedings, Part II; 01/2006
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    ABSTRACT: Characterization and new methods of generation of bijective fuzzy negations (involutive, contracting and expanding negations) are done. The approach is based on a symmetry of involutive negations with respect to the line f(x)=x,x∈[0,1]. Contracting and expanding negations are given by suitable deflections from this symmetry.
    Fuzzy Sets and Systems 11/2003; · 1.75 Impact Factor
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    ABSTRACT: The properties and applications of R-implication based on the left continuous t-norm are studied in this paper. Firstly, fourteen properties which are very important to the studies of implication operators are listed. Some interdependencies among the properties are also discussed. As a result, we obtain three mutually independent properties that can infer all the fourteen properties. Then we discuss that whether the R-implication based on the left continuous t-norm satisfy the fourteen properties. Finally the applications of the R-implication operators based on the left continuous t-norm are discussed, the triple-I method based on them are given, Moreover, the properties of triple-I algorithms based on the R-implication induced by the left continuous t-norm for FMP and FMT are given. we also compare the errors of three fuzzy systems when they use the same fuzzy reasoning rules.