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: 1.88). 11/1989; 33(2):155-164. 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: 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.
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    ABSTRACT: It is an interesting story to look at the development of new concepts in fuzzy set theory. One looks at the motivation, the first formulation and the subsequent development. In our case study we look at one of the early papers that interrelates the concept of fuzzy set inclusion, power set and many-valued implication operators, namely the paper of Bandler and Kohout [4]. This is followed by discussion of the subsequent related work by the fuzzy community.