Fuzzy Sets and Systems
Fuzzy logic for the management of uncertainty
Control of error in fuzzy logic modeling
Fuzzy Sets and Systems
Information Sciences: an International Journal
What are fuzzy rules and how to use them
Fuzzy Sets and Systems - Special issue dedicated to the memory of Professor Arnold Kaufmann
Fuzzy Sets and Systems - Implication operators
On the representation of fuzzy rules
International Journal of Approximate Reasoning
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A strong implication operator (S-implication) is a fuzzy material implication operator defined in terms of a t-norm and a strong negation as a generalization of the classical equivalence between ''IF A then B'' and ''Not(A and not B)''. This paper is concerned with a family of improper S-implications derived from an extension of the Schweizer-Sklar family of parameterized improper t-norms defined over (-~,+1]. Analysis of fuzzy and defuzzified interpolation outputs includes proper and improper fuzzy set outputs and exact defuzzified solutions for important special cases such as Kleene-Dienes, Reichenbach, and Lukasiewicz implications. The effect of the Schweizer-Sklar parameter on interpolation between fuzzy points is outlined. The final section of the paper illustrates the use of the method with two examples, one in political geography and the other in rule-based control.