Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
Formalized theory of general fuzzy reasoning
Information Sciences—Informatics and Computer Science: An International Journal
Unified forms of Triple I method
Computers & Mathematics with Applications
On the representation of intuitionistic fuzzy t-norms and t-conorms
IEEE Transactions on Fuzzy Systems
On the convex combination of TD and continuous triangular norms
Information Sciences: an International Journal
On the characterizations of fuzzy implications satisfying I(x,y)=I(x,I(x,y))
Information Sciences: an International Journal
Unified full implication algorithms of fuzzy reasoning
Information Sciences: an International Journal
Three and two-valued Łukasiewicz theories in the formal deductive system L* (NM-logic)
Fuzzy Sets and Systems
Information Sciences: an International Journal
Computers & Mathematics with Applications
Information Sciences: an International Journal
Differently implicational universal triple I method of (1, 2, 2) type
Computers & Mathematics with Applications
Some properties of fuzzy reasoning in propositional fuzzy logic systems
Information Sciences: an International Journal
Formalization of implication based fuzzy reasoning method
International Journal of Approximate Reasoning
Triple I algorithms based on Schweizer--Sklar operators in fuzzy reasoning
International Journal of Approximate Reasoning
Robustness analysis of full implication inference method
International Journal of Approximate Reasoning
Hierarchical structure and applications of fuzzy logical systems
International Journal of Approximate Reasoning
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The goal of this paper is to extend the scope of previously proposed ''fully implicational restriction methods'' for fuzzy reasoning, and provide a unified form of these methods which can employ diverse implications. By means of the residual implications generated by left-continuous t-norms, we obtain the supremum of triple I (the abbreviation of triple implications) restriction solutions for fuzzy modus ponens and the supremum of multiple I restriction solutions for general fuzzy reasoning respectively. Furthermore, we obtain the infimum of triple I restriction solutions and the supremum of triple I^* restriction solutions for fuzzy modus tolens. Finally, the optimal (i.e., the largest or smallest, depending on context) restriction solutions of both basic and general reasoning problems are derived for four specific residual implications.