On the distributivity of fuzzy implications over nilpotent or strict triangular conorms
IEEE Transactions on Fuzzy Systems
Fuzzy Sets and Systems
On the distributivity of fuzzy implications over continuous archimedean triangular norms
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
IUKM'11 Proceedings of the 2011 international conference on Integrated uncertainty in knowledge modelling and decision making
Fuzzy implications derived from additive generators of continuous Archimedean t-norms
International Journal of Intelligent Systems
On the distributivity of uninorms over nullnorms
Fuzzy Sets and Systems
A generalization of Yager's f-generated implications
International Journal of Approximate Reasoning
On the Ordering Property and Law of Importation in Fuzzy Logic
International Journal of Artificial Life Research
A new class of fuzzy implications derived from generalized h-generators
Fuzzy Sets and Systems
Information Sciences: an International Journal
Distributivity equations of implications based on continuous triangular conorms (II)
Fuzzy Sets and Systems
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In this paper, we explore the distributivity of implication operators [especially Residuated (R)- and Strong (S)-implications] over Takagi (T)- and Sugeno (S)-norms. The motivation behind this work is the on going discussion on the law [(p∧q)→r]≡[(p→r)Λ(q→r)] in fuzzy logic as given in the title of the paper by Trillas and Alsina. The above law is only one of the four basic distributive laws. The general form of the previous distributive law is J(T(p,q),r)≡S(J(p,r),J(q,r)). Similarly, the other three basic distributive laws can be generalized to give equations concerning distribution of fuzzy implications J on T- and S- norms. In this paper, we study the validity of these equations under various conditions on the implication operator J. We also propose some sufficiency conditions on a binary operator under which the general distributive equations are reduced to the basic distributive equations and are satisfied. Also in this work, we have solved one of the open problems posed by M. Baczynski (2002).