Showing papers by "Balasubramaniam Jayaram published in 2009"
TL;DR: In this paper, the authors presented characterizations of (U, N)-implications obtained from disjunctive uninorms and continuous negations as well as (U-N)-operations defined from (S, N) infinities and continous negations.
73 citations
TL;DR: This paper characterize functions I that satisfy the previous functional equation when S1,S2 are either both strict or nilpotent t-conorms, and I is a continuous fuzzy implication.
Abstract: Recently, many works have appeared in this very journal dealing with the distributivity of fuzzy implications over t-norms and t-conorms. These equations have a very important role to play in efficient inferencing in approximate reasoning, especially fuzzy control systems. Of all the four equations considered, the equation I(x, S1 (y,z)) = S2(I(x,y),I(x,z)), when S1,S2 are both t-conorms and I is an R-implication obtained from a strict t-norm, was not solved. In this paper, we characterize functions I that satisfy the previous functional equation when S1,S2 are either both strict or nilpotent t-conorms. Using the obtained characterizations, we show that the previous equation does not hold when S1,S2 are either both strict or nilpotent t-conorms, and I is a continuous fuzzy implication. Moreover, the previous equation does not hold when I is an R -implication obtained from a strict t-norm, and S1,S2 are both strict t-conorms, while it holds for an R-implication I obtained from a strict t-norm T if and only if the t-conorms S1 = S2 are Phi-conjugate to the Lukasiewicz t-conorm for some increasing bijection phi of the unit interval, which is also a multiplicative generator of T.
65 citations
TL;DR: It is shown that the class of duality fitting implicators I is much richer than the residuals of the dualityfitting conjunctors in the study of Mesiar et al, and also shows that the I-fuzzy partitions have a ''constant-wise'' structure.
55 citations
TL;DR: It is shown that there are infinitely many fuzzy implications that are special but cannot be obtained as residuals of t-norms, and some constructive procedures to obtain special fuzzy implications are proposed and methods of obtaining special implications from existing ones are given.
41 citations
02 Oct 2009
TL;DR: This work discusses the suitability of the Bandler-Kohout subproduct for an alternative inference mechanism from the computational point of view.
Abstract: The compositional rule of inference (CRI) is widely used in approximate reasoning schemes using fuzzy sets. In this work we discuss the suitability of the Bandler-Kohout subproduct for an alternative inference mechanism from the computational point of view.
4 citations
Proceedings Article•
01 Jan 2009TL;DR: This work shows that the Bandler-Kohout subproduct does possess all the important properties such as equivalent and rea- sonable conditions for their solvability, their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets, as cited in favor of using CRI.
1 citations
01 Jan 2009
TL;DR: The compositional rule of inference (CRI) introduced by Zadeh is widely used in approximate reasoning schemes using fuzzy sets as mentioned in this paper, and it is shown that the Bandler-Kohout subproduct does possess all the important properties such as equivalent and rea- sonable conditions for their solvability, their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets.
Abstract: The compositional rule of inference (CRI) introduced by Zadeh is widely used in approximate reasoning schemes using fuzzy sets. In this work we show that the Bandler-Kohout subproduct does possess all the important properties such as equivalent and rea- sonable conditions for their solvability, their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets, as cited in favor of using CRI. Keywords— Bandler-Kohout subproduct, compositional rule of inference, correctness and continuity of inference, fuzzy relation equations.
1 citations
Proceedings Article•
01 Jan 2009TL;DR: This work fully character- ized the class of continuous R-implications obtained from any arbi- trary t-norm and determines the exact inter- section between the continuous subsets of R- Implications and (S,N)- implications.
Abstract: In this work we have solved an open problem re- lated to the continuity of R-implications. We have fully character- ized the class of continuous R-implications obtained from any arbi- trary t-norm. Using this result, we also determine the exact inter- section between the continuous subsets of R-implications and (S,N)- implications.