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Constructive methods for intuitionistic fuzzy implication operators

Zeitschrift:: Soft Computing > Ausgabe 18/2017

Autoren:: Yiying Shi, Xuehai Yuan, Yuchun Zhang

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Communicated by A. Di Nola.

Abstract

In this paper, two novel constructive methods for fuzzy implication operators are proposed. And they can be used to resolve the questions about how to construct intuitionistic fuzzy implication operators to inference sentence “If x is A, then y is B,” where A and B are intuitionistic fuzzy sets over X and Y, respectively. In the first method, cut sets and representation theorem of intuitionistic fuzzy sets are utilized through triple valued fuzzy implications as well as fuzzy relations to obtain seven intuitionistic fuzzy implication operators. In the second method, the Lebesgue measure of the fuzzy implications with value one and zero is used, and one intuitionistic fuzzy implication operator can be obtained. Finally, properties of those operators are discussed.

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Titel: Constructive methods for intuitionistic fuzzy implication operators
Autoren:: Yiying Shi
Xuehai Yuan
Yuchun Zhang
Publikationsdatum: 05.07.2016
DOI: https://doi.org/10.1007/s00500-016-2239-2
Verlag: Springer Berlin Heidelberg
Zeitschrift: Soft Computing A Fusion of Foundations, Methodologies and Applications
Ausgabe 18/2017
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479

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