Function as the Generator of Parametric T-norms
American Journal of Applied Mathematics
Volume 5, Issue 4, August 2017, Pages: 114-118
Received: May 23, 2017; Accepted: Jun. 21, 2017; Published: Jul. 24, 2017
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Md. Shohel Babu, Computer Science & Engineering, Southeast University, Dhaka, Bangladesh
Shifat Ahmed, Electrical & Electronic Engineering, Southeast University, Dhaka, Bangladesh
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The method of constructing t-norms by generators consists in using a unary function (generator) to transform some known binary function (usually, addition or multiplication) into a T-norm. In order to allow using non-bijective generators, which do not have the inverse function, we have used the notion of pseudo-inverse function. Many families of related t-norms can be defined by an explicit formula depending on a parameter p. Firstly; some continuous and decreasing parametric functions have been selected. Then generate parametric T-norms by using those functions based on additive generator.
Pseudo-inverse, Additive generators, Parametric T-norms, Yager’s Product ,Dombi’s Product , Aczel-Alsina ,Frank Product , Schweizer and Sklar
To cite this article
Md. Shohel Babu, Shifat Ahmed, Function as the Generator of Parametric T-norms, American Journal of Applied Mathematics. Vol. 5, No. 4, 2017, pp. 114-118. doi: 10.11648/j.ajam.20170504.13
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Md. Shohel Babu, Dr. Abeda Sultana, Md. Abdul Alim, Continuous Functions as the Generators of T-norms, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 2 Ver. I (Mar - Apr. 2015), PP 35-38.
Shohel Babu, Fatema Tuj Johora, Abdul Alim, Investigation of Order among Some Known T-norms, American Journal of Applied Mathematics 2015; 3 (5): 229-232 Published online September 25, 2015 doi: 10.11648/j.ajam.20150305.14 ISSN: 2330-0043 (Print); ISSN: 2330-006X (Online).
George J Klir, Yuan Bo, Fuzzy Sets And Fuzzy Logic, Theory And Applications, Prentice-Hall Inc. N. J. U.S.A. 1995.
Mirko Navara (2007), “Triangular Norms And Conforms” Scholarpedia.
Peter J Crickmore, Fuzzy Sets And System, Centre For Environmental Investigation Inc.
Peter Vicenik, A Note On Generators Of T-Norms; Department Of Mathematics, Slovak Technical University, Radlinskeho 11, 813 68 Bratislava, Slovak Republic.
Didier Dobois, Prade Henri, FUZZY SET AND SYSTEM, THEORY AND APPLICATIONS, Academic press INC, New York.
Lowen, FUZZYSET THEORY, Department of Mathematics and Computer Science, University of Antwerp; Belgium, Basic Concepts, Techniques and Bibliography, Kluwer Academic Publishers Dordeecht/Boston/London.
Matteo Bianchi, The logic of the strongest and the weakest tnorms, Fuzzy Sets Syst. 276 (2015) 31–42, 13.
Wladyslaw Homenda, TRIANGULAR NORMS, UNI-AND NULLNORMS, BALANCED NORMS, THE CASES OF THE HIERACHY OF ITERATIVE OPERATORS, Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland.
Mirta N. K., FUZZY SET THEORY RELATIONAL STRUCTURE USING T-NORMS AND MATHLAB, Department of Mathematics, University of Dhaka.
Klement, Erich Perer; Mesiar, Radko; and Pap, Endre (2000), Triangular Norms. Dordrecht: Kluwer. ISBN 0-7923-6416-3.
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