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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Authors
Md. Shohel Babu, Computer Science & Engineering, Southeast University, Dhaka, Bangladesh
Shifat Ahmed, Electrical & Electronic Engineering, Southeast University, Dhaka, Bangladesh
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Abstract
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.
Keywords
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
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
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.
[2]
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).
[3]
George J Klir, Yuan Bo, Fuzzy Sets And Fuzzy Logic, Theory And Applications, Prentice-Hall Inc. N. J. U.S.A. 1995.
[4]
Mirko Navara (2007), “Triangular Norms And Conforms” Scholarpedia.
[5]
Peter J Crickmore, Fuzzy Sets And System, Centre For Environmental Investigation Inc.
[6]
Peter Vicenik, A Note On Generators Of T-Norms; Department Of Mathematics, Slovak Technical University, Radlinskeho 11, 813 68 Bratislava, Slovak Republic.
[7]
Didier Dobois, Prade Henri, FUZZY SET AND SYSTEM, THEORY AND APPLICATIONS, Academic press INC, New York.
[8]
Lowen, FUZZYSET THEORY, Department of Mathematics and Computer Science, University of Antwerp; Belgium, Basic Concepts, Techniques and Bibliography, Kluwer Academic Publishers Dordeecht/Boston/London.
[9]
Matteo Bianchi, The logic of the strongest and the weakest tnorms, Fuzzy Sets Syst. 276 (2015) 31–42, http://dx.doi.org/10.1016/j.fss.2015.01. 13.
[10]
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.
[11]
Mirta N. K., FUZZY SET THEORY RELATIONAL STRUCTURE USING T-NORMS AND MATHLAB, Department of Mathematics, University of Dhaka.
[12]
Klement, Erich Perer; Mesiar, Radko; and Pap, Endre (2000), Triangular Norms. Dordrecht: Kluwer. ISBN 0-7923-6416-3.
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