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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
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
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
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