A Theory of Approximate Reasoning with Type-2 Fuzzy Set

Sudin Mandal (1) , Injamam Ul Karim (2) , Swapan Raha (3)
(1) Department of Mathematics, Visva-Bharati, Santiniketan, West-Bengal, India-731235,, India,
(2) Department of Mathematics, Visva-Bharati, Santiniketan, West-Bengal, India-731235,, India,
(3) Visva-Bharati(, a Central University), India

Abstract

In this paper, an attempt is made to study approximate reasoning based on a Type-2 fuzzy set theory. In the process, we have examined the underlying fuzzy logic structure on which the reasoning is formulated. We have seen that the partial/incomplete/imprecise truth-values of elements of a type-2 fuzzy set under consideration forms a lattice. We propose two new lattice operations which ultimately help us to define a residual and thereby making the structure of truth- values a residuated lattice. We have focused upon two typical rules of inference used mostly in ordinary approximate reasoning methodology based on Type-1 fuzzy set theory. Our proposal is illustrated with typical artificial examples.

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Authors

Sudin Mandal
Injamam Ul Karim
Swapan Raha
swapan.raha@visva-bharati.ac.in (Primary Contact)
Mandal, S., Karim, I. U., & Raha, S. (2021). A Theory of Approximate Reasoning with Type-2 Fuzzy Set. Journal of the Indonesian Mathematical Society, 27(1), 9–28. https://doi.org/10.22342/jims.27.1.905.9-28
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