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Submitted
February 6, 2020
Accepted
February 12, 2021
Published
March 31, 2021
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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.

Keywords

Type-2 fuzzy set Type-2 fuzzy logic Generalised Modus Ponens Approximate reasoning

Article Details

How to Cite
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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