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Karim, Injamam Ul
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Mathematics

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A Theory of Approximate Reasoning with Type-2 Fuzzy Set Mandal, Sudin; Karim, Injamam Ul; Raha, Swapan
Journal of the Indonesian Mathematical Society VOLUME 27 NUMBER 1 (MARCH 2021)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.27.1.905.9-28

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.
Co-Authors Mandal, Sudin Raha, Swapan