### A Theory of Approximate Reasoning with Type-2 Fuzzy Set

Sudin Mandal, Injamam Ul Karim, Swapan Raha

#### 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

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DOI: https://doi.org/10.22342/jims.27.1.905.9-28

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