A Theory of Approximate Reasoning with Type-2 Fuzzy Set

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

Journal of the Indonesian Mathematical Society
VOLUME 27 NUMBER 1 (MARCH 2021)

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.