Monotonicity of SISO Fuzzy Relational Inference With an Implicative Rule Base

Mandal, Sayantan and Jayaram, Balasubramaniam (2016) Monotonicity of SISO Fuzzy Relational Inference With an Implicative Rule Base. IEEE Transactions on Fuzzy Systems, 24 (6). pp. 1475-1487. ISSN 1063-6706

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A fuzzy relational inference (FRI) mechanism is appraised based on the different desirable properties it possesses. Among these properties, monotonicity of an FRI has not received much attention. In this work, we investigate the monotonicity of a single-input single-output FRI with an implicative form of the rule base. In all the previous works that deal with monotonicity of an FRI with the implicative form of rule base, the employed fuzzy implications come from a residuated lattice. It can be noticed that this rich underlying structure plays a major role in proving the results. Further, we also modify the given monotone rule base. This work differs from the previous works in that: 1) the fuzzy implications employed in it do not come from any known residuated structure on [0, 1]; and 2) the original rule base is employed without any alteration. We determine conditions under which monotonicity of an FRI, where the rule base is modeled by a strict fuzzy implication, can be ensured without transforming the original rule base. Thus, the results in this work further augment the case for considering fuzzy implications, other than those from the residuated setting, to be used in applications.

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IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniam
Item Type: Article
Uncontrolled Keywords: Fuzzy logic, Fuzzy sets, Inference mechanisms, Lattices, Nickel, SISO, Cognition
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 23 Jan 2017 04:42
Last Modified: 20 Sep 2017 07:25
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