On the Suitability of the Bandler–Kohout Subproduct as an Inference Mechanism

Stepnicka, M and Jayaram, Balasubramaniam (2010) On the Suitability of the Bandler–Kohout Subproduct as an Inference Mechanism. IEEE Transactions on Fuzzy Systems, 18 (2). pp. 285-295. ISSN 1063-6706

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Fuzzy relational inference (FRI) systems form an important part of approximate reasoning schemes using fuzzy sets. The compositional rule of inference (CRI), which was introduced by Zadeh, has attracted the most attention so far. In this paper, we show that the FRI scheme that is based on the Bandler-Kohout (BK) subproduct, along with a suitable realization of the fuzzy rules, possesses all the important properties that are cited in favor of using CRI, viz., equivalent and reasonable conditions for their solvability, their interpolative properties, and the preservation of the indistinguishability that may be inherent in the input fuzzy sets. Moreover, we show that under certain conditions, the equivalence of first-infer-then-aggregate (FITA) and first-aggregate-then-infer (FATI) inference strategies can be shown for the BK subproduct, much like in the case of CRI. Finally, by addressing the computational complexity that may exist in the BK subproduct, we suggest a hierarchical inferencing scheme. Thus, this paper shows that the BK-subproduct-based FRI is as effective and efficient as the CRI itself.

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IITH Creators:
IITH CreatorsORCiD
Jayaram, Balasubramaniamhttp://orcid.org/0000-0001-7370-3821
Item Type: Article
Uncontrolled Keywords: computational complexity, fuzzy set theory, inference mechanisms,
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: Team Library
Date Deposited: 26 Nov 2014 09:27
Last Modified: 20 Sep 2017 08:48
URI: http://raiith.iith.ac.in/id/eprint/987
Publisher URL: https://doi.org/10.1109/TFUZZ.2010.2041007
OA policy: http://www.sherpa.ac.uk/romeo/issn/1063-6706/
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