The study of the product \(t\)-norm in the compositional rule of inference with various implications

Volume 41, Issue 3, pp 284--306 https://dx.doi.org/10.22436/jmcs.041.03.01

Publication Date: October 28, 2025 Submission Date: June 24, 2024 Revision Date: July 20, 2025 Accteptance Date: August 20, 2025

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Authors

S. B. H. Kacem - University of Carthage, Faculty of Economics and Management, Mrezga Campus, Nabeul 8000, Tunisia. N. Zerarka - University of Manouba, National School of Computer Sciences, Manouba 2010, Tunisia. M. Tagina - University of Manouba, National School of Computer Sciences, Manouba 2010, Tunisia.

Abstract

Fuzzy Inference Systems (FIS) are used to help people to take decisions in complex situations or when a human expert is needed. Their particularity is that they can manage the imprecision and vagueness of knowledge by applying approximate reasoning. The main approach of approximate reasoning is the Compositional Rule of Inference (CRI), whose definition contains two operators as parameters: a \(t\)-norm and a fuzzy implication. However, since its creation, the fuzzy community considers only one combination of (\(t\)-norm, implication) in fuzzy applications, which is (min, min). For that, we are interested in studying the behavior of other combinations (\(t\)-norm, implication) and in checking their efficiency. In this paper, we combine the product \(t\)-norm with fifteen implications in the CRI. Then, for every combination, we check the satisfaction of the axiomatics of approximate reasoning. This axiomatics is a set of criteria that model human intuitions. This study allows us to identify the best combinations that coincide with human reasoning in order to guarantee an inference result close to the expert's opinion.

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Keywords

• Compositional rule of inference
• fuzzy logic
• approximate reasoning
• product \(t\)-norm
• fuzzy implications

MSC

•  03B52
•  68T37

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