Modus ponens and modus tollens for the compositional rule of inference with aggregation functions
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The compositional rule of inference (CRI) proposed by Zadeh has been widely applied in artificial intelligence, control, data mining, image processing, decision making and so on. Recently, Li and Zeng [Li, D., Zeng, Q. Approximate reasoning with aggregation functions satisfying GMP rules, Artificial Intelligence Review (2022), https://doi.org/10.1007/s10462-022-10136-1] shown an A-compositional rule of inference (ACRI) method in which generalizes the t-norm to any aggregation function in CRI method and studied its validity using GMP rules. In this paper, we continue to investigate the validity of ACRI method from a logical view and an interpolative view. Specifically, to discuss the modus ponens (MP) and modus tollens (MT) properties of ACRI method based on well-known fuzzy implications with aggregation functions.
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