Consideration on Example 2 of "An Algorithm of General Fuzzy InferenceWith The Reductive Property"

TL;DR

This paper verifies previous fuzzy reasoning algorithms, corrects errors in a specific example from a prior publication, and provides an improved calculation example for fuzzy inference with the reductive property.

Contribution

It confirms the correctness of earlier fuzzy reasoning results and corrects a specific example, enhancing the understanding of fuzzy inference algorithms.

Findings

Previous fuzzy reasoning algorithms are validated.

An incorrect example in prior work is identified and corrected.

An improved calculation example for FMT is provided.

Abstract

In this paper, we will show that (1) the results about the fuzzy reasoning algoritm obtained in the paper "Computer Sciences Vol. 34, No.4, pp.145-148, 2007" according to the paper "IEEE Transactions On systems, Man and cybernetics, 18, pp.1049-1056, 1988" are correct; (2) example 2 in the paper "An Algorithm of General Fuzzy Inference With The Reductive Property" presented by He Ying-Si, Quan Hai-Jin and Deng Hui-Wen according to the paper "An approximate analogical reasoning approach based on similarity measures" presented by Tursken I.B. and Zhong zhao is incorrect; (3) the mistakes in their paper are modified and then a calculation example of FMT is supplemented.