Quantitative Method Based on Cotangent Similarity Degree in Three‐Valued Łukasiewicz Logic

The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three‐valued Łukasiewicz propositional logic system Ł3. We introduce the concepts of the cotangent similarity degree, cotangent pseudo‐distance and cotangent truth degree of...

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Bibliographic Details
Published inChinese Journal of Electronics Vol. 30; no. 1; pp. 134 - 144
Main Author Peng, Yu
Format Journal Article
LanguageEnglish
Published Published by the IET on behalf of the CIE 01.01.2021
Subjects
Approximate reasoning
Cotangent similarity degree
Quantitative logic
Three‐valued logic
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Summary:The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three‐valued Łukasiewicz propositional logic system Ł3. We introduce the concepts of the cotangent similarity degree, cotangent pseudo‐distance and cotangent truth degree of the propositions, together with their basic properties in Ł3. We investigate the relationship between the cotangent truth degree and contangent pseudo‐distance, and prove the continuity of the logical connectives ¬,∨ and → in the Ł3 logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F(S), and provide several examples and basic properties of it.
ISSN:1022-4653
2075-5597
DOI:10.1049/cje.2020.11.011