Quantitative Metho d Based on Cotangent Similarity Degree in Three-Valued ?ukasiewicz Logic

• 作者: YU Peng
• 来源期刊: 电子学报（英文）
• 年，卷（期）: 2021,（1）
• 所属期刊栏目: SIGNAL PROCESSING
• 页码范围: 134-144
• 页数: 11页
• 语种: 英文
• DOI: 10.1049/cje.2020.11.011

摘要

The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued?ukasiewicz propositional logic system ?3. 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 ?3. We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives ?,∨ and → in the?3 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.