Volume 30 Issue 1
Jan.  2021
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YU Peng. Quantitative Method Based on Cotangent Similarity Degree in Three-Valued Ł ukasiewicz Logic[J]. Chinese Journal of Electronics, 2021, 30(1): 134-144. doi: 10.1049/cje.2020.11.011
 Citation: YU Peng. Quantitative Method Based on Cotangent Similarity Degree in Three-Valued Ł ukasiewicz Logic[J]. Chinese Journal of Electronics, 2021, 30(1): 134-144.

# Quantitative Method Based on Cotangent Similarity Degree in Three-Valued Ł ukasiewicz Logic

##### doi: 10.1049/cje.2020.11.011
Funds:

the National Natural Science Foundation of China 61976130

the National Natural Science Foundation of China 61871260

Scientific Research Program Funded by Shaanxi Provincial Education Department 18JK0099

Natural Science Foundation of Shaanxi Province 2020JQ-698

• Corresponding author: YU Peng  (corresponding author)  was born in 1981. He received the Ph.D. degree in mathematics from shaanxi normal University in 2019. He is currently an associate professor of Shaanxi University of Science and Technology. His research interests include non-classic logic, fuzzy reasoning and rough set. (Email: yupeng@sust.edu.cn)
• Accepted Date: 2020-08-24
• Publish Date: 2021-01-01
• The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued Ł ukasiewicz propositional logic system $\text{Ł}_{3}$. 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 $\text{Ł}_{3}$. We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives $\neg, \vee$ and $\rightarrow$ in the $\text{Ł}_{3}$ 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.
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