Residual Operator of Type-2 Triangular Norms on Convex Normal Upper Semi-Continuous Fuzzy Truth Values
Received:May 29, 2023  Revised:December 15, 2023
Key Words: type-2 fuzzy set   triangular norm ($t$-norm)   residual operator  
Fund Project:Supported by the Natural Science Foundation of Sichuan Province (Grant No.2022NSFSC1821), the National Natural Science Foundation of China (Grant No.12261018), Universities Key Laboratory of Mathematical Modeling and Data Mining in Guizhou Province (Grant No.2023013), High Level Innovative Talent Training Plan Project of Guizhou Province (Grant No.GCC[2023]006) and the Key Natural Science Foundation of Universities in Guangdong Province (Grant No.2019KZDXM027).
Author NameAffiliation
Xinxing WU School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China 
Shuangfeng LUO School of Sciences, Southwest Petroleum University, Sichuan 610500, P. R. China 
Zhiyi ZHU School of Sciences, Southwest Petroleum University, Sichuan 610500, P. R. China 
Lidong WANG Zhuhai College of Science and Technology, Guangdong 519041, P. R. China 
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      Based on the residual implication of continuous triangular norms, we obtain the expression of residual operator for extended operators (type-2 triangular norms) of continuous triangular norms on convex normal upper semi-continuous fuzzy truth values, answering an open problem in [D. LI, Inf. Sci., 2015, {\bf 317}: 259--277].
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