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-...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.,2015,317:259-277].展开更多
Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy mo...Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).展开更多
This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization ...This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.展开更多
We propose two more general methods to construct nullnorms on bounded lattices. By some illustrative examples, we demonstrate that the new method differ from the existing approaches.
基金Supported by the Natural Science Foundation of Sichuan Province(Grant No.2022NSFSC1821)the National Natural Science Foundation of China(Grant No.12261018)+2 种基金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)the Key Natural Science Foundation of Universities in Guangdong Province(Grant No.2019KZDXM027)。
文摘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.,2015,317:259-277].
文摘Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).
基金supported by the National Science Foundation of the United States under Grant No. #DMI- 0553310
文摘This paper shows that the problem of minimizing a linear fractional function subject to asystem of sup-T equations with a continuous Archimedean triangular norm T can be reduced to a 0-1linear fractional optimization problem in polynomial time.Consequently,parametrization techniques,e.g.,Dinkelbach's algorithm,can be applied by solving a classical set covering problem in each iteration.Similar reduction can also be performed on the sup-T equation constrained optimization problems withan objective function being monotone in each variable separately.This method could be extended aswell to the case in which the triangular norm is non-Archimedean.
文摘We propose two more general methods to construct nullnorms on bounded lattices. By some illustrative examples, we demonstrate that the new method differ from the existing approaches.
