可信测度空间下的似乘算子模糊概率积分研究  

Research on Generalized Sugeno Fuzzy Probability Integral Based on t-Modular Operator

作　　者：赵辉 姜欣格 单云霄 ZHANO Hui;JIANG Xin-ge;SHAN Yun-xiao(College of Scienc, Harbin University of Science and Technology, Harbin 150080, China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2021年第2期161-166,共6页Journal of Harbin University of Science and Technology

基　　金：四川省科技计划项目(2016JZ0014-1);黑龙江省自然科学基金(A201214).

摘　　要：模糊概率积分是模糊数学的一个重要部分,是将模糊概率与积分相结合的一种积分形式。通过t-模和s-模定义条件设计了一个似乘算子和似和算子,又构建了一个全新的可信测度,并在可信测度空间下结合似乘算子重新定义了Sugeno模糊概率积分,根据新的Sugeno模糊概率积分定义获得了该积分相应的线性和非线性性质,并给出相应的证明,这为Sugeno模糊概率积分理论的丰富和发展提供依据。Fuzzy probability integral is an important part of fuzzy mathematics,and it is an integral form which combines fuzzy probability with integral.In this paper,a quasi-multiplication operator and a quasi-sum operator are designed by using the definition conditions of t-triangular module and s-triangular module.A new credible measure is constructed.The Sugeno fuzzy probability integral is redefined by combining the quasi-multiplication operator in the trusted measure space.According to the new definition of Sugeno fuzzy probability integral,the corresponding linear and nonlinear properties of the integral are obtained,giving the corresponding proof.All these provide the basis for the enrichment and development of Sugeno fuzzy probability integral theory.

关 键 词：T-模 s-模 似乘算子 似和算子 可信测度 Sugeno模糊概率积分 

分 类 号：O29[理学—应用数学]