K-拟可加模糊测度空间上的广义Sugeno模糊积分.doc

K-拟可加模糊测度空间上的广义Sugeno模糊积分关 键 词:诱导算子; 拟加法; 拟乘法; K-拟可加模糊测度; 广义Sugeno模糊积分 LI Yan-hong1, WANG Gui-jun2 (1.Department of Mathematics, Teachers College, Easten Liaoning University, Dandong 118000, Liaoning Province, China; 2.School of Mathematics Science, Tianjin Normal University, Tianjin 300387, China) Generalized Sugeno fuzzy integrals on K-quasi-additive fuzzy measure space Journal of Zhejiang University(Science Edition), 2010,37(4):376-380 Abstract: On K-quasi-additive fuzzy measure space, the generalized Sugeno fuzzy integral model is set up by K-quasi-multiplication operation, aiming at a class of non-negative integrable functions, representations of supremum about the fuzzy integral are discussed, and then an important integral inequality and its characteristics which describe relations between K-quasi-addition and K-quasi-multiplication operations are given. This has laid the foundation of further researching its convergence theorem. Key Words: Inductive operator; quasi-addition; quasi-multiplication; K-quasi-additive fuzzy measure; generalized Sugeno fuzzy integrals. 0 引 言 自从1974年日本学者SUGENO1首次提出模糊测度与模糊积分概念以来,模糊测度论这一新理论得到了巨大的发展.1987年,SUGENO2针对模糊积分不满足普通可加性这一特点提出了拟加法、拟乘法的概念,并初步建立了拟可加模糊测度与积分的理论框架,这为研究非可加的模糊积分理论开辟了一条新的理论途径.1993年,文献3通过引入乘法算子“”,把Sugeno模糊积分定义中的取小运算用以乘法算子替代,给出一种广义模糊积分概念,同年,文献4在文献2基础上针对给定的K算子和t算子,定义了拟加法、拟乘法及其运算,并给出了tK积分和Kt积分及其转换定理.2007年,文献5针对文献3乘法算子的缺欠进行了改进,重新给出了广义模糊积分定义.文献6引入了区别于上述吴乘法算子“”的拟乘法算子“?帷?,给出了所谓广义Sugeno模糊积分定义.本文在文献6的基础上,针对一类非负可积函数研究这种广义Sugeno模糊积分的确界表示及其等价形式,并进一步讨论这种模糊积分的运算特性.