Further Research Of The G_λ Fuzzy Measure And Fuzzy Integral And Its Application

As an newly emerging discipline, fuzzy mathematics with important theoreticalsignificance is a important popularity of classical mathematics. After decades ofbrief development, by interpenetrating with classical mathematics it has formedmany new subjects, such as fuzzy topology, random fuzzy mathematics, fuzzyanalysis and fuzzy logic theory and so on. And each branch is with rich connotation.Many domestic and foreign scholars have achieved many good conclusions bydoingresearch on Fuzzy measure and Fuzzy integral since the concept of fuzzymeasure and fuzzy integral was first introduced by Sugeno M in1974. In recentyears, fuzzy measure and fuzzy integral has been successfully applied to patternrecognition, computer vision, information fusion. Therefore, the research of specialstructure of fuzzy measure and fuzzy integral is very necessary.In this paper, the research problems are as follows:First, this paper introduces the related contents of fuzzy measure and fuzzyintegral, and then introduces the definition and related properties of g_λfuzzymeasure, which laid a foundation for the subsequent content.Secondly, studied the convergence or divergence of g_λfuzzy measure infiniteseries, with the introduction of the concept of generalized additive, discussed thetransformation theorem of g_λfuzzy measure and g_λ probability measure. At thesame time, the properties of g_λfuzzy integral are proved, and its convergencetheorems are discussed.Finally, using the knowledge of fuzzy mathematics, level1and multistage fuzzycomprehensive evaluation model is given, comprehensive evaluation whichcombined with the interaction role is discussed, with the capability of g_λfuzzymeasure said interaction role is given. And apply the theory of comprehensiveevaluation to teaching quality evaluation and student assessment, etc.