Integral Of Complex Fuzzy Set - Valued Functions And Its Application

This dissertation establishes the integral theory of complex fuzzy set-valued functions based on the complex fuzzy set-valued measures, which generalizes the theory of fuzzy measuresand fuzzy integrals. The notions of complex fuzzy set-valued measure and complex fuzzy set-valued measurable function are introduced, and their properties are discussed. Integrals of complex fuzzy set-valued functions based on the complex fuzzy set-valued measures are defined, and related properties are studied. Taking an integral of a complex fuzzy set-valued function as a fusion operator, it presents several methodsto fusion classifiers relay on integrals of a complex fuzzy set-valued functions. The feasibility, validity and superiority of the fusion method are also confirmed by experiment. The detailed contents of the dissertation are as follows:Chapter 1 reviews somepreliminary notions (such as classicalmeasure, fuzzy measure, fuzzy integral, etc.) used in the subsequent chapters.Chapter 2 establishes the complex fuzzy set-valued complex fuzzy measure theory. It gives the definition of complex fuzzy set-valued complex fuzzy measure and further investigates their properties.Chapter 3 begins with the concept of complex fuzzy set-valued complex fuzzy measurable function based on the notion complex fuzzy set-valued complex fuzzy measure, and then studies the related properties of complex fuzzy set-valued complex fuzzy measurable functions.In Chapter 4, the concept of complex fuzzy set-valued complex fuzzy integral of a complexfuzzy-valued function is given based on the notion complex fuzzy-valued measure, and basic properties of complex fuzzy set-valued complex fuzzy integrals are studied. As in the case of classical integral theory, the monotone convergence theorem, the Fatou’s lemma, and the Lebesgue control convergence theorem on complex fuzzy set-valued complex fuzzy integrals are proved. Finally, complex fuzzy set-valued complex fuzzy integrals ofseveral special kinds of functions are given, and their properties are established.Chapter 5 is on applications of complex fuzzy set-valued complex fuzzy integral theory in classification technology of classifier.Classifier models, designed according to the unique property of complex fuzzy set-valued complex fuzzy integrals, have good fusion effect, higher precision and better performance.It also reduces the uncertainty of classifications.