Research On Theory And Application Of Fuzzy Integrals Inequalities

As a classical linear integral, Lebesgue integral has an important role in clas-sical analysis. However, Lebesgue integral based on additive measure and semiring([a, b],+,·) can not reveal the interactive function in many practice problems such asmachine leaning. Many scholars generalized the Lebesgue integral such as Sugenointegral, universal integral, pseudo integral and so on.Integral inequalities have an important role in in various aspects of mathematics,such as in probability theory, differential equations, decision making under risk, in-formation sciences, decision analysis, fuzzy recognise, classify and information fusing.However, majority of those problems are non-linear structure, so it is an important issueto generalize classical integral inequalities to non-linear integralsThis work main investigate three classes of fuzzy integral inequalities. The mainresults are as follow:(1) Hermite-Hadamard type inequality for Sugeno integral based on (α, m)-convex function. Firstly, Hermite-Hadamard type inequality for Sugeno integral re-stricted in [0,1] is discussed. Then, related results are generalized to [a, b]. Some ex-amples are given to illustrate the validity of our results. Finally, Sugeno integral basedon some special (α, m)-concave functions are discussed and some important results areobtained.(2) Berwald type inequality for extremal universal integral based on (α, m)-concave function. Some theorems are given as special cases of (α, m)-concave func-tions. Finally, some examples are given to illustrate the validity of our results.(3) Generalization of the Lyapunov type inequality for pseudo-integrals. we dealwith two cases of Lyapunov type inequalities for pseudo integrals. The first case dis-cusses pseudo-integrals where pseudo operations⊕,⊙are given by a monotone andcontinuous function g. The second case focuses on the pseudo-integrals based on asemiring ([0,1], sup,⊙) with respect to sup-measure. Finally, some examples are giv-en to illustrate the validity of our results.(4) Application of fuzzy technology in intelligence control. Approximation offunction and System experiments on Neural Network control has been studied to illus-trate the advance of fuzzy technology in intelligence control.There are totaly5figures and124references in this paper.