Some Properties And Extensions Of The Fuzzy Choquet Integral

In this dissertation,fundamental properties of the fuzzy Choquet integral and three kinds of extentions of this integral are investigated,the main results are included as follows:1.Some properties of the fuzzy Choquet integral different from those of the Choquet integral are investigated,the right-continuity of the integrand of the fuzzy Choquet integral is proved,a Minkowski type inequality of the fuzzy Choquet integral is obtained,an example is given to show the exponent of the Minkowski type inequality has upper-bound,it is also proved that the set function defined by the fuzzy Choquet integral preserves some structural characteristics of the original fuzzy measure,such as subaddtivity,F-multiplicativity,null- addtivity,strong order continuity and so on .2.The fuzzy Choquet integral is extended by Lebesgue-Stieltjes measure ,the basic concepts of the Lebesgue-Stieltjes type fuzzy Choquet integral are established,especially,the convergence theorems are discussed .3.By the method of Aumann,s set-valued integral,the set-valued fuzzy Choquet integral is defined and some properties of this new integral are obtained .4.The fuzzy Choquet integral with respect to fuzzy sets is introduced and its absolute continuity and convergence are discussed .