Computation on Fuzzy Riemann Integral of Type Ⅱ and Order Structure on Ordered Weighted Geometric Operators
|School||Zhejiang University of Technology|
|Keywords||Fuzzy Riemann integral endograph metric Monte Carlo method OWG operators join-irreducible elements|
In this thesis, first we discuss the computations of fuzzy Riemann integral of the form . Then we consider the comparison of OWG operators.The thesis is divided into four parts.The first part is introduction. This chapter first gives background material and current trend of development of the topic. Then preliminary materials required in the thesis are given.The second part is about fuzzy Riemann integral and its computational method. In this chapter we consider fuzzy valued integral of the form: . Computations of the fuzzy integral are discussed fully in this chapter. Our approach is mainly based on the endograph metric via finitely many level sets.The third part is about order structure on ordered weighted geometric (OWG) operators. We are primarily concerned with the comparisons of the set of all OWG operators. It is proved that the set of all OWG operators form a complete lattice according to the order on the set of all weight vectors. The structure of the set of all join-irreducible elements are described. Furthermore, the method as how to express all weight vectors via join-irreducible elements is demonstrated.The last is conclusions and prospect for further study.