| Summary: | 博士 === 淡江大學 === 管理科學研究所 === 70 === The feasibility of the application of fuzzy sets theory to decision making is investigated in this research. The arithmetic operations on level sets of convex fuzzy numbers are studied in detail, on the basis of the extension principle which was introduced by Professor L. A. zadeh in 1975. It is shown that these operations are convenient and efficient in the computation of linguistic variables.
By means of the concept of level sets, a new method to rank various fuzzy alternatives is presented. The presented method is then applied to two kinds of fuzzy numbers, one is discrete fuzzy numbers and the other is strictly convex fuzzy numbers. Five illustrations for the latter are shown, which imply that the capability of the proposed method is much more improved than those which have been published in the literature.
Through the extended operations on linguistic variables as well as linguistic hedges, an algorithm is proposed to evaluate a binary linguistic decision tree. The advantage of the linguistic decision tree is to relax the necessity for the determination of the precise numbers and thus this linguistic approach is considered an approximate and yet practical means to describe the behavior of systems, which are either too complex or too ill-defined to give an exact description.
Several case studies are illustrated to employ the proposed algorithm. Bayesian analysis to a binary decision tree is also presented. The results are shown to be in good agreement with those in the conventional case.
|
|---|
