Incomplete Linguistic Preference Relations and Their Fusion

1. Incomplete Linguistic Preference Relations and Their Fusion Information Fusion, vol. 7, no. 3, pp. 331-337, 2006. Zeshui Xu 報告者:王志煌 96.7.25

2. Outline • Introduction • Main Results • Illustrative Example • Conclusions

3. Introduction Preference Relation AHP

4. Introduction (Cont.)

5. Linguistic Term

6. Linguistic Preference Relation Satisfy additive transitivity:

7. Acceptable incomplete Linguistic Preference Relation with the Least judgments (n-1 judgments)

8. Simple Method for Constructing a Complete Linguistic Preference Relation

9. Multi-Person Decision Making Based on the Acceptable Incomplete Linguistic Preference Relations with the Least Judgments

11. Example • The evaluation of eight schools xi (i = 1, 2, …, 8) of a university • There are three decision makers dk (k = 1, 2, 3), whose weight vector x = (0.5, 0.3, 0.2)T. • Step 1:

13. Step 2: Utilize the known elements in Ak (k = 1,2,3) and Eq. (2) to determine all the unknown elements in Ak (k = 1,2,3):

15. Step 3: Utilize Eq. (3) to fuse all the consistent complete linguistic preference relations into a collective complete linguistic preference relation

17. Conclusions • In this paper, Xu has developed a simple and practical method, which utilizes the acceptable incomplete linguistic preference relation with the least judgments (i.e., n-1 judgments) to construct a consistent complete linguistic preference relation. • In this paper, Xu has also developed an approach to multi-person decision making based on the acceptable incomplete linguistic preference relations with the least judgments.

18. Thank You