Incomplete linguistic preference relations and their fusion
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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. Outline. Introduction Main Results Illustrative Example Conclusions. Introduction. Preference Relation. AHP. Introduction (Cont.).

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Incomplete Linguistic Preference Relations and Their Fusion

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Incomplete linguistic preference relations and their fusion

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


Outline

Outline

  • Introduction

  • Main Results

  • Illustrative Example

  • Conclusions


Introduction

Introduction

Preference Relation

AHP


Incomplete linguistic preference relations and their fusion

Introduction (Cont.)


Linguistic term

Linguistic Term


Linguistic preference relation

Linguistic Preference Relation

Satisfy additive transitivity:


Acceptable incomplete linguistic preference relation with the least judgments n 1 judgments

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


Simple method for constructing a complete linguistic preference relation

Simple Method for Constructing a Complete Linguistic Preference Relation


Incomplete linguistic preference relations and their fusion

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


Example

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:


Incomplete linguistic preference relations and their fusion

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):


Incomplete linguistic preference relations and their fusion

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


Conclusions

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.


Thank you

Thank You


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