On possibility-degree formulae for ranking interval numbers
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Since interval numbers are used to evaluate the opinions of decision makers and express the weights of alternatives in various decision making problems, it is requisite to give a feasible method to rank them. In the present paper, the two existing possibility degree formulae for ranking interval numbers are proved to be equivalent. A generalized possibility degree formula is proposed by considering the attitude of decision makers with a prescribed function. Some known possibility degree formulae for ranking interval numbers can be recovered by choosing a special function. The proposed method is applied to uniformly define the weak transitivity of interval multiplicative and additive reciprocal preference relations. Numerical examples are carried out to illustrate the new formula.
KeywordsDecision making Interval numbers Possibility degree formula Ranking
The work was supported by the National Natural Science Foundation of China (Nos. 71571054, 71201037), the Guangxi Natural Science Foundation (No. 2014GXNSFAA118013), and the Guangxi Natural Science Foundation for Distinguished Young Scholars (No. 2016GXNSFFA380004).
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Conflict of interest
All authors declare that they have no conflict of interest.
- Da QL, Liu XW (1999) Interval number linear programming and its satisfactory solution. Syst Eng Theory Pract 19:3–7Google Scholar
- Guo KH, Mou YJ (2010) Multiple attribute decision-making method with intervals based on possibility degree matrix. J Comput Appl 32:218–222Google Scholar
- Moorse RE (1966) Interval analysis. Prentice-Hall, Englewood CliffsGoogle Scholar
- Moorse RE (1995) Methods and applications of interval analysis. SIAM, Philadelphia (Second Printing)Google Scholar
- Sun HB, Yao WX (2010) Comments on methods for ranking interval numbers. J Syst Eng 25:305–312Google Scholar
- Xu ZS, Da QL (2003) Possibility degree method for ranking interval numbers and its application. J Syst Eng 18:67–70Google Scholar
- Xu ZS (2004) On compatibility of interval fuzzy preference matrices. Fuzzy Optim Decis Mak 3:217–225Google Scholar
- Zhang Q, Fan ZP, Pan DH (1999) A ranking approach with possibilities for multiple attribute decision making problems with interval. Control Decis 14(6):703–706Google Scholar
- Zhang Z (2016) Logarithmic least squares approaches to deriving interval weights, rectifying inconsistency and estimating missing values for interval multiplicative preference relations. Soft Comput. doi: 10.1007/s00500-016-2049-6