Journal
INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS
Volume 21, Issue 2, Pages 223-243Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218488513500128
Keywords
Multi-attribute decision making; triangular intuitionistic fuzzy number; possibility mean; possibility variance; possibility variance coefficient
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Funding
- National Natural Science Foundation of China [71061006, 61263018]
- Humanities Social Science Programming Project of Ministry of Education of China [09YGC630107]
- Natural Science Foundation of Jiangxi Province of China [20114BAB201012]
- Science and Technology Project of Jiangxi province educational department of China [GJJ12265]
- Excellent Young Academic Talent Support Program of Jiangxi University of Finance and Economics
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Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.
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