Centroid defuzzification and the maximizing set and minimizing set ranking based on alpha level sets

Computers and Industrial Engineering

Volumn 57, Issue 1, 2009, Pages 228-236

  Wang, Ying Ming ^a  

^a FUZHOU UNIVERSITY   (China)

Author keywords

Alpha level sets; Centroid defuzzification; Maximizing set and minimizing set; Risk assessment

Indexed keywords

ALPHA LEVEL SETS; ANALYTICAL FORMULAS; CENTROID DEFUZZIFICATION; COMPUTATIONAL PROCESS; DECISION SUPPORTS; LEVEL SET; MAXIMIZING SET AND MINIMIZING SET; NUMERICAL EXAMPLE; PIECE-WISE LINEAR FUNCTIONS; RANKING FUZZY NUMBERS; SOFTWARE DEVELOPMENT;

DECISION SUPPORT SYSTEMS; FUZZY SETS; LEVEL MEASUREMENT; MEMBERSHIP FUNCTIONS; OPTIMIZATION; PIECEWISE LINEAR TECHNIQUES; RISK ASSESSMENT; RISK MANAGEMENT; RISK PERCEPTION;

SET THEORY;

EID: 67349185072     PISSN: 03608352     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cie.2008.11.014     Document Type: Article

References (35)

1. Chen S.H. Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets and Systems 17 (1985) 113-129
2. Chen S.M. Fuzzy group decision making for evaluating the rate of aggregative risk in software development. Fuzzy Sets and Systems 118 (2001) 75-88
3. Chen C.B., and Klein C.M. An efficient approach to solving fuzzy MADM problems. Fuzzy Sets and Systems 88 (1997) 51-67
4. Chen C.B., and Klein C.M. A simple approach to ranking a group of aggregated fuzzy utilities. IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics 27 (1997) 26-35
5. Detyniecki D., and Yager R.R. Ranking fuzzy numbers using α-weighted valuations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8 (2000) 573-591
6. Dong W.M., and Wong F.S. Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets and Systems 21 (1987) 183-199
7. Dubois D., and Prade H. Fuzzy sets and systems: Theory and application (1980), Academic Press, New York
8. Dubois D., and Prade H. Ranking fuzzy numbers in the setting of possibility theory. Information Sciences 30 (1983) 183-224
9. Filev D.P., and Yager R.R. An adaptive approach to defuzzification based on level sets. Fuzzy Sets and Systems 54 (1993) 355-360
10. Guh Y.Y., Hon C.C., and Lee E.S. Fuzzy weighted average: The linear programming approach via Charnes and Cooper's rule. Fuzzy Sets and Systems 117 (2001) 157-160
11. Guh Y.Y., Hon C.C., Wang K.M., and Lee E.S. Fuzzy weighted average: A max-min paired elimination method. Computers & Mathematics with Applications 32 (1996) 115-123
12. Guu S.M. Fuzzy weighted averages revisited. Fuzzy Sets and Systems 126 (2002) 411-414
13. Hon C.C., Guh Y.Y., Wang K.M., and Lee E.S. Fuzzy multiple attributes and multiple hierarchical decision making. Computers & Mathematics with Applications 32 (1996) 109-119
14. Kao C., and Liu S.T. Competitiveness of manufacturing firms: An application of fuzzy-weighted average. IEEE Transactions on Systems, Man and Cybernetics - Part A: Systems and Humans 29 (1999) 661-667
15. Kao C., and Liu S.T. Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Systems 113 (2000) 427-437
16. Kao C., and Liu S.T. Fractional programming approach to fuzzy weighted average. Fuzzy Sets and Systems 120 (2001) 435-444
17. Kao C., and Liu S.T. A mathematical programming approach to fuzzy efficiency ranking. International Journal of Production Economics 86 (2003) 145-154
18. Lee H.M. Applying fuzzy set theory to evaluate the rate of aggregative risk in software development. Fuzzy Sets and Systems 79 (1996) 323-336
19. Lee H.M. Group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in software development. Fuzzy Sets and Systems 80 (1996) 261-271
20. Lee H.M. Generalization of the group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in software development. Information Sciences 113 (1999) 301-311
21. Lee H.M., Lee S.Y., Lee T.Y., and Chen J.J. A new algorithm for applying fuzzy set theory to evaluate the rate of aggregative risk in software development. Information Sciences 153 (2003) 177-197
22. Lee H.M., Lee T.Y., Lee S.Y., and Chen J.J. A fuzzy group assessment model for evaluating the rate of aggregative risk in software development. International Journal of Reliability, Quality and Safety Engineering 11 (2004) 17-33
23. Lee D.H., and Park D. An efficient algorithm for fuzzy weighted average. Fuzzy Sets and Systems 87 (1997) 39-45
24. León T., Liern V., Ruiz J.L., and Sirvent I. A fuzzy mathematical programming approach to the assessment of efficiency with DEA models. Fuzzy Sets and Systems 139 (2003) 407-419
25. Matarazzo B., and Munda G. New approaches for the comparison of L-R fuzzy numbers: A theoretical and operational analysis. Fuzzy Sets and Systems 118 (2001) 407-418
26. Oussalah M. On the compatibility between defuzzification and fuzzy arithmetic operations. Fuzzy Sets and Systems 128 (2002) 247-260
27. Raj P.A., and Kumar D.N. Ranking alternatives with fuzzy weights using maximizing set and minimizing set. Fuzzy Sets and Systems 105 (1999) 365-375
28. Raja P.A., and Kumar D.N. Ranking multi-criterion river basin planning alternatives using fuzzy numbers. Fuzzy Sets and Systems 100 (1998) 89-99
29. Tseng T.Y., and Klein C.M. A new algorithm for fuzzy multicriteria decision making. International Journal of Approximate Reasoning 6 (1992) 45-66
30. Uehara K., and Hirota K. Parallel and multistage fuzzy inference based on families of α-level sets. Information Sciences 106 (1998) 159-195
31. Vanegas L.V., and Labib A.W. Application of new fuzzy-weighted average (NFWA) method to engineering design evaluation. International Journal of Production Research 39 (2001) 1147-1162
32. Wang Y.M., Greatbanks R., and Yang J.B. Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems 153 (2005) 347-370
33. Wang W.J., and Luoh L. Simple computation for the defuzzifications of center of sum and center of gravity. Journal of Intelligent and Fuzzy Systems 9 (2000) 53-59
34. Yager R.R. A procedure for ordering fuzzy subsets of the unit interval. Information Sciences 24 (1981) 143-161
35. Yager R.R., and Filev D. On ranking fuzzy numbers using valuations. International Journal of Intelligent Systems 14 (1999) 1249-1268