×

Development and evaluation of five fuzzy multiattribute decision-making methods. (English) Zbl 0956.68535

Summary: We present the development of five fuzzy multiattribute decision-making methods. These methods are based on the analytic hierarchy process (original and ideal mode), the weighted-sum model, the weighted-product model, and the TOPSIS method. Moreover, these methods are examined in terms of two evaluative criteria. Computational results on test problems suggest that although all the methods are inaccurate, some of them seem to be more accurate than the others. The proposed evaluation methodology can easily be used in evaluating more fuzzy multiattribute decision making methods.

MSC:

68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baas, S. J.; Kwakernaak, H., Rating and ranking of multi-aspect alternatives using fuzzy sets, Automatica, 13, 47-58 (1977) · Zbl 0363.90010
[2] Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Management Sci., 17, 212-223 (1970) · Zbl 0224.90032
[3] Belton, V.; Gear, T., On a short-coming of Saaty’s method of analytic hierarchies, Omega, 228-230 (Dec. 1983)
[4] Ben-Arieh, D.; Triantaphyllou, E., Quantifying data for group technology with weighted fuzzy features, Internat. J. Production Res., 30, 1285-1299 (1992)
[5] Benayoun, R.; Roy, B.; Sussman, N., (Manual de reference du programme electre, Note de Synthese et Formation (1966), Direction Scientifique SEMA: Direction Scientifique SEMA Paris), No. 25
[6] Boender, C. G.E.; de Graan, J. G.; Lootsma, F. A., Multi-criteria decision analysis with fuzzy pairwise comparisons, Fuzzy Sets and Systems, 29, 133-143 (1989) · Zbl 0663.62017
[7] Bridgman, P. W., Dimensional Analysis (1922), Yale U.P: Yale U.P New Haven · Zbl 0117.17901
[8] Buckley, J. J., Ranking alternatives using fuzzy numbers, Fuzzy Sets and Systems, 15, 21-31 (1985) · Zbl 0567.90057
[9] Dubois, D.; Prade, H., Fuzzy Sets and Systems (1980), Academic: Academic New York
[10] Dubois, D.; Prade, H., Fuzzy real algebra: Some results, Fuzzy Sets and Systems, 2, 327-348 (1979) · Zbl 0412.03035
[11] Chen, S. J.; Hwang, C. L., Fuzzy Multiple Decision Making, (Lecture Notes in Econom. and Math. Systems, 375 (1992), Springer-Verlag: Springer-Verlag New York)
[12] Fishburn, P. C., Additive utilities with incomplete product set: Applications to priorities and assignments, Oper. Res. Soc. of America (1967)
[13] Hwang, C. L.; Yoon, K., Multiple Attribute Decision Making: Methods and Applications (1981), Springer-Verlag: Springer-Verlag New York
[14] Ichihashi, H.; Türksen, I. B., A neuro-fuzzy approach to data analysis of pairwise comparisons, Approx. Reasoning, 9, 227-248 (1993)
[15] Tseng, T. Y.; Klein, C. M., A new algorithm for fuzzy multicriteria decision making, Approx. Reasoning, 6, 45-66 (1992) · Zbl 0749.90089
[16] Laarhoven, P. J.M.; Pedrycz, W., A fuzzy extension of Saaty’s priority theory, Fuzzy Sets and Systems, 11, 229-241 (1983) · Zbl 0528.90054
[17] Lootsma, F. A., Numerical scaling of human judgment in pairwise-comparison methods for fuzzy multi-criteria decision analysis, Math. Models Decision Support, 48, 57-88 (1988)
[18] McCahon, C. S.; Lee, E. S., Comparing fuzzy numbers: The proportion of the optimum method, Approx. Reasoning, 4, 159-163 (1990) · Zbl 0709.03534
[19] Miller, D. W.; Starr, M. K., Executive Decisions and Operations Research (1969), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J
[20] Saaty, T. L., The Analytic Hierarchy Process (1980), McGraw-Hill: McGraw-Hill New York · Zbl 1176.90315
[21] Saaty, T. L., Fundamentals of Decision Making and Priority Theory with the AHP (1994), RWS Publications: RWS Publications Pittsburgh · Zbl 0816.90001
[22] Tong, R. M.; Bonissone, P. P., A linguistic approach to decision making with fuzzy sets, IEEE Trans. Systems Man Cybernet, SMC-10, 11, 716-723 (1980)
[23] Triantaphyllou, E.; Mann, S. H., An examination of the effectiveness of multi-dimensional decision-making methods: A decision-making paradox, Decision Support Systems, 5, 303-312 (1989)
[24] Triantaphyllou, E.; Pardalos, P. M.; Mann, S. H., A minimization approach to membership evaluation in fuzzy sets and error analysis, J. Optim. Theory Appl., 66, 275-287 (1990) · Zbl 0683.90005
[25] Triantaphyllou, E.; Mann, S. H., An evaluation of the eigenvalue approach for determining the membership values in fuzzy sets, Fuzzy Sets and Systems, 35, 295-301 (1990)
[26] Triantaphyllou, E.; Pardalos, P. M.; Mann, S. H., The problem of determining membership values in fuzzy sets in real world situations, (Brown, D. E.; White, C. C., Operations Research and Artificial Intelligence: The Integration of Problem Solving Strategies (1990), Kluwer Academic), 197-214
[27] Triantaphyllou, E., A quadratic programming approach in estimating similarity relations, IEEE Trans. Fuzzy Systems, 1, 138-145 (1993)
[28] Triantaphyllou, E.; Mann, S. H., A computational evaluation of the AHP and the revised AHP when the eigenvalue method is used under a continuity assumption, Comput. and Indust. Eng., 26, 609-618 (1994)
[29] Triantaphyllou, E.; Lootsma, F. A.; Pardalos, P. M.; Mann, S. H., On the evaluation and application of different scales for quantifying pairwise comparisons in fuzzy sets, Multi-Criteria Decision Anal., 3, 133-155 (1994) · Zbl 0851.90002
[30] Triantaphyllou, E., A linear programming based decomposition approach in evaluating relative priorities from pairwise comparisons and error analysis, J. Optim. Theory Appl., 84, 207-234 (1995) · Zbl 0827.90087
[31] Triantaphyllou, E.; Mann, S. H., Some critical issues in making decisions with pairwise comparisons, (Proceedings of the Third International Symposium on the Analytic Hierarchy Process (11-13 July 1994), George Washington Univ: George Washington Univ Washington), 225-236
[32] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
[33] Zhu, Q.; Lee, E. S., Comparison and ranking of fuzzy numbers, (Fuzzy Regression Analysis (1992), Omnitech Press: Omnitech Press Warsaw), 132-145
[34] Zimmermann, H. J., Fuzzy Set Theory—and Its Applications (1985), Kluwer Academic: Kluwer Academic Amsterdam · Zbl 0578.90095
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.