Fuzzy inferior ratio method for multiple attribute decision making problems. (English) Zbl 1354.91038
Summary: Multiple attribute decision making forms an important part of the decision process for both small (individual) and large (organization) problems. When available information is precise, many methods exist to solve this problem. But the uncertainty and fuzziness inherent in the structure of information make rigorous mathematical models inappropriate for solving this type of problems. This paper incorporates the fuzzy set theory and the basic nature of subjectivity due to the ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environment. The proposed method can take both real and fuzzy inputs. An outranking intensity is introduced to determine the degree of overall outranking between competing alternatives, which are represented by fuzzy numbers. Numerical examples finally illustrate the approach.
MSC:
| 91B06 | Decision theory |
References:
| [1] | Abo-Sinna, M. A.; Amer, A. H., Extensions of the TOPSIS for multi-objective large-scale nonlinear programming problems, Appl. Math. Comput., 162, 243-256 (2005) · Zbl 1061.65045 |
| [2] | Agrawal, V. P.; Kohli, V.; Gupta, S., Computer aided robot selection: the multiple attribute decision making approach, Int. J. Prod. Res., 29, 1629-1644 (1991) |
| [3] | Alonso, S.; Herrera-Viedma, E.; Chiclana, F.; Herrera, F., A web based consensus support system for group decision making problems and incomplete preferences, Inform. Sci., 180, 23, 4477-4495 (2010) |
| [4] | Bustince, H.; Barrenechea, E.; Pagola, M., Restricted equivalence functions, Fuzzy Sets Syst., 157, 2337-2346 (2006) · Zbl 1110.68158 |
| [5] | Bustince, H.; Barrenechea, E.; Pagola, M., Relationship between restricted dissimilarity functions, restricted equivalence functions and normal \(E_N\)-functions: Image thresholding invariant, Pattern Recogn. Lett., 29, 525-536 (2008) |
| [6] | Chen, C. T., Extensions of the TOPSIS for group decision making under fuzzy environment, Fuzzy Sets Syst., 114, 1-9 (2000) · Zbl 0963.91030 |
| [7] | Chen, J.; Liu, Y., A model and its application for uncertainly group decision making, World J. Model. Simulat., 2, 1, 45-54 (2006) |
| [8] | Chen, M. F.; Tzeng, G. H., Combining grey relation and TOPSIS concepts for selecting an expatriate host country, Math. Comput. Model., 40, 1473-1490 (2004) · Zbl 1099.90549 |
| [9] | Cheng, S.; Chan, C. W.; Huang, G. H., An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management, Eng. Appl. Artif. Intell., 16, 543-554 (2003) |
| [10] | Chu, T. C., Facility location selection using fuzzy TOPSIS under group decisions, Int. J. Uncertainty, 10, 687-701 (2002) · Zbl 1065.90085 |
| [11] | Chu, T. C., Selecting plant location via a fuzzy TOPSIS approach, Int. J. Adv. Manuf. Technol., 20, 859-864 (2002) |
| [12] | Chu, T. C.; Lin, Y. C., A fuzzy TOPSIS method for robot selection, Int. J. Adv. Manuf. Technol., 21, 284-290 (2003) |
| [13] | Deng, H.; Yeh, C. H.; Willis, R. J., Inter-company comparison using modified TOPSIS with objective weights, Comput. Oper. Res., 27, 963-973 (2000) · Zbl 0970.90038 |
| [14] | Feng, C. M.; Wang, R. T., Performance evaluation for airlines including the consideration of financial ratios, J. Air Transp. Manage., 6, 133-142 (2000) |
| [15] | Feng, C. M.; Wang, R. T., Considering the financial ratios on the performance evaluation of highway bus industry, Transp. Rev., 21, 449-467 (2001) |
| [16] | Feng-Li, D., An approach to fuzzy multiattribute decision making under uncertainty, Inform. Sci., 169, 1-2, 97-112 (2005) · Zbl 1101.68840 |
| [17] | Figueira, J.; Greco, S.; Ehrgott, M., Multiple Criteria Decision Analysis: State of the Art Surveys (2005), Springer Science + Business Media: Springer Science + Business Media Boston · Zbl 1060.90002 |
| [18] | Hadi-Vencheh, A.; Mokhtarian, M. N., A new fuzzy MCDM approach based on centroid of fuzzy numbers, Expert Syst. Appl., 38, 5226-5230 (2011) |
| [19] | Hwang, C. L.; Yoon, K., Multiple Attributes Decision Making Methods and Applications (1981), Springer: Springer Berlin Heidelberg · Zbl 0453.90002 |
| [20] | Jee, D. H.; Kang, K. J., A method for optimal material selection aided with decision making theory, Mater. Des., 21, 199-206 (2000) |
| [21] | Kahraman, C., Fuzzy Multiple Criteria Decision Making (2008), Springer: Springer Istanbul |
| [22] | Kaufmann, A.; Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications (1991), VanNostrand-Reinhold: VanNostrand-Reinhold New York · Zbl 0754.26012 |
| [23] | Khademolqorani, S.; Zeinal Hamadani, A., An adjusted decision support system through data mining and multiple criteria decision making, Proc. - Soc. Behav. Sci., 73, 388-395 (2013) |
| [24] | Kim, G.; Park, C. S.; Yoon, K. P., Identifying investment opportunities for advanced manufacturing systems with comparative-integrated performance measurement, Int. J. Prod. Econ., 50, 23-33 (1997) |
| [25] | Klir, G. J.; Folger, T. A., Fuzzy Sets, Uncertainty, and Information (2006), Prentice-Hall of India: Prentice-Hall of India New Delhi |
| [26] | Klir, G. J.; Yuan, B., Fuzzy Sets and Fuzzy Logics - Theory and Applications (2007), Prentice-Hall of India: Prentice-Hall of India New Delhi |
| [27] | Li, D-F., Relative ratio method for multiple attribute decision making problems, Int. J. Inform. Technol. Decis. Mak., 8, 2, 289-297 (2009) · Zbl 1178.90185 |
| [28] | Liu, X.; Mendel, J. M.; Wu, D., Analytical solution methods for the fuzzy weighted average, Inform. Sci., 187, 151-170 (2012) · Zbl 1248.03072 |
| [29] | Meng, D.; Zheng, P., On weighted unbalanced linguistic aggregation operators in group decision making, Inform. Sci., 223, 31-41 (2013) · Zbl 1293.91050 |
| [30] | Merigó, J. M.; Gil-Lafuente, A. M., New decision-making techniques and their application in the selection of financial products, Inform. Sci., 180, 2085-2094 (2010) · Zbl 1194.91070 |
| [31] | Mokhtarian, M. N.; Hadi-Vencheh, A., A new fuzzy TOPSIS method based on left and right scores: an application for determining an industrial zone for dairy products factory, Appl. Soft Comput., 12, 2496-2505 (2012) |
| [32] | Parreiras, R. O.; Ekel, P. Y.; Martini, J. S.C.; Palhares, R. M., A flexible consensus scheme for multicriteria group decision making under linguistic assessments, Inform. Sci., 180, 7, 1075-1089 (2010) |
| [33] | Paternain, D.; Jurio, A.; Barrenechea, E.; Bustince, H.; Bedregal, B.; Szmidt, E., An alternative to fuzzy methods in decision-making problems, Fuzzy Sets Syst., 39, 7729-7735 (2012) |
| [34] | Pedrycz, W., Granular Computing: Analysis and Design of Intelligent Systems (2013), CRC Press/Taylor & Francis: CRC Press/Taylor & Francis Boca Raton |
| [35] | Triantaphyllou, E.; Lin, C. T., Development and evaluation of five fuzzy multi-attribute decision-making methods, Int. J. Approx. Reason., 14, 281-310 (1996) · Zbl 0956.68535 |
| [36] | Tsaur, S. H.; Chang, T. Y.; Yen, C. H., The evaluation of airline service quality by fuzzy MCDM, Tourism Manage., 23, 107-115 (2002) |
| [37] | Wang, Y. M.; Elhag, T. M.S., Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment, Expert Syst. Appl., 31, 309-319 (2006) |
| [38] | Xu, Z., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment, Inform. Sci., 168, 171-184 (2004) · Zbl 1170.91328 |
| [39] | Xu, Z., A method based on the dynamic weighted geometric aggregation operator for dynamic hybrid multi-attribute group decision making, Int. J. Uncertainty, Fuzz. Knowl. - Based Syst., 17, 1, 15-33 (2008) · Zbl 1158.90366 |
| [40] | Yan, H. B.; Huynh, V. N.; Ma, T.; Nakamori, Y., Non-additive multi-attribute fuzzy target-oriented decision analysis, Inform. Sci., 240, 21-44 (2013) · Zbl 1320.91051 |
| [41] | Zadeh, L. A., Fuzzy sets, Inform. Contr., 8, 338-353 (1965) · Zbl 0139.24606 |
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.
