This paper presents a new, nonlinear, multicriteria, decision-making method: the characteristic objects (COMET). This approach, which can be characterized as a fuzzy reference model, determines a measurement standard for decision-making problems. This model is distinguished by a constant set of specially chosen characteristic objects that are independent of the alternatives. After identifying a multicriteria model, this method can be used to compare any number of decisional objects (alternatives) and select the best one. In the COMET, in contrast to other methods, the rank-reversal phenomenon is not observed. Rank-reversal is a paradoxical feature in the decision-making methods, which is caused by determining the absolute evaluations of considered alternatives on the basis of the alternatives themselves. In the Analytic Hierarchy Process (AHP) method and similar methods, when a new alternative is added to the original alternative set, the evaluation base and the resulting evaluations of all objects change. A great advantage of the COMET is its ability to identify not only linear but also nonlinear multicriteria models of decision makers. This identification is based not on a ranking of component criteria of the multicriterion but on a ranking of a larger set of characteristic objects (characteristic alternatives) that are independent of the small set of alternatives analyzed in a given problem. As a result, the COMET is free of the faults of other methods. 1. Introduction The subject of criteria is often misunderstood, both by laypeople and scientists. Expert criterions exist in the mind of the decision maker for use in the evaluation of alternatives, allowing for determination of the attractiveness of a considered object (absolute evaluation) or relative attractiveness of two or more objects (comparative evaluation). The alternatives evaluated can include anything (e.g., internet pages, films, cars, machines and technical devices, bridges, homes, motorbikes, horses, dogs, exam projects of students, other people, feminine beauty, the choice of a firm for a task realization, etc.) and each individual problem has various mental multicriteria models that are applied during evaluation. These individual criteria are usually called subjective criteria [1–3], which can often mistakenly evoke a negative interpretation akin to fuzzy or unclear. Therefore, rather than subjective criteria, the term individual multicriteria will hereafter be used to describe these criteria [4, 5]. As well as person-specific multicriteria, objective multicriteria criteria also
References
[1]
T.-C. Chu and Y. Lin, “An extension to fuzzy MCDM,” Computers and Mathematics with Applications, vol. 57, no. 3, pp. 445–454, 2009.
[2]
？. Ertu？rul, “Fuzzy group decision making for the selection of facility location,” Group Decision and Negotiation, vol. 20, no. 6, pp. 725–740, 2011.
[3]
B. Vahdani, R. Tavakkoli-Moghaddam, S. M. Mousavi, and A. Ghodratnama, “Soft computing based on new interval-valued fuzzy modified multi-criteria decision-making method,” Applied Soft Computing Journal, vol. 13, no. 1, pp. 165–172, 2013.
[4]
P. Guo, “Private teal estate investment analysis within one-shot decision framework,” International Real Estate Review, vol. 13, no. 3, pp. 238–260, 2010.
[5]
P. Guo, “One-shot decision theory,” IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, vol. 41, no. 5, pp. 917–926, 2011.
[6]
E. Garmendia and G. Gamboa, “Weighting social preferences in participatory multi-criteria evaluations: a case study on sustainable natural resource management,” Ecological Economics, vol. 84, pp. 110–120, 2012.
[7]
G. A. Mendoza and H. Martins, “Multi-criteria decision analysis in natural resource management: a critical review of methods and new modelling paradigms,” Forest Ecology and Management, vol. 230, no. 1–3, pp. 1–22, 2006.
[8]
W. Pedrycz, P. Ekel, and R. Parreiras, Fuzzy Multicriteria Decision-Making: Models, Methods and Applications, John Wiley & Sons, Chichester, UK, 2011.
[9]
M. Amiri, M. Zandieh, R. Soltani, and B. Vahdani, “A hybrid multi-criteria decision-making model for firms competence evaluation,” Expert Systems with Applications, vol. 36, no. 10, pp. 12314–12322, 2009.
[10]
T. Gal and T. Hanne, “Nonessential objectives within network approaches for MCDM,” European Journal of Operational Research, vol. 168, no. 2, pp. 584–592, 2006.
[11]
A. Piegat and W. Sa？abun, “Nonlinearity of human multi-criteria in decision-making,” Journal of Theoretical and Applied Computer Science, vol. 6, no. 3, pp. 36–49, 2012.
[12]
M. Zarghami and F. Szidarovszky, Multicriteria Analysis: Applications to Water and Environment Managment, Springer, New York, NY, USA, 2011.
[13]
S. French, Decision Behavior, Analysis and Support, Cambridge University Press, New York, NY, USA, 2009.
[14]
T. D. Kontos, D. P. Komilis, and C. P. Halvadakis, “Siting MSW landfills with a spatial multiple criteria analysis methodology,” Waste Management, vol. 25, no. 8, pp. 818–832, 2005.
[15]
R. Simanaviciene and L. Ustinovichius, “Sensitivity analysis for multiple criteria decision making methods: TOPSIS and SAW,” in Proceedings of the 6th International Conference on Sensitivity Analysis of Model Output (SAMO '10), pp. 7743–7744, July 2010.
[16]
J. Stadnicki, Theory and Practice of Solving Optimization Problems, WNT, Warszawa, Poland, 2006.
[17]
A. R. Blair, G. N. Mandelker, T. L. Saaty, and R. Whitaker, “Forecasting the resurgence of the U.S. economy in 2010: an expert judgment approach,” Socio-Economic Planning Sciences, vol. 44, no. 3, pp. 114–121, 2010.
[18]
Y. Dong, G. Zhang, W.-C. Hong, and Y. Xu, “Consensus models for AHP group decision making under row geometric mean prioritization method,” Decision Support Systems, vol. 49, no. 3, pp. 281–289, 2010.
[19]
E. Karami, “Appropriateness of farmers' adoption of irrigation methods: the application of the AHP model,” Agricultural Systems, vol. 87, no. 1, pp. 101–119, 2006.
[20]
M. Kim, Y.-C. Jang, and S. Lee, “Application of Delphi-AHP methods to select the priorities of WEEE for recycling in a waste management decision-making tool,” Journal of Environmental Management, vol. 128, pp. 941–948, 2013.
[21]
N. J. Mamat and J. K. Daniel, “Statistical analyses on time complexity and rank consistency between singular value decomposition and the duality approach in AHP: a case study of faculty member selection,” Mathematical and Computer Modelling, vol. 46, no. 7-8, pp. 1099–1106, 2007.
[22]
T. L. Saaty, “Decision making the analytic hierarchy and network processes (AHP/ANP),” International Journal Services Sciences, vol. 1, no. 1, pp. 83–98, 2008.
[23]
T. L. Saaty and J. S. Shang, “An innovative orders-of-magnitude approach to AHP-based multi-criteria decision making: prioritizing divergent intangible humane acts,” European Journal of Operational Research, vol. 214, no. 3, pp. 703–715, 2011.
[24]
T. L. Saaty and L. T. Tran, “On the invalidity of fuzzifying numerical judgments in the analytic hierarchy process,” Mathematical and Computer Modelling, vol. 46, no. 7-8, pp. 962–975, 2007.
[25]
A. Szczypińska and E. W. Piotrowski, “Inconsistency of the judgment matrix in the AHP method and the decision maker's knowledge,” Physica A: Statistical Mechanics and its Applications, vol. 388, no. 6, pp. 907–915, 2009.
[26]
T.-H. Hsu, L.-C. Hung, and J.-W. Tang, “A hybrid ANP evaluation model for electronic service quality,” Applied Soft Computing Journal, vol. 12, no. 1, pp. 72–81, 2012.
[27]
K. Kirytopoulos, D. Voulgaridou, A. Platis, and V. Leopoulos, “An effective Markov based approach for calculating the Limit Matrix in the analytic network process,” European Journal of Operational Research, vol. 214, no. 1, pp. 85–90, 2011.
[28]
M. P. Niemira and T. L. Saaty, “An analytic network process model for financial-crisis forecasting,” International Journal of Forecasting, vol. 20, no. 4, pp. 573–587, 2004.
[29]
T. L. Saaty, “Decision making—the analytic hierarchy and network processes (AHP/ANP),” Journal of Systems Science and Systems Engineering, vol. 13, no. 1, pp. 1–35, 2004.
[30]
T. L. Saaty, “Time dependent decision-making; dynamic priorities in the AHP/ANP: generalizing from points to functions and from real to complex variables,” Mathematical and Computer Modelling, vol. 46, no. 7-8, pp. 860–891, 2007.
[31]
T. L. Saaty and C. Brandy, The Encyclicon, Volume 2: A Dictionary of Complex Decisions Using the Analytic Network Process, RWS Publications, Pittsburgh, Pa, USA, 2009.
[32]
Y.-L. Wang and G.-H. Tzeng, “Brand marketing for creating brand value based on a MCDM model combining DEMATEL with ANP and VIKOR methods,” Expert Systems with Applications, vol. 39, no. 5, pp. 5600–5615, 2012.
[33]
J. L. Yang and G.-H. Tzeng, “An integrated MCDM technique combined with DEMATEL for a novel cluster-weighted with ANP method,” Expert Systems with Applications, vol. 38, no. 3, pp. 1417–1424, 2011.
[34]
M. Behzadian, S. K. Otaghsara, M. Yazdani, and J. Ignatius, “A state-of the-art survey of TOPSIS applications,” Expert Systems with Applications, vol. 39, no. 17, pp. 13051–13069, 2012.
[35]
L. Dymova, P. Sevastjanov, and A. Tikhonenko, “An approach to generalization of fuzzy TOPSIS method,” Information Sciences, vol. 238, pp. 149–162, 2013.
[36]
K. Khalili-Damghani, S. Sadi-Nezhad, and M. Tavana, “Solving multi-period project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation,” Information Sciences, vol. 252, pp. 42–61, 2013.
[37]
M. Nakhaeinejad and N. Nahavandi, “An interactive algorithm for multi-objective flow shop scheduling with fuzzy processing time through resolution method and TOPSIS,” International Journal of Advanced Manufacturing Technology, vol. 66, no. 5–8, pp. 1047–1064, 2013.
[38]
S. Rouhani, M. Ghazanfari, and M. Jafari, “Evaluation model of business intelligence for enterprise systems using fuzzy TOPSIS,” Expert Systems with Applications, vol. 39, no. 3, pp. 3764–3771, 2012.
[39]
M. S. García-Cascales and M. T. Lamata, “On rank reversal and TOPSIS method,” Mathematical and Computer Modelling, vol. 56, no. 5-6, pp. 123–132, 2012.
[40]
D. Yong, “Plant location selection based on fuzzy TOPSIS,” International Journal of Advanced Manufacturing Technology, vol. 28, no. 7-8, pp. 839–844, 2006.
[41]
A. J. Brito, A. T. de Almeida, and C. M. M. Mota, “A multicriteria model for risk sorting of natural gas pipelines based on ELECTRE TRI integrating Utility Theory,” European Journal of Operational Research, vol. 200, no. 3, pp. 812–821, 2010.
[42]
J. Figueira, S. Greco, and M. Ehrgott, Multiple Criteria Decision Analysis: State of the Art Surveys, Springer, New York, NY, USA, 2004.
[43]
A. Hatami-Marbini and M. Tavana, “An extension of the Electre I method for group decision-making under a fuzzy environment,” Omega, vol. 39, no. 4, pp. 373–386, 2011.
[44]
G. A. Montazer, H. Q. Saremi, and M. Ramezani, “Design a new mixed expert decision aiding system using fuzzy ELECTRE III method for vendor selection,” Expert Systems with Applications, vol. 36, no. 8, pp. 10837–10847, 2009.
[45]
V. Mousseau and L. Dias, “Valued outranking relations in ELECTRE providing manageable disaggregation procedures,” European Journal of Operational Research, vol. 156, no. 2, pp. 467–482, 2004.
[46]
M. Behzadian, R. B. Kazemzadeh, A. Albadvi, and M. Aghdasi, “Promethee: a comprehensive literature review on methodologies and applications,” European Journal of Operational Research, vol. 200, no. 1, pp. 198–215, 2010.
[47]
Y.-C. Hu and C.-J. Chen, “A PROMETHEE-based classification method using concordance and discordance relations and its application to bankruptcy prediction,” Information Sciences, vol. 181, no. 22, pp. 4959–4968, 2011.
[48]
A. Ishizaka and P. Nemery, “Selecting the best statistical distribution with PROMETHEE and GAIA,” Computers and Industrial Engineering, vol. 61, no. 4, pp. 958–969, 2011.
[49]
R. Vetschera and A. T. de Almeida, “A PROMETHEE-based approach to portfolio selection problems,” Computers & Operations Research, vol. 39, no. 5, pp. 1010–1020, 2012.
[50]
B. Yilmaz and M. Da？deviren, “A combined approach for equipment selection: F-PROMETHEE method and zero-one goal programming,” Expert Systems with Applications, vol. 38, no. 9, pp. 11641–11650, 2011.
[51]
E. Triantaphyllou, Multi-Criteria Decision-Making: A Comparative Study, Kluwer Academic, Dordrecht, The Netherlands, 2000.
[52]
E. Triantaphyllou and S. H. Mann, “An examination of the effectiveness of multi-dimensional decision-making methods: a decision-making paradox,” Decision Support Systems, vol. 5, no. 3, pp. 303–312, 1989.
[53]
I. Ertu？rul and N. Karaka？o？lu, “Comparison of fuzzy AHP and fuzzy TOPSIS methods for facility location selection,” International Journal of Advanced Manufacturing Technology, vol. 39, no. 7-8, pp. 783–795, 2008.
[54]
P. van Laarhoven and W. Pedrycz, “A fuzzy extension of Saaty's priority theory,” Fuzzy Sets and Systems, vol. 11, no. 13, pp. 199–227, 1983.
[55]
J. H. May, J. Shang, Y. C. Tjader, and L. G. Vargas, “A new methodology for sensitivity and stability analysis of analytic network models,” European Journal of Operational Research, vol. 224, no. 1, pp. 180–188, 2013.
[56]
L. G. Vargas, “Comments on Barzilai and Lootsma: why the multiplicative AHP is invalid: a practical counterexample,” Journal of Multi-Criteria Decision Analysis, vol. 6, no. 3, pp. 169–170, 1997.
[57]
W. Pedrycz, “Statistically grounded logic operators in fuzzy sets,” European Journal of Operational Research, vol. 193, no. 2, pp. 520–529, 2009.
[58]
W. Pedrycz and F. Gomide, Fuzzy Systems Engineering: Toward Human-Centric Computing, John Wiley & Sons, New York, NY, USA, 2011.
[59]
A. Piegat, Fuzzy Modeling and Control, Springer, New York, NY, USA, 2001.
[60]
W. Sa？abun, “The use of fuzzy logic to evaluate the nonlinearity of human multi-criteria used in decision making,” Przeglad Elektrotechniczny, vol. 88, no. 10b, pp. 235–238, 2012.
