Reduction in the Number of Comparisons Required to Create Matrix of Expert Judgment in the Comet Method

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Multi-criteria decision-making (MCDM) methods are associated with the ranking of alternatives based on expert judgments made using a number of criteria. In the MCDM field, the distance-based approach is one popular method for receiving a final ranking. One of the newest MCDM method, which uses the distance-based approach, is the Characteristic Objects Method (COMET). In this method, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic ob jects and their values. For this purpose, the domain and fuzzy numbers set for all the considered criteria are determined. The characteristic objects are obtained as the combination of the crisp values of all the fuzzy numbers. The preference values of all the characteristic ob ject are determined based on the tournament method and the principle of indifference. Finally, the fuzzy model is constructed and is used to calculate preference values of the alternatives. In this way, a multi-criteria model is created and it is free of rank reversal phenomenon. In this approach, the matrix of expert judgment is necessary to create. For this purpose, an expert has to compare all the characteristic ob jects with each other. The number of necessary comparisons depends squarely to the number of ob jects. This study proposes the improvement of the COMET method by using the transitivity of pairwise comparisons. Three numerical examples are used to illustrate the efficiency of the proposed improvement with respect to results from the original approach. The proposed improvement reduces significantly the number of necessary comparisons to create the matrix of expert judgment.

[1] Afshari A., Mojahed M., Yusuff R., Simple Additive Weighting approach to Personnel Selection problem, International Journal of Innovation, Management and Technology, 1, 5, 511-515, 2010.

[2] Salih Y., See O., Ibrahim R., Yussof S., Iqbal A., A Novel Noncooperative Game Competing Model Using Generalized Simple Additive Weighting Method to Perform Network Selection in Heterogeneous Wireless Networks, International Journal of Communication Systems, first published online, 3 FEB 2014.

[3] Huang Y.S., Chang W.C., Li W.H., Lin Z.L., Aggregation of utility-based individual preferences for group decision-making, European Journal of Operational Research, 229, 2, 462-469, 2013.

[4] French S., Decision behavior, analysis and support, Cambridge, New York, 2013.

[5] Kontos T.D., Komilis D.P., Halvadakis C.P., Siting MSW landfills with a spatial multiple criteria analysis methodoloy, Waste Management, 25, 8, 818-832, 2005.

[6] Simanaviciene R., Ustinovichius L., Sensitivity analysis for multiple criteria decision making methods: TOPSIS and SAW, Procedia - Social and Behavioral Sciences, 2, 6, 7743-7744, 2010.

[7] Zavadskas E.K., Turskis Z., Antucheviciene J., Za-karevicius A., Optimization of Weighted Aggregated Sum Product Assessment, Electronics & Electrical Engineering, 122, 3-6, 2012.

[8] Triantaphyllou E., Multi-Criteria Decision Making Methods, Springer, New York, 2000.

[9] Savitha K., Chandrasekar C., Vertical Handover decision schemes using SAW and WPM for Network selection in Heterogeneous Wireless Networks, Global Journal of Computer Science and Technology, 11, 9, 19-24, 2011. [10] Brito A.J., de Almeida A.T., Mota C.M., A mul- ticriteria model for risk sorting of natural gas pipelines based on ELECTRE TRI integratingutility theory, European Journal of Operational Research, 200, 3, 812-821, 2010.

[11] Figueira J., Greco S., Ehrgott M., Multiple Criteria Decision Analysis: State of the Art Surveys, Springer, New York, 2004.

[12] Hatami-Marbini A., Tavana M., An extension of the ELECTRE I method for group decision-making under a fuzzy environment, Omega, 39, 4, 373-386, 2011.

[13] Montazer G.A., Saremi H.Q., Ramezani M., Design a new mixed expert decision aiding system using fuzzy ELECTRE III method for vendor selection, Expert Systems with Applications, 36, 8, 10, 83710, 847, 2009.

[14] Mousseau V., Dias L., Valued outranking relations in ELECTRE providing manageable disaggregation procedures, European Journal of Operational Research, 156, 2, 467-482, 2004.

[15] Blair A.R., Mandelker G.N., Saaty T.L., Whitaker R., Forecasting the resurgence of the u.s. economy in 2010: An expert judgment approach, SocioEconomic Planning Sciences, 44, 3, 114-121, 2010.

[16] Dong Y., Zhang G., Hong W.C., Xu Y., Consensus models for AHP group decision making under row geometric mean prioritization method, Decision Support Systems, 49, 3, 281-289, 2010.

[17] Karami E., Appropriateness of farmers adoption of irrigation methods: The application of the AHP model, Agricultural Systems, 87, 1, 101-119, 2006.

[18] Saaty T.L., Decision making the analytic hierarchy and network processes (AHP/ANP), Journal of Systems Science and Systems Engineering, 13, 1, 1-35, 2004.

[19] Saaty T.L., 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, 46, 78, 860-891, 2007.

[20] Saaty T.L., Decision making the analytic hierarchy and network processes (AHP/ANP), International Journal Services Sciences, 1,1, 83-98, 2008.

[21] Saaty T.L., Brandy C., The encyclicon, volume 2: a dictionary of complex decisions using the analytic network process, RWS Publications, Pittsburgh, 2009.

[22] Saaty T.L., Shang J.S., An innovative orders-of-magnitude approach to AHP-based mutli-criteria decision making: Prioritizing divergent intangible humane acts, European Journal of Operational Research, 214, 3, 703-715, 2011.

[23] Saaty T.L., Tran L.T., On the invalidity of fuzzi-fying numerical judgments in the analytic hierarchy process, Mathematical and Computer Modelling, 46, 78, 962-975, 2007.

[24] Hsu T.H., Hung L.C., Tang J.W., A hybrid ANP evaluation model for electronic service quality, Applied Soft Computing, 12, 1, 72-81, 2012.

[25] Kirytopoulos K., Voulgaridou D., Platis A., Leopou-los V., An effective markov based approach for calculating the limit matrix in the analytic network process, European Journal of Operational Research, 214, 1, 85-90, 2011.

[26] Niemira M.P., Saaty T.L., An analytic network process model for financial-crisis forecasting, International Journal of Forecasting, 20, 4, 573-587, 2004.

[27] Wang Y.L., Tzeng G.H., Brand marketing for creating brand value based on a MCDM model combining DEMATEL with ANP and VIKOR methods, Expert Systems with Applications, 39, 5, 5600-5615, 2012.

[28] Yang J.L., Tzeng G.H., An integrated MCDM technique combined with DEMATEL for a novel cluster-weighted with ANP method, Expert Systems with Applications, 38, 3, 1410-1424, 2011.

[29] Kwanyoung I., Hyunbo C., A systematic approach for developing a new business model using morphological analysis and integrated fuzzy approach, Expert Systems with Applications, 40, 11, 4463-4477, 2013.

[30] Kuo R.J., Wu Y.H., Hsu T.S., Integration of fuzzy set theory and TOPSIS into HFMEA to improve outpatient service for elderly patients in Taiwan, Journal of the Chinese Medical Association, 75, 7, 341-348, 2012.

[31] La Scalia G., Aiello G., Rastellini C., Micale R., Cicalese L., Multi-criteria decision making support system for pancreatic islet transplantation, Expert Systems with Applications, 38, 4, 3091-3097, 2011.

[32] Taleizadeh A.A., Akhavan Niaki S.T., Aryanezhad M.B., A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multicon-straint inventory control systems with random fuzzy replenishments, Mathematical and Computer Modeling, 49, 5-6, 1044-1057, 2009.

[33] Kim Y., Chung E.S., Jun S.M., Kim S.U., Prioritizing the best sites for treated wastewater instream use in an urban watershed using fuzzy TOPSIS, Resources Conservation and Recycling, 73, 23-32, 2013.

[34] Sun Y.F., Liang Z.S., Shan C.J., Viernstein H., Unger F., Comprehensive evaluation ofnatural an-tioxidants and antioxidant potentials in Ziziphus jujuba Mill. var. spinosa (Bunge) Huex H. F. Chou fruits based on geographical origin by TOPSIS method, Food Chemistry, 124, 4, 1612-1619, 2011.

[35] Sałabun W., The mean error estimation of TOP-SIS method using a fuzzy reference models, Journal of Theoretical and Applied Computer Science, 7, 3, 40-50, 2013.

[36] Eppe S., De Smet Y., Approximating Promethee Il’s net flow scores by piecewise linear value functions, European Journal of Operational Research, 233, 3, 651-659, 2014.

[37] Amaral T.M., Costa A.P.C., Improving decision-making and management of hospital resources: An application of the PROMETHEE II method in an Emergency Department, Operations Research for Health Care, 3, 1, 1-6, 2014.

[38] Makan A., Mountadar M. Sustainable management of municipal solid waste in Morocco: Application of PROMETHEE method for choosing the optimal management scheme, African Journal of Environmental and Waste Management, 1, 1, 1-13, 2013.

[39] Ziolkowska J.R., Evaluating sustainability of biofuels feedstocks: A multi-objective framework for supporting decision making, Biomass and Bioenergy, 55, 425-440, 2013.

[40] Zadeh L.A., Fuzzy sets, Information and Control, 8, 3, 338-353, 1965.

[41] Zimmermann H.J., Fuzzy Set Theory - and Its Applications, Kluwer, Boston, 2001.

[42] Kaufmann A., Gupta M.M., Fuzzy mathematical models in engineering and management science, Elsevier Science Publishers, Amsterdam, Netherlands, 1988.

[43] Piegat A., Fuzzy Modeling and Control, Springer-Verlag, New York, 2001.

[44] Kumar A., Singh P., Kaur A., Kaur P., RM approach for ranking of generalized trapezoidal Fuzzy numbers, Fuzzy Information and Engineering, 2, 1, 37-47, 2010.

[45] Pedrycz W., Ekel P., Parreiras R., Fuzzy Multicri-teria Decision-making: Models, Methods and Applications, John Wiley & Sons, Chichester, 2011.

[46] Wang G., Wang H., Non-Fuzzy versions of Fuzzy reasoning in classical logics, Information Sciences, 138, 1-4, 211-236, 2001.

[47] Ross T.J., Fuzzy Logic with Engineering Applications, John Wiley & Sons, Chichester, 2010.

[48] Piegat A., Sałabun W., Nonlinearity of human mul-ticriteria in decision-making, Journal of Theoretical and Applied Computer Science, 6, 3, 3-49, 2012.

[49] Sałabun W., The use of Fuzzy logic to evaluate the nonlinearity of human multi-criteria used in decision making, Przegląd Elektrotechniczny, 88, 10b, 235-238, 2012.

[50] Xu Y., Gupta J.N.D., Wang H., The ordinal consistency ofan incomplete reciprocal preference relation, Fuzzy Sets and Systems, 246, 62-77, 2014.

Management and Production Engineering Review

The Journal of Production Engineering Committee of Polish Academy of Sciences and Polish Association for Production Management

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CiteScore 2016: 0.48

SCImago Journal Rank (SJR) 2016: 0.126
Source Normalized Impact per Paper (SNIP) 2016: 0.551


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