IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 138 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 ABOUT A HUNDRED YEARS OF CREATIVITY IN DECISION MAKING Thomas L. Saaty Distinguished University Professor University of Pittsburgh saaty@katz.pitt.edu Can all the methods that people have invented to do decision making be right all the time? This may be the case for trivial decisions, but not for decisions that involve dependence and feedback and that need complete analysis of benefits, opportunities, costs and risks to get an overall justifiable outcome. According to the great philosopher Karl Popper, a theory is scientific only if it can provide grounds for its own falsifiability. In decision making, a theory would not be scientific if it could not provide examples of where it would be false if it does not work. A theory cannot universally explain everything, and must define the limits of its applicability, or give examples of where it would not work. For example, for the AHP (Analytic Hierarchy Process) we could say that just because it is a decision making theory that can be used on intangibles, the question still remains about whether the procedures of that theory can provide a correct estimate when we have tangible measurements to check against. The AHP would not work well in the hands of a neophyte who does not understand the problem being addressed. A decision making theory that claims to be valid for intangibles but not for tangibles is more like garbage in and garbage out. A decision theory should also be able to make tradeoffs possible, and thus be useful in resolving conflicts. Following is a list of only a few of the decision making methods that are circulating. The kinds of numbers they use and how they combine these numbers is a challenge. What follows is taken from a section in a forthcoming paper (Saaty & Ergu, 2015). Over the past few decades a number of MCDM methods have been developed to deal with the measurement of tangible/intangible (and conflicting) criteria and with the measurement of the alternatives of a decision with respect to these criteria (Kou et al 2013, 2014a). Some of the most popular methods include: the Analytic Hierarchy Process (AHP), the Analytic Network Process (ANP) (Saaty 1972; Saaty 1980; Saaty 2005), Additive Ratio Assessment (ARAS) (Turskis and Zavadskas, 2010), Complex Proportional Assessment of Alternatives (COPRAS) (Zavadskas and Kaklauskas, 1996), Compromise Programming (CP) (Zeleny, 1973), Decision Making Trial and Evaluation Laboratory (DEMATEL) (Gabus and Fontela, 1972), Dominance Based Rough Set Approach (DRSA) (Greco, Matarazzo et al., 1999; Greco, Matarazzo et al., 2002), Elimination Et Choice Translating Reality (ELECTRE) (Roy, Benayoun et al., 1966; Roy, 1990), Evidential Reasoning (ER) (Lowrance and Garvey, 1982), GUESS method (Buchanan, 1997), Goal programming (GP) (Lee, 1972), Grey Relational Analysis (GRA) (Deng, 1989), Inner Product of Vectors (IPV), Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH) (Bana e Costa and Vansnick, 1994), Multi-Attribute Global Inference of Quality (MAGIQ) (McCaffrey, 2009), Multi-attribute utility theory (MAUT) (Raiffa and Keeney, 1976; Humphreys 1977), Multi-attribute value theory (MAVT) (Raiffa and Keeney, 1976), Maximal Entropy Ordered Weighted Averaging mailto:saaty@katz.pitt.edu file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_49 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_50 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_52 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_62 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_68 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_69 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_12 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_14 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_15 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_48 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_47 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_31 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_5 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_5 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_29 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_9 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_9 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_2 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_33 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_46 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_23 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_46 IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 139 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 (ME-OWA) (Yager, 1988; Filev and Yager, 1995), New Approach to Appraisal (NATA), Nonstructural Fuzzy Decision Support System (NSFDSS) (Tam, Tong et al., 2002; Tam, Tong et al., 2006), Potentially all pairwise rankings of all possible alternatives (PAPRIKA) (Hansen and Ombler, 2008), Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) (Brans, Vincke et al., 1986; Brans and Mareschal, 2005), Simple Additive Weighting (SAW) (Churchman and Ackoff, 1954), Superiority and Inferiority Ranking Method (SIR) (Xu, 2001), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) (Hwang and Yoon, 1981), Utility Additive (UTA) (Jacquet-Lagreze and Siskos, 1982), Value analysis (VA) (Keen, 1981), Value engineering (VE) (Zimmerman and Hart, 1982; Parker, 1985; Mudge, 1989), VIKOR method (Opricović, 1980; Opricovic and Tzeng, 2007), Weighted product model (WPM) (Triantaphyllou and Mann, 1989),Weighted sum model (WSM) (Fishburn, 1967; Von Winterfeldt and Edwards, 1986) and on and on ad infinitum. Many of the original MCDM methods have also been extended or adapted by the creators of those theories and by researchers on these methods. With these variations we have more than a hundred MCDM methods. This wide variety of available methods bewilders potential users, resulting in the difficulty of selecting an appropriate method (Hobbs, 1986).That is, the existence of many MCDM methods itself becomes a decision problem! REFERENCES Aczel, J. and F. S. Roberts (1989). On the possible merging functions. Mathematical Social Sciences,17(3), 205-243. Bana e Costa, C. A. and J.-C. Vansnick (1994). MACBETH—An interactive path towards the construction of cardinal value functions. International Transactions in Operational Research,1(4), 489-500. Brans, J.-P. and B. Mareschal (2005). PROMETHEE methods. Multiple criteria decision analysis: state of the art surveys. New York: Springer. Brans, J.-P., P. Vincke, et al. (1986). How to select and how to rank projects: The PROMETHEE method. European Journal of Operational Research, 24(2), 228-238. Buchanan, J. T. (1997). A naive approach for solving MCDM problems: The GUESS method. Journal of the Operational Research Society,48(2), 202-206. Cho, K. T. (2003). Multicriteria decision methods: an attempt to evaluate and unify. Mathematical and computer modelling, 37(9), 1099-1119. Churchman, C. W. and R. L. Ackoff (1954). An approximate measure of value. Operations Research,2(2), 172-187. Currim, I. S. and R. K. Sarin (1984). A comparative evaluation of multi-attribute consumer preference models. Management Science,30(5), 543-561. file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_66 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_10 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_58 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_59 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_59 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_20 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_4 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_3 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_3 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_7 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_65 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_24 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_25 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_27 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_70 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_43 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_34 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_37 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_39 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_61 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_11 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_63 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_21 file:///C:/Users/saaty/Desktop/2015%20papers/Saaty-Ergu-MCDM%20paper-2-26-2015-revised%20version.doc%23_ENREF_21 IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 140 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 Deng, J.-L. (1989). Introduction to grey system theory. The Journal of Grey System, 1(1), 1-24. Filev, D. and R. R. Yager (1995). Analytic properties of maximum entropy OWA operators. Information Sciences,85(1), 11-27. Fishburn, P. C. (1967). Letter to the editor—Additive utilities with incomplete product sets: Application to priorities and assignments. Operations Research,15(3), 537-542. Gabus, A. and E. Fontela (1972). World problems, an invitation to further thought within the framework of DEMATEL. Geneva, Switzerland: Battelle Geneva Research Center. Geldermann, J. and A. Schöbel (2011). On the similarities of some Multi‐Criteria Decision Analysis Methods. Journal of Multi‐Criteria Decision Analysis, 18(3-4), 219- 230. Greco, S., B. Matarazzo, et al. (1999). Rough approximation of a preference relation by dominance relations. European Journal of Operational Research,117(1), 63-83. Greco, S., B. Matarazzo, et al. (2002). Rough approximation by dominance relations. International Journal of Intelligent Systems,17(2), 153-171. Guba, E. G. (1981). Criteria for assessing the trustworthiness of naturalistic inquiries. ECTJ, 29(2), 75-91. Guitouni, A. and J.-M. Martel (1998). Tentative guidelines to help choosing an appropriate MCDA method. European Journal of Operational Research, 109(2), 501- 521. Hajkowicz, S. and A. Higgins (2008). A comparison of multiple criteria analysis techniques for water resource management. European Journal of Operational Research,184(1), 255-265. Hanne, T. (2001). Intelligent strategies for meta multiple criteria decision making. Dordrecht: Kluwer Academic Publishers. Hansen, P. and F. Ombler (2008). A new method for scoring additive multi‐attribute value models using pairwise rankings of alternatives. Journal of Multi‐Criteria Decision Analysis,15(3‐4), 87-107. Hobbs, B. F. (1986). What can we learn from experiments in multiobjective decision analysis?, IEEE Transactions on Systems, Man and Cybernetics, 16(3), 384-394. Hobbs, B. F., V. Chankong, et al. (1992). Does choice of multicriteria method matter? An experiment in water resources planning. Water Resources Research, 28(7), 1767-1779. Humphreys, P. (1977). Application of multi-attribute utility theory. Decision making and change in human affairs. New York: Springer. IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 141 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 Hwang, C.-L. and K. Yoon (1981). Multiple attribute decision making. New York: Springer. Jacquet-Lagreze, E. and J. Siskos (1982). Assessing a set of additive utility functions for multicriteria decision-making, the UTA method. European Journal of Operational Research, 10(2), 151-164. Karni, R., P. Sanchez, et al. (1990). A comparative study of multiattribute decision making methodologies. Theory and Decision, 29(3), 203-222. Keen, P. G. (1981). Value analysis: justifying decision support systems. MIS Quarterly, 5(1), 1-15. Kou, G., Lu,Y.,Peng,Y.,and Shi, Y.(2012), Evaluation of classification algorithms using MCDM and rank correlation. International Journal of Information Technology & Decision Making, 11(1),197-225. DOI: http://dx.doi.org/10.1142/S0219622012500095 Kou, G. Ergu, D., Shang, J., (2013). Enhancing dataconsistency in decision matrix: Adapting Hadamard Model to mitigate judgement contradiction, European Journal of Operational Research, 236 (1), 261-271. DOI: http://dx.doi.org/10.1016/j.ejor.2013.11.035 Kou, G.,Lin, C. (2014a). A cosine maximization method for the priority vector derivation in AHP, European Journal, 235, 225–232. Kou, G., Peng, Y., Wang, G., (2014 b). Evaluation of clustering algorithms for financial risk analysis using MCDM methods, Journal of the Operational Research Society, 1-12. Khairullah, Z. Y. and S. Zionts (1980). An experiment with some algorithms for multiple criteria decision making. In Fandel, G., Gal, T. (Eds), Multiple criteria decision making theory and application, (150-159). Berlin: Springer. Lee, S. M. (1972). Goal programming for decision analysis. Philadelphia: Auerbach. LeShan, L. L. and H. Margenau (1982). Einstein's space and Van Gogh's sky: Physical reality and beyond. New York: Macmillan. Lowrance, J. D. and T. D. Garvey (1982). Evidential reasoning: A developing concept. Proceedings on the International Conference of Cybernetics and Society, 6-9. MacCrimmon, K. R. (1973). An overview of multiple objective decision making. In Cochrane, J.L. and Zeleny M. (Eds), Multiple Criteria Decision Making (18-44). Columbia, South Carolina: The University of South Carolina Press. McCaffrey, J. D. (2009). Using the Multi-Attribute Global Inference of Quality (MAGIQ) technique for software testing. Information Technology: New Generations, 2009. ITNG'09. Sixth International Conference. IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 142 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 Mudge, A. E. (1989). Value engineering: a systematic approach. Pittsburgh, PA: J. Pohl Associates. Olson, D. L. (2001). Comparison of three multicriteria methods to predict known outcomes. European Journal of Operational Research,130(3), 576-587. Olson, D. L. (2004). Comparison of weights in TOPSIS models. Mathematical and Computer Modelling, 40(7-8), 721-727. Opricović, S. (1980). An extension of compromise programming to the solution of dynamic multicriteria problem. In Iracki, K., Malanowski, K., Walukiewicz, S. (Eds), Optimization Techniques, (508-517), Springer. Opricovic, S. and G.-H. Tzeng (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445-455. Opricovic, S. and G.-H. Tzeng (2007). Extended VIKOR method in comparison with outranking methods. European Journal of Operational Research, 178(2), 514-529. Ozernoy, V. M. (1987). A framework for choosing the most appropriate discrete alternative multiple criteria decision-making method in decision support systems and expert systems. In Sawaragi, Y. (Ed), Toward interactive and intelligent decision Support systems (56-64). Berlin: Springer. Ozernoy, V. M. (1992). Choosing the “best” multiple criteria decision-making method. INFOR, 30(2), 159-171. Park, C. W. (1978). A conflict resolution choice model. Journal of Consumer Research, 5 124-137. Parker, D. E. (1985). Value engineering theory. Washington D.C.: Lawrence D Miles Value Foundation. Peniwati, K. (2007). Criteria for evaluating group decision-making methods. Mathematical and Computer Modelling, 46(7), 935-947. Raiffa, H. and R. Keeney (1976). Decisions with multiple objectives: Preferences and value tradeoffs. New York: Wiley. Roy, B. (1990). The outranking approach and the foundations of ELECTRE methods. In C.A. Bana e Costa (Ed.) Readings in multiple criteria decision aid (155-183). Berlin: Springer-Verlag. Roy, B., R. Benayoun, et al. (1966). ELECTRE. Paris: Société d’Economie et de Mathématique appliquées. Saaty, T. L. (1980). The Analytical Hirarchical Process. New York: Wiley. IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 143 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 Saaty, T. L. (2004). Fundamentals of the analytic network process—Dependence and feedback in decision-making with a single network. Journal of Systems Science and Systems Engineering, 13(2), 129-157. Saaty, T. L. (2005). The analytic hierarchy and analytic network processes for the measurement of intangible criteria and for decision-making. In Multiple criteria decision analysis: State of the art surveys (345-405). New York: Springer. Saaty, T. L. (2008). Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the Analytic Hierarchy/Network Process (to the memory of my beloved friend Professor Sixto Rios Garcia). Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie a-Matematicas, 102(2), 251-318. Saaty, T. L., & Ergu, D. (2015). When is a Decision Making Method Trustworthy? Criteria for Evaluating Multi-criteria Decision Making Methods. 14. Saaty, T. L. and N. Begicevic (2010). The scope of human values and human activities in decision making. Applied Soft Computing, 10(4), 963-974. Salminen, P., J. Hokkanen, et al. (1998). Comparing multicriteria methods in the context of environmental problems. European Journal of Operational Research,104(3), 485-496. Saltelli, A., M. Ratto, et al. (2008). Global sensitivity analysis: The primer. New York: Wiley-Interscience. Saltelli, A., S. Tarantola, et al. (1999). A quantitative model-independent method for global sensitivity analysis of model output. Technometrics, 41(1), 39-56. Tam, C., T. K. Tong, et al. (2002). Non-structural fuzzy decision support system for evaluation of construction safety management system. International Journal of Project Management, 20(4), 303-313. Tam, C., T. K. Tong, et al. (2006). Comparing non-structural fuzzy decision support system and analytical hierarchy process in decision-making for construction problems. European Journal of Operational Research,174(2), 1317-1324. Tam, C., T. K. Tong, et al. (2002). Site layout planning using nonstructural fuzzy decision support system. Journal of Construction Engineering and Management, 128(3), 220-231. Triantaphyllou, E. and S. H. Mann (1989). An examination of the effectiveness of multi- dimensional decision-making methods: A decision-making paradox. Decision Support Systems, 5(3), 303-312. Turskis, Z. and E. K. Zavadskas (2010). A new additive ratio assessment (ARAS) method in multicriteria decision-making. Technological and Economic Development of Economy,16(2), 159-172. IJAHP: Saaty/About a Hundred Years of Creativity in Decision Making International Journal of the Analytic Hierarchy Process 144 Vol. 7 Issue 1 2015 ISSN 1936-6744 http://dx.doi.org/10.13033/ijahp.v7i1.321 Von Winterfeldt, D. and W. Edwards (1986). Decision analysis and behavioral research. Cambridge: Cambridge University Press. Wagner, H. M. (1995). Global sensitivity analysis. Operations Research,43(6), 948-969. Xu, X. (2001). The SIR method: A superiority and inferiority ranking method for multiple criteria decision making. European Journal of Operational Research,131(3), 587-602. Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. Systems, Man and Cybernetics, IEEE Transactions 18(1), 183-190. Zanakis, S. H., A. Solomon, et al. (1998). Multi-attribute decision making: A simulation comparison of select methods. European Journal of Operational Research,107(3), 507- 529. Zavadskas, E. and A. Kaklauskas (1996). Multicriteria evaluation of building (Pastatų sistemotechninis įvertinimas). Vilnius: Technika. Zeleny, M. (1973). Compromise programming. In Cochrane J.L. and Zeleny M. (Eds), Multiple Criteria Decision Making (262-301). Columbia, South Carolina: University of South Carolina Press. Zimmerman, L. W. and G. D. Hart (1982). Value engineering: A practical approach for owners, designers, and contractors. New York: Van Nostrand Reinhold.