Abstract
The methods for Multiobjective Decision Making in the fuzzy setting in context of Investment Evaluation Problem are analyzed. The problems typical for Multiobjective Decision Making are indicated and new solutions of them are proposed as well. The problem of appropriate common scale for representation of objective and subjective criteria is solved using the simple subsethood measure based on α-cut representation of fuzzy values. To elaborate an appropriate method for aggregation of aggregating modes, we use the synthesis of the tools of Type 2 and Level 2 Fuzzy Sets. As the result the final assessments of compared alternatives are presented in form of fuzzy valued membership function defined on the support composed of considered alternatives. To compare obtained fuzzy assessments we use the probabilistic approach to fuzzy values comparison. In is shown that Investment Evaluation Problem is frequently a hierarchical one and a new method for solving such problems, different from commonly used fuzzy AHP method, is proposed.To make the presentation more transparent, it is illustrated throughout the chapter with use of two examples. The first of them is well known Tool Steel Material Selection problem which can be considered as the typical investment problem and relevant test charged by all difficulties concerned with the problems of Multiobjective Decision Making. The next example is a simplified investment project evaluation problem we have used to show that even when project’s estimation is based on the budgeting, i.e., only financial parameters are taking into account, we are dealing with multiple-criteria task in the fuzzy setting.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bana, E., Costa, C.A.: Reading in multiple criteria decision aid. Springer, Berlin (1990)
Bana, E., Costa, C.A., Stewart, T.J., Vansnick, J.C.: Multicriteria decision analysis: Some thoughts based on the tutorial and discussion session of the ESIGMA meetings. European Jurnal of Operational Research 99, 28–37 (1997)
Beynon, M., Peel, M.J., Tang, Y.C.: The application of fuzzy decision tree analysis in an exposition of the antecedents of audit fees. Omega 32, 231–244 (2004)
Borisov, A.N., Korneeva, G.V.: Linguistic approach to decision making model building under uncertainty: Methods of decision making under uncertainty. Riga 7, 4–6 (1980)
Chanas, S., Delgado, M., Verdegay, J.L., Vila, M.A.: Ranking fuzzy interval numbers in the setting of random sets. Information Sciences 69, 201–217 (1993)
Chang, P.T., Lee, E.S.: The estimation of normalized fuzzy weights. Computers and Mathematics with Applications 29, 21–42 (1995)
Chen, C., Klein, C.M.: An efficient approach to solving fuzzy MADM problems. Fuzzy Sets and Systems 88, 51–67 (1997)
Chen-Tung, C.: A fuzzy approach to select the location of distribution center. Fuzzy sets and systems 118, 65–73 (2001)
Choi, D.Y., Oh, K.W.: Asa and its application to multi-criteria decision making. Fuzzy Sets and Systems 114, 89–102 (2000)
Choo, E.U., Schoner, B., Wedley, W.C.: Interpretation of criteria weights in multicriteria decision making. Computers and Industrial Engineering 37, 527–541 (1999)
Chu, A., Kalaba, R., Springarn, R.A.: Comparison of two methods for determining the weights of belonging to fuzzy sets. Journal Of Optimization Theory And Applications 27, 531–538 (1979)
Delgado, M., Verdegay, J.L., Vila, M.A.: Linguistic decision making models. Internat. J. Intell. Systems 7, 479–492 (1992)
Dimova, L., Sevastianov, D., Sevastianov, P.: Application of fuzzy sets theory, methods for the evaluation of investment efficiency parameters. Fuzzy Economic Review 5, 34–48 (2000)
Doumpos, M., Kosmidou, K., Baourakis, G., Zopounidis, C.: Credit risk assessment using a multicriteria hierarchical discrimination approach: A comparative analysis. European Journal of Operational Research 1389, 392–412 (2002)
Dubois, D., Koenig, J.L.: Social choice axioms for fuzzy set aggregation. Fuzzy Sets and Systems 43, 257–274 (1991)
Dyckhoff, H.: Basic concepts for theory of evaluation: hierarchical aggregation via autodistributive connectives in fuzzy set theory. European Journal of Operational Research 20, 221–233 (1985)
Dymova, L.: A constructive approach to managing fuzzy subsets of type 2 in decision making. TASK Quarterly 7, 157–164 (2003)
Dymova, L., Rog, P., Sewastianow, P.: Hyperfuzzy estimations of financial parameters. In: Proceeding of the 2th International Conference on Mathematical Methods in Finance and Econometrics, pp. 78–84 (2002)
Dymova, L., Sewastianow, P., Sewastianow, D.: MCDM in a fuzzy setting: investment projects assessment application. International Journal of Production Economics 100(1), 10–29 (2006)
Gottwald, S.: Set theory for fuzzy sets of higher level. Fuzzy Sets and Systems 2, 125–151 (1979)
Hauke, W.: Using Yager’s t-norms for aggregation of fuzzy intervals. Fuzzy Sets and Systems 101, 59–65 (1999)
Helmer, O.H.: The Delphi Method for Systematizing Judgments about the Future. Institute of Government and Public Aairs, University of California (1966)
Herrera, F., Herrera-Vieda, E., Verdegay, J.L.: Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and Systems 79(2), 175–190 (1996)
Kahraman, C., Ruan, D., Tolga, E.: Capital budgeting techniques using discounted fuzzy versus probabilistic cash flows. Information Sciences 142, 57–76 (2002)
Karnik, N.N., Mendel, J.M.: Application of type-2 fuzzy logic systems to forecasting of time-series. Information Sciences 120, 89–111 (1999)
Kaufmann, A., Gupta, M.: Introduction to fuzzy arithmetic-theory and applications. Van Nostrand Reinhold, New York (1985)
Kosko, B.: Fuzzy entropy and conditioning. Information Science 30, 165–174 (1986)
Krishnapuram, R., Keller, J.M., Ma, Y.: Quantitative analysis of properties and spatial relations of fuzzy image regions. IEEE Trans. Fuzzy Systems 1, 222–233 (1993)
Kuchta, D.: Fuzzy capital budgeting. Fuzzy Sets and Systems 111, 367–385 (2000)
Kundu, S.: Min-transitivity of fuzzy leftness relationship and its application to decision making. Fuzzy Sets and Systems 86(5), 357–367 (1997)
Kundu, S.: Preference relation on fuzzy utilities based on fuzzy leftness relation on interval. Fuzzy Sets and Systems 97, 183–191 (1998)
Lee, H.: Group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in software development. Fuzzy Sets and Systems 80(3), 261–271 (1996)
Li, Q., Sterali, H.D.: An approach for analyzing foreign direct investment projects with application to China’s Tumen River Area development. Computers & Operations Research 3, 1467–1485 (2000)
Liu, D., Stewart, T.J.: Object-oriented decision support system modeling for multicriteria decision making in natural resource managment. Computers & Operations Research 31, 985–999 (2004)
Lootsma, F.A.: Performance evaluation of non-linear optimization methods via multi-criteria decision analysis and via linear model analysis. In: Powell, M.J.D. (ed.) Nonlinear Optimization (1981)
Lopes, M., Flavel, R.: Project appraisal-a framework to assess non-financial aspects of projects during the project life cycle. International Journal of Project Management 16, 223–233 (1998)
Mao-Jiun, J.W., Tien-Chien, C.: Tool steel materials selection under fuzzy environment. Fuzzy Sets and Systems 72(3), 263–270 (1995)
Masaharu, M., Kokichi, T.: Fuzzy sets of type II under algebraic product and algebraic sum. Fuzzy Sets and Systems 5, 277–290 (1981)
Migdalas, A., Pardalos, P.M.: Editorial: hierarchical and bilevel programming. J. Global Optimization 8(3), 209–215 (1996)
Mikhailov, L.: Deriving priorities from fuzzy pairwise comparison judgments. Fuzzy Sets and Systems 134, 365–385 (2003)
Miller, G.A.: The magical number seven plus or minus two: some limits on our capacity for processing information. Psychological Review 63, 81–97 (1956)
Milner, P.M.: Physiological psychology. Holt, New York (1970)
Mitra, G.: Mathematical models for decision support. Springer, Berlin (1988)
Mohamed, S., McCowan, A.K.: Modelling project investment decisions under uncertainty using possibility theory. International Journal of Project Management 19, 231–241 (2001)
Nakamura, K.: Preference relations on set of fuzzy utilities as a basis for decision making. Fuzzy Sets and Systems 20, 147–162 (1986)
Pardalos, P.M., Siskos, Y., Zopounidis, C.: Advances in multicriteria analysis. Kluwer Academic Publishers, Dordrecht (1995)
Peneva, V., Popchev, I.: Properties of the aggregation operators related with fuzzy relations. Fuzzy Sets and Systems 139, 615–633 (2003)
Ribeiro, R.A.: Fuzzy multiple attribute decision making: a review and new preference elicitation techniques. Fuzzy Sets and Systems 78, 155–181 (1996)
Roubens, M.: Fuzzy sets and decision analysis. Fuzzy Sets and Systems 90, 199–206 (1997)
Roy, B.: Multicriteria methodology for decision aiding. Kluwer Academic Publlishers, Boston (1996)
Saaty, T.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 234–281 (1977)
Sengupta, A., Pal, T.K.: On comparing interval numbers. European Journal of Operational Research 127, 28–43 (2000)
Sevastianov, P., Tumanov, N.: Multi-criteria identification and optimization of technological processes. Science and Engineering, Minsk (1990)
Sewastianow, P., Jończyk, M.: Bicriterial fuzzy portfolio selection. Operations Research And Decisions 4, 149–165 (2003)
Sewastianow, P., Rog, P.: A probabilistic approach to fuzzy and interval ordering, Task Quarterly. Special Issue Artificial and Computational Intelligence 7(1), 147–156 (2002)
Sewastianow, P., Rog, P.: Fuzzy modeling of manufacturing and logistic systems. Mathematics and Computers in Simulation 63, 569–585 (2003)
Sewastianow, P., Rog, P.: Two-objective method for crisp and fuzzy interval comparison in Optimization. Computers & Operations Research 33, 115–131 (2006)
Sewastianow, P., Róg, P., Venberg, A.: The constructive numerical method of interval comparison. In: Proceeding of Int. Conf. PPAM 2001, Naleczow (2001)
Shih, H.S., Lee, E.: Compensatory fuzzy multiple level decision making. Fuzzy Sets and Systems 114, 71–87 (2000)
Shyi-Ming, C.: A new method for tool steel materials selection under fuzzy environment. Fuzzy sets and systems 92(3), 265–274 (1997)
Silvert, W.: Ecological impact classification with fuzzy sets. Ecological Moddeling (1997)
Steuer, R.E.: Multiple criteria optimisation: theory, computation and application. Wiley, New York (1986)
Steuer, R.E., Na, P.: Multiple criteria decision making combined with finance. A categorical bibliographic study. European Journal of Operational Research 150, 496–515 (2003)
Stewart, T.J.: A critical survey on the status of multiple criteria decision making. OriON 5, 1–23 (1989)
Tong, M., Bonissone, P.P.: A linguistic approach to decision making with fuzzy sets. IEEE Trans. Systems Man Cybernet 10, 716–723 (1980)
Tre, G., Caluwe, R.: Level-2 fuzzy sets and their usefulness in object-oriented database modeling. Fuzzy Sets and Systems 140, 29–49 (2003)
Valls, A., Torra, V.: Using classification as an aggregation tool in MCDM. Fuzzy Sets and Systems 115, 159–168 (2000)
Wadman, D., Schneider, M., Schnaider, E.: On the use of interval mathematics in fuzzy expert system. International Journal of Intelligent Systems 9, 241–259 (1994)
Wagenknecht, M., Hartmann, K.: On fuzzy rank ordering in polyoptimisation. Fuzzy Sets and Systems 11, 253–264 (1983)
Wang, W.C.: Supporting project cost threshold decisions via a mathematical cost model. International Journal of Project Management 22, 99–108 (2004)
Wang, X., Kerre, E.E.: Reasonable properties for the ordering of fuzzy quantities (I) , (II). Fuzzy Sets and Systems 112, 375–405 (2001)
Ward, T.L.: Discounted fuzzy cash flow analysis. In: Proceeding of the 1985 Fall Industrial Engineering Conference, pp. 476–481 (1985)
Weck, M., Klocke, F., Schell, H., Ruenauver, E.: Evaluating alternative production cycles using the extended fuzzy AHP method. European Journal of Operational Research 100, 351–366 (1997)
Yager, R.R.: Multiple objective decision-making using fuzzy sets. International Journal of Man-Machine Studies 9, 375–382 (1979)
Yager, R.R.: A foundation for a theory of possibility. Journal of Cybernetics 10, 177–209 (1980)
Yager, R.R.: Fuzzy subsets of type II in decisions. Journal of Cybernetics 10, 137–159 (1980)
Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems Man and Cybern 18(1), 183–190 (1988)
Yager, R.R., Detyniecki, M., Bouchon-Meunier, B.: A context-dependent method for ordering fuzzy numbers using probabilities. Information Sciences 138, 237–255 (2001)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–358 (1965)
Zadeh, L.A.: Quantitative fuzzy semantics. Information Sciences 3, 177–200 (1971)
Zadeh, L.A.: Fuzzy logic and its application to approximate reasoning. Information Processing 74, 591–594 (1974)
Zadeh, L.A.: The Concept of linguistic Variable and its Application to approximate Reasoning- I. Information Sciences 8, 199–249 (1975)
Zimmerman, H.J.: Fuzzy Sets, Decision-Making and Expert Systems. Kluwer Academic Publishers, Dordrecht (1987)
Zimmerman, H.J., Zysno, P.: Latent connectives in human decision making. Fuzzy Sets and Systems 4, 37–51 (1980)
Zimmerman, H.J., Zysno, P.: Decision and evaluations by hierarchical aggregation of information. Fuzzy Sets and Systems 104, 243–260 (1983)
Zollo, G., Iandoli, L., Cannavacciuolo, A.: The performance requirements analysis with fuzzy logic. Fuzzy economic review 4, 35–69 (1999)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dymova, L., Sevastjanov, P. (2008). Fuzzy Multiobjective Evaluation of Investments with Applications. In: Kahraman, C. (eds) Fuzzy Engineering Economics with Applications. Studies in Fuzziness and Soft Computing, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70810-0_15
Download citation
DOI: https://doi.org/10.1007/978-3-540-70810-0_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70809-4
Online ISBN: 978-3-540-70810-0
eBook Packages: EngineeringEngineering (R0)