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Soft Computing as Transdisciplinary Science and Technology pp 83–92Cite as

Fuzzy Preference Relations and Multiobjective Decision Making

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Part of the book series: Advances in Soft Computing ((AINSC,volume 29))

Summary

Analysis of < X, R > models is considered as part of a general approach to solving optimization problems with fuzzy coefficients. This approach consists in formulating and solving one and the same problem within the framework of mutually interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. The use of the approach allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty regions is based on reduction of the problem to models of multiobjective decision-making in a fuzzy environment with the use of fuzzy preference relation techniques for analyzing these models. Three techniques are considered in the paper. The first technique is of a lexicographic character and consists in step-by-step introducing criteria (fuzzy preference relations). The second technique is based on building of a membership function of a subset of nondominated alternatives with simultaneous considering all preference relations. The third technique is related to aggregating membership functions of subsets of nondominated alternatives corresponding to each preference relation. The results of the paper are of a universal character and are already being used to solve problems of power engineering and management.

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References

  1. Zimmermann, H.-J.: Fuzzy Set Theory and Its Application, Kluwer Academic Publishers, Boston Dordrecht London (1990).

    Google Scholar 

  2. Ekel, P.Ya.: Fuzzy Sets and Models of Decision Making. Int. J. Comp. Math. Appl. 44 (2002) 863–875.

    Article  MATH  MathSciNet  Google Scholar 

  3. Ekel, P., Pedrycz, W., Schinzinger, R.: A General Approach to Solving a Wide Class of Fuzzy Optimization Problems. Fuzzy Sets Syst. 97 (1998) 49–66.

    Article  MATH  MathSciNet  Google Scholar 

  4. Ekel, P.Ya., Galperin, E.A.: Box-triangular Multiobjective Linear Programs for Resource Allocation with Application to Load Management and Energy Market Problems. Math. Comp. Mod. 37 (2003) 1–17.

    Article  MATH  MathSciNet  Google Scholar 

  5. Carvalho, M.B., Ekel, P.Ya., Martins, C.A.P.S., Pereira Jr., J.G.: Fuzzy Set Based Multiobjective Allocation of Resources: Solution Algorithms and Applications. Nonlin. Anal., accepted.

    Google Scholar 

  6. Ekel, P.Ya.: Models and Methods of Discrete Optimization of Power Supply Systems (in Russian). KPI, Kiev (1990).

    Google Scholar 

  7. Chen, S.J., Hwang, C.L.: Fuzzy Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, Berlin Heidelberg New York (1992).

    MATH  Google Scholar 

  8. Lee-Kwang, H.: A Method for Ranking Fuzzy Numbers and Its Application to Decision-Making. IEEE Trans. Fuzzy Syst. 7 (1999) 677–685.

    Article  Google Scholar 

  9. Wang, X., Kerre, E.E.: Reasonable Properties for the Ordering of Fuzzy Quantities (I), (II). Fuzzy Sets Syst. 118 (2001) 375–405.

    Article  MATH  MathSciNet  Google Scholar 

  10. Horiuchi, K., Tamura, N.: VSOP Fuzzy Numbers and Their Fuzzy Ordering. Fuzzy Sets Syst. 93 (1998) 197–210.

    Article  MATH  MathSciNet  Google Scholar 

  11. Orlovsky, S.A.: Problems of Decision Making with Fuzzy Information (in Russian). Nauka, Moscow (1981).

    Google Scholar 

  12. Galperin, E.A., Ekel, P.Ya.: Synthetic Realization Approach to Fuzzy Global Optimization via Gamma Algorithm. Mathematical and Computer Modelling, accepted.

    Google Scholar 

  13. Cheng, C.H.: A New Approach for Ranking Fuzzy Numbers by Distance Methods. Fuzzy Sets Syst. 95 (1998) 307–313.

    Article  MATH  Google Scholar 

  14. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Boston Dordrecht London (1994).

    MATH  Google Scholar 

  15. Orlovski, S.A.: Decision Making with a Fuzzy Preference Relation. Fuzzy Sets Syst. 3 (1978) 155–167.

    Article  Google Scholar 

  16. De Baets, B., Van de Walle, B., Kerre E.E.: Fuzzy Preference Structures Without Incomparability. Fuzzy Sets Syst., 76 (1995) 333–348.

    Article  MATH  Google Scholar 

  17. Barrett, C.R., Pattanaik, P.K., Salles, M.: On Choosing Rationally When Preferences Are Fuzzy. Fuzzy Sets Syst., 34 (1990) 197–212.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate Program in Electrical Engineering, Pontifical Catholic University of Minas Gerais, Ave. Dom José Gaspar, 500, 30535-610, Belo Horizonte — MG, Brazil

    Petr Ekel & Carlos Martins

  2. Department of Electronics Engineering and Telecommunication, Pontifical Catholic University of Minas Gerais, Ave. Dom José Gaspar, 500, 30535-610, Belo Horizonte — MG, Brazil

    Cláudio Campos & Fernando Schuffner Neto

  3. Department of Electronics Engineering, Federal University of Minas Gerais, Ave. Antônio Carlos, 6627, 31270-010, Belo Horizonte — MG, Brazil

    Reinaldo Palhares

Authors
  1. Petr Ekel
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  2. Carlos Martins
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  3. Cláudio Campos
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  4. Fernando Schuffner Neto
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  5. Reinaldo Palhares
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, Oklahoma State University, North Greenwood Avenue 700, 74106, Tulsa, USA

    Ajith Abraham

  2. Dept. of Computer Science and Systems Engineering, Muroran Institute of Technology, Mizumoto-cho 27-1, 050-8585, Muroran, Hokkaido, Japan

    Yasuhiko Dote

  3. Dept. of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, 464-8601, Nagoya, Aichi-ken, Japan

    Takeshi Furuhashi

  4. Institut für Sicherheits-/Prüftechnik, Fraunhofer IPK Berlin, Pascalstr. 8-9, 10587, Berlin, Germany

    Mario Köppen

  5. Division of Complex Systems Technology Graduate School of Engineering, University of Hokkaido, N-13, W-8 060 KITA-KU, Sapporo, Japan

    Azuma Ohuchi

  6. PRESTO Japan Science & Technology Corp. GSSM, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, 12-0012, Tokyo, Japan

    Yukio Ohsawa

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© 2005 Springer-Verlag Berlin Heidelberg

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Ekel, P., Martins, C., Campos, C., Neto, F.S., Palhares, R. (2005). Fuzzy Preference Relations and Multiobjective Decision Making. In: Abraham, A., Dote, Y., Furuhashi, T., Köppen, M., Ohuchi, A., Ohsawa, Y. (eds) Soft Computing as Transdisciplinary Science and Technology. Advances in Soft Computing, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32391-0_16

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  • DOI: https://doi.org/10.1007/3-540-32391-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25055-5

  • Online ISBN: 978-3-540-32391-4

  • eBook Packages: EngineeringEngineering (R0)

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