Fuzzy Optimization and Decision Making

, Volume 12, Issue 4, pp 357–372 | Cite as

Fuzzy optimality based decision making under imperfect information without utility

  • Rafik A. Aliev
  • Witold Pedrycz
  • Akif V. Alizadeh
  • Oleg H. Huseynov


In the realm of decision making under uncertainty, the general approach is the use of the utility theories. The main disadvantage of this approach is that it is based on an evaluation of a vector-valued alternative by means of a scalar-valued quantity. This transformation is counterintuitive and leads to loss of information. The latter is related to restrictive assumptions on preferences underlying utility models like independence, completeness, transitivity etc. Relaxation of these assumptions results into more adequate but less tractable models. In contrast, humans conduct direct comparison of alternatives as vectors of attributes’ values and don’t use artificial scalar values. Although vector-valued utility function-based methods exist, a fundamental axiomatic theory is absent and the problem of a direct comparison of vectors remains a challenge with a wide scope of research and applications. In the realm of multicriteria decision making there exist approaches like TOPSIS and AHP to various extent utilizing components-wise comparison of vectors. Basic principle of such comparison is the Pareto optimality which is based on a counterintuitive assumption that all alternatives within a Pareto optimal set are considered equally optimal. The above mentioned mandates necessity to develop new decision approaches based on direct comparison of vector-valued alternatives. In this paper we suggest a fuzzy Pareto optimality (FPO) based approach to decision making with fuzzy probabilities representing linguistic decision-relevant information. We use FPO concept to differentiate “more optimal” solutions from “less optimal” solutions. This is intuitive, especially when dealing with imperfect information. An example is solved to show the validity of the suggested ideas.


Decision making Imprecise probabilities Fuzzy \(k\)-optimality  Degree of optimality 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Rafik A. Aliev
    • 1
  • Witold Pedrycz
    • 2
    • 3
  • Akif V. Alizadeh
    • 4
  • Oleg H. Huseynov
    • 4
  1. 1.Azerbaijan State Oil AcademyBakuAzerbaijan
  2. 2.Department of Electrical and Computer EngineeringUniversity of AlbertaEdmontonCanada
  3. 3.System Research InstitutePolish Academy of SciencesWarsawPoland
  4. 4.Azerbaijan Association of “Zadeh’s Legacy and Artificial Intelligence”BakuAzerbaijan

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