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Optimization of Linear Objective Function Under \(\min -\)Probabilistic Sum Fuzzy Linear Equations Constraint

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Recent Contributions in Intelligent Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 657))

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Abstract

We present here linear optimization problem resolution, when the cost function is subject to fuzzy linear systems of equations as constraint.

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References

  1. Chen, L., Wang, P.: Fuzzy relational equations (I): the general and specialized solving algorithms. Soft Comput. 6, 428–435 (2002)

    Article  MATH  Google Scholar 

  2. De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) Handbooks of Fuzzy Sets Series: Fundamentals of Fuzzy Sets, vol. 1, pp. 291–340. Kluwer Academic Publishers (2000)

    Google Scholar 

  3. Di Nola, A., Pedrycz, W., Sessa, S., Sanchez, E.: Fuzzy Relation Equations and Their Application to Knowledge Engineering. Kluwer Academic Press, Dordrecht (1989)

    Book  MATH  Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA (1979)

    MATH  Google Scholar 

  5. Grätzer, G.: General Lattice Theory. Akademie-Verlag, Berlin (1978)

    Book  MATH  Google Scholar 

  6. Guu, S.M., Wu, Y.-K.: Minimizing a linear objective function with fuzzy relation equation constraints. Fuzzy Optim. Decis. Making 4(1), 347–360 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Klir, G.J., Clair, U.H.S., Yuan, B.: Fuzzy Set Theory Foundations and Applications. Prentice Hall PRT (1977)

    Google Scholar 

  8. Loetamonphong, J., Fang, S.-C.: An efficient solution procedure for fuzzy relational equations with max-product composition. IEEE Trans. Fuzzy Syst. 7(4), 441–445 (1999)

    Article  Google Scholar 

  9. MacLane, S., Birkhoff, G.: Algebra. Macmillan, New York (1979)

    MATH  Google Scholar 

  10. Peeva, K.: Resolution of Fuzzy relational equations—method, algorithm and software with applications, information sciences. Special Issue (2011). doi:10.1016/j.ins.2011.04.011

  11. Peeva, K.: Inverse Problem Resolution for min-probabilistic sum Fuzzy relational equations—method and algorithm. In: 2012 VIth International IEEE Conference “Intelligent Systems”, vol. 1, pp. 489– 494. Sofia 6–8 Sept. (2012). ISBN 978-1-4673-2277-5

    Google Scholar 

  12. Peeva, K., Kyosev, Y.: Fuzzy relational calculus-theory, applications and software (with CD-ROM). In the Series Advances in Fuzzy Systems—Applications and Theory, vol. 22. World Scientific Publishing Company (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8, Kl. Ohridski St. Sofia, 1000, Sofia, Bulgaria

    Ketty Peeva

Authors
  1. Ketty Peeva
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Correspondence to Ketty Peeva .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vassil Sgurev

  2. Machine Intelligence Institute, Hagan School of Business, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  4. Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

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Peeva, K. (2017). Optimization of Linear Objective Function Under \(\min -\)Probabilistic Sum Fuzzy Linear Equations Constraint. In: Sgurev, V., Yager, R., Kacprzyk, J., Atanassov, K. (eds) Recent Contributions in Intelligent Systems. Studies in Computational Intelligence, vol 657. Springer, Cham. https://doi.org/10.1007/978-3-319-41438-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-41438-6_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41437-9

  • Online ISBN: 978-3-319-41438-6

  • eBook Packages: EngineeringEngineering (R0)

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