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Bipolar Max-Product Fuzzy Relation Equations with the Product Negation

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Trends in Mathematics and Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 796))

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Abstract

This paper will study the bipolar fuzzy relation equation based on the max-product composition and the adjoint negation operator obtained from the product residuated implication. Interesting properties and different examples of this bipolar max-product fuzzy relation equation will be introduced.

Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (ERDF) project TIN2016-76653-P, and by the research and transfer program of the University of Cádiz.

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References

  1. Bělohlávek, R.: Sup-t-norm and inf-residuum are one type of relational product: Unifying framework and consequences. Fuzzy Sets Syst. 197, 45–58 (2012)

    Article  MathSciNet  Google Scholar 

  2. Cornejo, M., Lobo, D., Medina, J.: Bipolar fuzzy relation equations based on product t-norm. In: 2017 IEEE International Conference on Fuzzy Systems. IEEE Press (2017)

    Google Scholar 

  3. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: A comparative study of adjoint triples. Fuzzy Sets Syst. 211, 1–14 (2013)

    Article  MathSciNet  Google Scholar 

  4. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Adjoint negations, more than residuated negations. Inf. Sci. 345, 355–371 (2016)

    Article  MathSciNet  Google Scholar 

  5. De Baets, B.: Analytical solution methods for fuzzy relation equations. In: Dubois, D., Prade, H. (eds.) The Handbooks of Fuzzy Sets Series, vol. 1, pp. 291–340. Kluwer, Dordrecht (1999)

    Google Scholar 

  6. Di Nola, A., Sanchez, E., Pedrycz, W., Sessa, S.: Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Kluwer Academic Publishers, Norwell, MA, USA (1989)

    Book  Google Scholar 

  7. Díaz, J.C., Medina, J.: Multi-adjoint relation equations: definition, properties and solutions using concept lattices. Inf. Sci. 253, 100–109 (2013)

    Article  MathSciNet  Google Scholar 

  8. Díaz-Moreno, J.C., Medina, J., Turunen, E.: Minimal solutions of general fuzzy relation equations on linear carriers. an algebraic characterization. Fuzzy Sets Syst. 311, 112–123 (2017)

    Article  MathSciNet  Google Scholar 

  9. Freson, S., Baets, B.D., Meyer, H.D.: Linear optimization with bipolar max-min constraints. Inf. Sci., 234, 3–15 (2013). Fuzzy Relation Equations: New Trends and Applications

    Google Scholar 

  10. Ignjatović, J., Ćirić, M., Šešelja, B., Tepavčević, A.: Fuzzy relational inequalities and equations, fuzzy quasi-orders, closures and openings of fuzzy sets. Fuzzy Sets Syst. 260, 1–24 (2015). Theme: Algebraic Structures

    Google Scholar 

  11. Li, D.-C., Geng, S.-L.: Optimal solution of multi-objective linear programming with inf-\(\rightarrow \) fuzzy relation equations constraint. Inf. Sci. 271, 159–178 (2014)

    Article  MathSciNet  Google Scholar 

  12. Li, P., Jin, Q.: On the resolution of bipolar max-min equations. Kybernetika 52(4), 514–530 (2016)

    MathSciNet  MATH  Google Scholar 

  13. Medina, J.: Minimal solutions of generalized fuzzy relational equations: Clarifications and corrections towards a more flexible setting. Int. J. Approx. Reason. 84, 33–38 (2017)

    Article  MathSciNet  Google Scholar 

  14. Medina, J.: Notes on ‘solution sets of inf-\(\alpha _{T}\) fuzzy relational equations on complete brouwerian lattice’ and ‘fuzzy relational equations on complete brouwerian lattices’. Inf. Sci. 402, 82–90 (2017)

    Article  Google Scholar 

  15. Peeva, K.: Imprecision and Uncertainty in Information Representation and Processing: New Tools Based on Intuitionistic Fuzzy Sets and Generalized Nets, pp. 73–85. Springer International Publishing, Cham (2016)

    Google Scholar 

  16. Perfilieva, I., Nosková, L.: System of fuzzy relation equations with inf-\(\rightarrow \) composition: complete set of solutions. Fuzzy Sets Syst. 159(17), 2256–2271 (2008)

    Article  Google Scholar 

  17. Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30(1), 38–48 (1976)

    Article  MathSciNet  Google Scholar 

  18. Sanchez, E.: Inverses of fuzzy relations. application to possibility distributions and medical diagnosis. Fuzzy Sets Syst. 2(1), 75–86 (1979)

    Article  MathSciNet  Google Scholar 

  19. Zhou, J., Yu, Y., Liu, Y., Zhang, Y.: Solving nonlinear optimization problems with bipolar fuzzy relational equation constraints. J. Inequal. Appl. 2016(1), 126 (2016)

    Article  MathSciNet  Google Scholar 

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Correspondence to M. Eugenia Cornejo .

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Cornejo, M.E., Lobo, D., Medina, J. (2019). Bipolar Max-Product Fuzzy Relation Equations with the Product Negation. In: Cornejo, M., Kóczy, L., Medina, J., De Barros Ruano, A. (eds) Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, vol 796. Springer, Cham. https://doi.org/10.1007/978-3-030-00485-9_17

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