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Convexity and level sets for interval-valued fuzzy sets

Author

Listed:
  • Pedro Huidobro

    (University of Oviedo
    Matej Bel University)

  • Pedro Alonso

    (University of Oviedo)

  • Vladimír Janiš

    (Matej Bel University
    Tomas Bata University in Zlín)

  • Susana Montes

    (University of Oviedo)

Abstract

Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems.

Suggested Citation

  • Pedro Huidobro & Pedro Alonso & Vladimír Janiš & Susana Montes, 2022. "Convexity and level sets for interval-valued fuzzy sets," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 553-580, December.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:4:d:10.1007_s10700-021-09376-7
    DOI: 10.1007/s10700-021-09376-7
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Meimei Xia & Jian Chen, 2015. "Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(1), pages 115-144, January.
    3. Bing-yuan Cao, 2009. "Convexity Study of Interval Functions and Functionals & Fuzzy Functions and Functionals," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 1(4), pages 421-434, December.
    4. Jaroslav Ramík & Milan Vlach, 2016. "Intuitionistic fuzzy linear programming and duality: a level sets approach," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 457-489, December.
    5. Bing-yuan Cao, 2009. "Convexity study of interval functions and functionals & fuzzy functions and functionals," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 421-434, December.
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