Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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HYPO-CONVERGENCE OF SEQUENCES OF FUZZY SETS AND MAXIMIZATION

  • Tortop, Sukru (Department of Mathematics, Faculty of Art and Sciences, Afyon Kocatepe University) ;
  • Dundar, ErdInC (Department of Mathematics, Faculty of Art and Sciences, Afyon Kocatepe University)
  • Received : 2022.06.09
  • Accepted : 2022.07.28
  • Published : 2022.09.01
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Abstract

In optimization theory, hypo-convergence is considered as an effective tool by providing the convergence of supremum values under some conditions. This feature makes it different from other types of convergence. Therefore, we have defined the hypo-convergence of a sequence of fuzzy sets due to the increasing interest in fuzzy set theory in recent years. After giving a theoretical framework, we deal with the optimization process by using a sequential characterization of hypo-convergence of sequence of fuzzy sets. Since the maximization process in optimization theory is beyond the presence of hypo-convergence, we give some conditions to satisfy the convergence of supremum values. Furthermore, we show how sequence of fuzzy sets and fuzzy numbers differ in the convergence of the supremum values.

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