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Hesitant fuzzy sets and hesitant fuzzy relations with membership values in power set quantales | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 23، شماره 6، بهمن و اسفند 2026، صفحه 67-98 اصل مقاله (554.88 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.52427.9390 | ||
| نویسندگان | ||
| M. Tasić* 1؛ S. Stanimirović2؛ J. Ignjatović2؛ M. Ćirić2؛ M. Stanković1 | ||
| 1Department of Sciences, Mathematics and Technical Sciences, Pedagogical Faculty in Vranje, University of Niš, Vranje, Serbia | ||
| 2Department of Computer Science, Faculty of Science and Mathematics, University of Niš, Niš, Serbia | ||
| چکیده | ||
| A hesitant fuzzy set extends the notion of a fuzzy set by allowing membership values to be represented as sets of values drawn from a predefined domain, typically the real unit interval. In this paper, we introduce a novel framework in which membership values are instead drawn from the power set quantale of a semigroup. This shift is motivated by the fact that such a power set quantale admits residuation, thereby offering a rich algebraic setting for the development of the theory of hesitant fuzzy sets and hesitant fuzzy relations. We provide several characterizations of hesitant fuzzy relations, with particular emphasis on hesitant fuzzy equivalences, their classes and partitions, as well as hesitant fuzzy quasi-orders. | ||
| کلیدواژه‌ها | ||
| Hesitant fuzzy sets؛ Power set quantale؛ Hesitant fuzzy equivalences؛ Hesitant fuzzy partitions؛ Hesitant fuzzy quasi-orders | ||
| مراجع | ||
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