Al-Zalzali, M.M. Rand Shafe'a Ghanem (2026) Gamma-Type Hesitant Fuzzy Ring. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 7 (3). ISSN 2660-5309

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Abstract

The main purpose of this research is to formally define a "  -Hesitant Fuzzy Ring" and discuss the fundamental algebraic properties of it, including ideals and quotient rings, and to investigate the effect of the parameter  on the degree of hesitancy. Traditional fuzzy algebraic models with an effective representation of states of "hesitancy" that result from several opinions or heterogeneous sources are lacking, since they assume that the membership value of each element is a single value. This constraint is a challenge for modelling in real-world applications where uncertainty is more complex. The main research question is What algebraic ring structure will allow for several "hesitancy values" to be assigned to elements of the ring, and the degree of this hesitancy to be controlled by a mathematical parameter, and the consistency of the algebraic operations (addition and multiplication) within the ring? The results indicate that the use of   as an upper limit for the number of hesitant membership values results in a more flexible and adaptable algebraic structure. The authors also find that it is not easy to build a consistent membership function (closure under addition and multiplication) and it demands exact conditions to relate the membership values of different elements. The presented theorem shows strong connections between the membership values of an element and its additive inverse, which opens new possibilities for the development of the whole algebra of such structures and their applications in multi-criteria decision support systems.

Item Type:	Article
Uncontrolled Keywords:	Hesitant Fuzzy Sets, Gamma-Type Hesitant Fuzzy Ring, Fuzzy Algebra, Decision Support Systems, Parameterized Fuzziness
Subjects:	H Social Sciences
Depositing User:	admin eprints
Date Deposited:	30 Jul 2026 16:05
Last Modified:	30 Jul 2026 16:05
URI:	http://eprints.umsida.ac.id/id/eprint/16867

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