• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.521-538
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• 2024

In this paper, using the notion of the imprecise set, the idea of an imprecise group is introduced including some examples. The two key rules of classical set theory are obeyed by this extended version of fuzzy sets, which the existing complement definition of a fuzzy set failed to do. With the support from general group theory, the paper also provides some fundamental properties of an imprecise group here. Additionally, it includes a few characteristics of imprecise subgroups, and abelian imprecise group.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 춘계학술대회 학술발표 논문집
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• pp.3-6
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• 1998

We introduce the notion of TL-p-subgroups that is an extension of the notion of fuzzy p-subgroups and show that a torsion TL-subgroup of an Abelian group with T=∧ can be written as the intersection of its minimal TL-p-subgroups.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.769-783
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• 2021

Demirci ((1999) Vague groups. J. Math. Anal. Appl. 230, 142-156) introduced the concept of vague groups as one of uncertain reasoning structures where indistinguishable operators separate points. In this paper, we consider vague groups in which an indistinguishable operator does not need to separate points because it seems more appropriate to handle ambiguous situations. For our purposes we generalize or redefine some notions such as: vague closed subset, vague subgroup, vague kernel and vague injectiveness. Consequently we generalize most of the known results and obtain some new additional fundamental properties of vague groups, some of which are similar to ones of ordinary groups.