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FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 3، شماره 2، دی 2006، صفحه 75-91 اصل مقاله (284.44 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2006.469 | ||
| نویسنده | ||
| APARNA JAIN | ||
| DEPARTMENT OF MATHEMATICS, SHIVAJI COLLEGE, UNIVERSITY OF DELHI, NEW DELHI, INDIA | ||
| چکیده | ||
| In this paper, we study an equivalence relation on the set of fuzzy subgroups of an arbitrary group G and give four equivalent conditions each of which characterizes this relation. We demonstrate that with this equivalence relation each equivalence class constitutes a lattice under the ordering of fuzzy set inclusion. Moreover, we study the behavior of these equivalence classes under the action of a group homomorphism. | ||
| کلیدواژهها | ||
| Fuzzy subgroup؛ Equivalence relation؛ Lattice؛ $alpha$– cut؛ Strong $alpha$– cut؛ homomorphism | ||
| مراجع | ||
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