Generalized fuzzy filters in ordered semigroups | ||
| Iranian Journal of Science | ||
| مقاله 10، دوره 36، شماره 1، اردیبهشت 2012، صفحه 77-86 اصل مقاله (138 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2012.2059 | ||
| نویسندگان | ||
| B. Davvaz* 1؛ A. Khan2 | ||
| 1Department of Mathematics, College of Sciences, Yazd University, Yazd, Iran | ||
| 2Department of Mathematics, Comsats Institute of Information Technology, Abbottabad 22060, Pakistan | ||
| چکیده | ||
| coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an (, )-fuzzy filter of an ordered semigroup , where , , , , with . Since the concept of (, )-fuzzy filter is an important and useful generalization of ordinary fuzzy filter, we discuss some fundamental aspects of (, )-fuzzy filters. An (, )-fuzzy filter is a generalization of the existing concept of a fuzzy filter. The concept of (, )-fuzzy filters is also introduced and some related properties are investigated. The relationships among ordinary fuzzy filters, (, )-fuzzy filters and (, )-fuzzy filters are discussed. We discuss the concept of (, )-fuzzy left (right and bi)-filters and provide some characterization theorems. Finally, we extend the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy left (right and bi)-filter with thresholds of . | ||
| کلیدواژهها | ||
| Semigroup؛ ordered semigroup؛ Fuzzy Set؛ filter؛ generalized fuzzy filter | ||
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