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$C^\infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^\infty$ $LG$-fuzzy mappings of them | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 17، شماره 6، بهمن و اسفند 2020، صفحه 157-174 اصل مقاله (482.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5608 | ||
| نویسنده | ||
| M. Mostafavi* | ||
| Department of Mathematics, University of Qom, Qom, Iran | ||
| چکیده | ||
| In this paper, we generalize all of the fuzzy structures which we have discussed in \cite{MM} to $L$-fuzzy set theory, where $L= <L,\leq,\bigwedge,\bigvee, '>$ denotes a complete distributive lattice with at least two elements. We define the concept of an $LG$-fuzzy topological space $(X, \mathfrak{T} )$ which $X$ is itself an $L$-fuzzy subset of a crisp set M and $\mathfrak{T}$ is an $L$-gradation of openness of $L$-fuzzy subsets of $M$ which are less than or equal to $ X $. Then we define $C^\infty$ $L$-fuzzy manifolds with $L$-gradation of openness and $C^\infty$ $LG$-fuzzy mappings of them such as $LG$-fuzzy immersions and $LG$-fuzzy imbeddings. We fuzzify the concept of the product manifolds with $L$-gradation of openness and define $LG$-fuzzy quotient manifolds when we have an equivalence relation on $M$ and investigate the conditions of the existence of the quotient manifolds. We also introduce $LG$-fuzzy immersed, imbedded and regular submanifolds. | ||
| کلیدواژه‌ها | ||
| $C^infty$ $LG$-fuzzy n-manifolds؛ $C^infty$ $LG$ -fuzzy mappings؛ $LG$-fuzzy quotient manifolds؛ $LG$-fuzzy immersion؛ regular $LG$-fuzzy submanifolds | ||
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آمار تعداد مشاهده مقاله: 98 تعداد دریافت فایل اصل مقاله: 60 |
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