Sains Ma1aysiana 28: 151-159 (1999) Pengajian Kuantitatif/
Quantitative Studies
Penggredan Pada Ruang Topologi Kabur
(Gradation on a fuzzy topological space)
Abu Osman Bin Md Tap
Jabatan Matematik, Fakulti Sains Matematik
Universiti Kebangsaan Malaysia
43600 UKM Bangi, Selangor D.E. Malaysia
Abd Fatah Bin Wahab
Unit Sains Matematik, Fakulti Sains dan Sastera Ikhtisas
Universiti Putra Malaysia Terengganu
21030 Kuala Terengganu Terengganu D.I..
ABSTRAK
Hazra et al. telah memperkenalkan takrif baru topologi kabur pada X melalui penggredan keterbukaan (ketertutupan) subset kabur bagi X dan mengkaji pemetaan pengawetan penggredan. Dalam makalah ini, kami selanjutnya mengkaji konsep penggredan teraruh, pemetaan penggredan mengecut, pemetaan penggredan mengembang, pemetaan penggredan tetap dan pemetaan penggredan mengawet pada ruang topologi kabur.
ABSTRACT
Hazra et al. introduced a new definition of fuzzy topology via the gradation of openness (closedness) for fuzzy subset of X and studied the gradation preserving map. In this paper, we further study the concepts of induced gradation, gradation contraction map, gradation expansion map, gradation fixing map and the gradation preserving map on a fuzzy topological space.
RUJUKAN/REFERENCES
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Chattopadhyay, K.C., Hazra, R.N. & Samanta, S.K 1992. Gradation of openness: fuzzy topology. Fuzzy Sets and Systems 49: 237-242.
Chattopadhyay, K.C. & Samanta, S.K 1993. Fuzzy topology: Fuzzy closure operator, fuzzy compactness and fuzzy connectedness. Fuzzy Sets and Systems 54: 207-212.
El-Gayyar, M.K., Kerre, E.E. & Ramadan, AA 1994. Almost compactness and near compactness in smooth topological spaces. Fuzzy Sets and Systems 62: 193-202.
Hazra, R.N., Samanta, S.K & Chattopadhyay, K.C. 1992. Fuzzy topology redefined. Fuzzy Sets and Systems 45: 78-82.
Ramadan, A.A 1992. Smooth topological spaces. Fuzzy Sets and Systems 48: 371-375.
Warren, R.H. 1978. Neighbourhood, base and continuity in fuzzy topological spaces. Rocky Mountain J. Math. 8: 459-470.
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