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

Chang, C.L. 1968. Fuzzy topological spaces. J. Math. Anal. Appl. 24: 182-190.

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.