# zbMATH — the first resource for mathematics

Fuzzy $$f$$-proximities. (English) Zbl 0839.54006
Summary: In the present paper the study of fuzzy $$f$$-proximities is continued. A new fuzzy generalized proximity, viz. fuzzy RI (or Riesz) proximity and the notions of fuzzy $$R_0$$ and fuzzy $$R_1$$-closure spaces are introduced and studied. In terms of fuzzy grill operators a fuzzy RI proximity turns out to be a fuzzy $$f$$-proximity for $$f = r$$. An analysis of the order structure and in particular of the lattice structure of the family $$M_f (X,c)$$ is undertaken. The least element of this family is also specified.

##### MSC:
 54A40 Fuzzy topology 54E05 Proximity structures and generalizations
Full Text:
##### References:
 [1] Azad, K.K., Fuzzy grills and a characterization of fuzzy proximity, J. math. anal. appl., 79, 13-17, (1981) · Zbl 0452.54008 [2] Čech, E., (), rev. [3] Chattopadhyay, K.C.; Vasudeva, H.L., On the lattice of f-proximities, (), 521-525 · Zbl 0448.54028 [4] Choquet, G., Sur LES notions de filtre et de grille, Comptes rendus acad. sci. Paris, 224, 171-173, (1947) · Zbl 0029.07602 [5] Katsaras, A.K., On fuzzy proximity spaces, J. math. anal. appl., 75, 571-583, (1980) · Zbl 0443.54006 [6] Mashhour, A.S.; Ghanim, M.H.; Fath Alla, M.A., Fuzzy ultrafilters and fuzzy grills, Simon stevin, 60, 3-14, (1986) · Zbl 0589.54012 [7] Naimpally, S.A.; Warrack, B.D., Proximity spaces, (1970), Cambridge University Press London · Zbl 0206.24601 [8] Ori, Ramesh; Thron, W.J., Bounded families and their relations to largest members of certain classes of proximities, Math. student, 43, 73-83, (1975) · Zbl 0544.54020 [9] Srivastava, P.; Gupta, R.L., Fuzzy symmetric generalized proximity spaces, J. math. anal. appl., 78, 588-597, (1980) · Zbl 0481.54006 [10] Srivastava, P.; Gupta, R.L., Fuzzy proximity structures and fuzzy ultrafilters, J. math. anal. appl., 94, 298-311, (1983) · Zbl 0542.54007 [11] Thron, W.J., Proximity structures and grills, Math. ann., 206, 35-62, (1973) · Zbl 0247.54027 [12] Thron, W.J.; Warren, R.H., On the lattice of proximities of čech compatible with a given closure space, Pac. J. math., 49, 519-535, (1973) · Zbl 0237.54016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.