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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
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