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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/10836

Title: Invariant probabilistic metrizability of fuzzy neighborhood groups
Authors: T. M. G. Ahsanullah
N. N. Morsi
Keywords: N-local compactness
N-openess
Issue Date: 1992
Publisher: International J. Fuzzy Sets and Sysstems
Citation: 47(1992), 233-245.
Abstract: We introduce the notions of N-local compactness and N-openess in fuzzy neighbourhood spaces and in fuzzy neighbourhood groups, together with some characterizations for them. In particular, we prove that a fuzzy neighbourhood space is N-locally compact if and only if its α-level spaces, for all 0<α<1, are locally compact. A similar criterion is established for N-open functions. We also introduce the notion of fuzzy absolute value functions on groups. We show that there exists a 1-1 correspondence between invariant fuzzy (probabilistic) pseudo-metrics on groups and fuzzy absolute value functions. We establish theorems on fuzzy (probabilistic) pseudo-metrizability of fuzzy neighbourhood groups. Finally, fuzzy (probabilistic) metrizability of quotient fuzzy neighbourhood groups is also taken into account.
URI: http://hdl.handle.net/123456789/10836
Appears in Collections:College of Science

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