6533b822fe1ef96bd127d625

RESEARCH PRODUCT

L -valued bornologies on powersets

Alexander OstakIngrda Ujane

subject

Discrete mathematicsIdeal (set theory)Logic010102 general mathematicsFuzzy set02 engineering and technology01 natural sciencesFuzzy logicFuzzy topologyAlgebraSet (abstract data type)Artificial Intelligence0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsAxiomMathematics

description

In M. Abel and A. ostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the family LX of L-fuzzy subsets of a set X. Here we propose an alternative approach to fuzzification of the concept of bornology. We define an L-valued bornology on a set X as an L-fuzzy subset B of the powerset 2X satisfying L-valued analogues of the axioms of a bornology. Basic properties of L-valued bornological spaces are studied. Our special interest concerns L-valued bornologies induced by fuzzy metrics and relative compactness-type L-valued bornologies in ChangGoguen L-topological spaces.

yearjournalcountryeditionlanguage
2016-07-01Fuzzy Sets and Systems
https://doi.org/10.1016/j.fss.2015.07.016