Non-commutative fuzzy Galois connections |
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Authors: | G Georgescu A Popescu |
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Affiliation: | (1) Institute of Mathematics, Calea Grivitei Nr. 21, P.O. Box 1-767, Bucharest, Romania e-mail: georgescu@funinf.math.unibuc.ro, RO;(2) Fundamentals of Computer Science, Faculty of Mathematics, Univeresity of Bucharest, Str. Academic Nr 14, 70109 Bucharest, Romania e-mail: uuomul@yahoo.com, RO |
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Abstract: | Fuzzy Galois connections were introduced by Bělohlávek in 4]. The structure considered there for the set of truth values
is a complete residuated lattice, which places the discussion in a “commutative fuzzy world”. What we are doing in this paper
is dropping down the commutativity, getting the corresponding notion of Galois connection and generalizing some results obtained
by Bělohlávek in 4] and 7]. The lack of the commutative law in the structure of truth values makes it appropriate for dealing
with a sentences conjunction where the order between the terms of the conjunction counts, gaining thus a temporal dimension
for the statements. In this “non-commutative world”, we have not one, but two implications (15]). As a consequence, a Galois
connection will not be a pair, but a quadruple of functions, which is in fact two pairs of functions, each function being
in a symmetric situation to his pair. Stating that these two pairs are compatible in some sense, we get the notion of strong
L-Galois connection, a more operative and prolific notion, repairing the “damage” done by non-commutativity.
Dedicated to Prof. Ján Jakubík on the occasion of his 80th birthday. |
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Keywords: | Non-commutative fuzzy logic Fuzzy Galois connection Fuzzy relation Non-commutative conjunction |
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