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doi:10.1016/j.fss.2004.06.017 
Copyright © 2004 Elsevier B.V. All rights reserved.
A theory of vague lattices based on many-valued equivalence relations—I: general representation results
Mustafa Demirci
, 1, 
Received 9 May 2003;
revised 25 May 2004;
accepted 18 June 2004.
Available online 3 August 2004.
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Abstract
The present work introduces a new and general theory of ordering relations and lattices based on many-valued equivalence relations under the name vague ordering relations and vague lattices, respectively. Representations and constructions of vague ordering relations and vague lattices are the main subjects of this paper, and various desirable results in this direction are established. Furthermore algebraic characterizations of vague lattices are studied.
Keywords: Lattice; Fuzzy lattice; Fuzzy ordering; Fuzzy equivalence relation; Fuzzy equality; Indistinguishability operator
