A theory of vague lattices based on many-valued equivalence relations. I: General representation results
Fuzzy orderings in the sense of \textit{U. Bodenhofer} [Fuzzy Sets Syst. 137, No. 1, 113--136 (2003; Zbl 1052.91032)] are extended to integral, commutative, complete, quasi-monoidal lattices in the sense of the author [Int. J. Gen. Syst. 32, No. 2, 123--155 (2003; Zbl 1028.03044)] and defined as vague orderings. Known notions of fuzzy orderings due to \textit{U. Bodenhofer} [loc. cit.] and \textit{U. Höhle} and \textit{N. Blanchard} [Inf. Sci. 35, 133--144 (1985; Zbl 0576.06004)] are seen as special cases of vague orderings. The author then defines the concept of vague lattice and shows how such lattices can be constructed, represented and algebraically characterized. Other related papers are due to the same author [Int. J. Gen. Syst. 32, No. 2, 157--175 (2003; Zbl 1028.03045); ibid. 32, No. 2, 177--201 (2003; Zbl 1028.03046); ibid. 32, No. 5, 431--458 (2003; Zbl 1051.93019)].
scientific article; zbMATH DE number 2160228
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