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A theory of vague lattices based on many-valued equivalence relations. I: General representation results. (English) Zbl 1067.06006
Fuzzy orderings in the sense of 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 U. Bodenhofer [loc. cit.] and U. Höhle and 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)].

MSC:
06D72 Fuzzy lattices (soft algebras) and related topics
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