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Representation theorems for fuzzy orders and quasi-metrics

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Abstract

Given a complete residuated lattice (L,∨,∧,*,→,0,1), we show that any *-preorder can be represented both by an implication-based graded inclusion as defined [1] and by a similarity-based graded inclusion as defined in [2]. Also, in accordance with a duality between fuzzy orders and quasi-metrics, we obtain two corresponding representation theorems for quasi-metrics.

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  1. Department of Mathematics and Computer Sciences, University of Salerno, via S. Allende, 84081, Baronissi (SA), Italy

    G. Gerla

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  1. G. Gerla
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Correspondence to G. Gerla.

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Gerla, G. Representation theorems for fuzzy orders and quasi-metrics. Soft Computing 8, 571–580 (2004). https://doi.org/10.1007/s00500-003-0316-9

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  • DOI: https://doi.org/10.1007/s00500-003-0316-9

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