Bivalent and other solutions of fuzzy relational equations via linguistic hedges.

*(English)*Zbl 1258.03080In the paper, it is shown that constrained solutions of ordinary fuzzy relational equations appear as solutions of a new type of fuzzy relational equations, i.e., equations which use modified compositions of fuzzy relations. The mentioned modification consists in using linguistic hedges in the description of the compositions. It is proved that the well-known results regarding solutions of fuzzy relational equations may be generalized to the more general case which involves intensifying or relaxing hedges. This idea emphasizes the role of linguistic hedges as constraints. Results are developed for complete residuated lattices as the structure of truth degrees. In the paper, both the intensifying (truth-stressing) hedges as “very” or “highly”, and the relaxing (truth-depressing) hedges such as “more or less” or “roughly” are applied. These hedges are understood as unary functions on the set of truth degrees. Moreover, an illustrative example is provided which demonstrates the results of the paper and the usefulness of constrained solutions of fuzzy relational equations.

Reviewer: Urszula Bentkowska (Rzeszów)

##### Keywords:

fuzzy logic; fuzzy relation; fuzzy relational equation; linguistic hedge; residuated lattice
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\textit{E. Bartl} et al., Fuzzy Sets Syst. 187, No. 1, 103--112 (2012; Zbl 1258.03080)

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