L-fuzzy strongest postcondition predicate transformers as L-idempotent linear or affine operators between semimodules of monotonic predicates

Authors:
Oleh Nykyforchyn;Duan Repov
Affiliations:
Vasyl Stefanyk Precarpathian National University, Shevchenka 57, Ivano-Frankivsk, 76025, Ukraine;Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

For a completely distributive quantale L, L-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous L-idempotent semimodules of L-fuzzy monotonic predicates.