Abstract
Hájek introduced the logic \(BL_{vt}\) enriching the logic BL by a unary connective vt which is a formalization of Zadeh’s fuzzy truth value “very true”. \(\hbox{BL}_{vt}\) algebras, i.e., BL-algebras with unary operations, called vt-operators, which are among others subdiagonal, are an algebraic counterpart of \(BL_{vt}.\) Partially ordered commutative integral residuated monoids (pocrims) are common generalizations of both BL-algebras and Heyting algebras. The aim of our paper is to introduce and study algebraic properties of pocrims endowed by “very-true” and “very-false”-like operators.
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Research is supported by the Research and Development Council of Czech Government via project MSN 6198959214.
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Halaš, R., Botur, M. On very true operators on pocrims. Soft Comput 13, 1063–1072 (2009). https://doi.org/10.1007/s00500-008-0379-8
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DOI: https://doi.org/10.1007/s00500-008-0379-8