Generalized Bosbach states: part I |
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Authors: | Lavinia Corina Ciungu George Georgescu Claudia Mureşan |
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Affiliation: | 1. Department of Mathematics and Statistics, University of Central Oklahoma, 100 N University Drive, Edmond, OK, 73034, USA 2. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, Bucharest, Romania
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Abstract: | States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics. |
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