caa a22 4500 60546877X CHVBK 20210128100318.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00500-015-1671-z doi (NATIONALLICENCE)springer-10.1007/s00500-015-1671-z Algebraic study to generalized Bosbach states on residuated lattices [Elektronische Daten] [Zhen Ma, Zun Fu] Generalized Bosbach states of type I and II, which are also called type I and II states, are useful for the development of algebraic theory of probabilistic models for fuzzy logics. In this paper, a pure algebraic study to the generalization of Bosbach states on residuated lattices is made. By rewriting the equations of Bosbach states, an alternative definition of type II states is given, and five types of generalized Bosbach states of type III, IV, V, VI and VII (or simply, type III, IV, V, VI and VII states) are introduced. The relationships among these generalized Bosbach states and properties of them are investigated by some examples and results. Particularly, type IV states are a new type of generalized Bosbach states which are different from type I, II and III states; type V (resp. VI) states can be equivalently defined by both type I (resp. II) states and type IV states; type I, II and III states are equivalent when the codomain is an MV-algebra as well as type V and type VI states. Springer-Verlag Berlin Heidelberg, 2015 Non-classical logics nationallicence Residuated lattice nationallicence Generalized Bosbach state of type III (resp. IV, V, VI and VII) nationallicence Ma Zhen School of Science, Linyi University, 276005, Linyi, People's Republic of China aut Fu Zun School of Science, Linyi University, 276005, Linyi, People's Republic of China aut Soft Computing Springer Berlin Heidelberg 19/9(2015-09-01), 2541-2550 1432-7643 19:9<2541 2015 19 500 https://doi.org/10.1007/s00500-015-1671-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-015-1671-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ma Zhen School of Science, Linyi University, 276005, Linyi, People's Republic of China aut NATIONALLICENCE 700 1- Fu Zun School of Science, Linyi University, 276005, Linyi, People's Republic of China aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/9(2015-09-01), 2541-2550 1432-7643 19:9<2541 2015 19 500