Filters








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Involutive filters of pseudo-hoops [article]

Lavinia Corina Ciungu
2017 arXiv   pre-print
For a bounded Wajsberg pseudo-hoop we prove that the kernel of any state operator is an involutive filter.  ...  We give characterizations of involutive filters of a bounded pseudo-hoop and we prove that in the case of bounded Wajsberg pseudo-hoops the notions of fantastic and involutive filters coincide.  ...  Important results on probabilistic models on algebras of non-classical logic have been proved based on involutive filters.  ... 
arXiv:1711.08409v1 fatcat:ssvdecwovvcvfgi4uagoyffboa

State pseudo equality algebras [article]

Lavinia Corina Ciungu
2016 arXiv   pre-print
We define and study new classes of pseudo equality algebras, such as commutative, symmetric, pointed and compatible pseudo equality algebras.  ...  Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras  ...  In other words, a pseudo-hoop is a meet-semilattice ordered residuated, integral and divisible monoid. 6] ) (1) Every linearly ordered pseudo BCK-algebra is a pseudo BCK(pP)algebra.  ... 
arXiv:1602.07828v1 fatcat:of2uoiaalbc5lo3llzfh2i3n4e

Bounded pseudo-hoops with internal states

Lavinia Ciungu
2013 Mathematica Slovaca  
In this paper we study these concepts for more general fuzzy structures, namely pseudo-hoops and we present state pseudo-hoops and state-morphism pseudo-hoops.  ...  Rachůnek and Šalounová introduced state GMV-algebras (pseudo-MV algebras) and state-morphism GMV-algebras, while the state BL-algebras and state-morphism BL-algebras were defined by Ciungu, Dvurečenskij  ...  Acknowledgementº The author is very grateful to the anonimous referees for their useful remarks and suggestions on the subject that helped improving the presentation.  ... 
doi:10.2478/s12175-013-0144-z fatcat:c7bnhfpv65acti5qdlvms7w5ry

Measures, states and de Finetti maps on pseudo-BCK algebras [article]

Lavinia Corina Ciungu, Anatolij Dvurečenskij
2009 arXiv   pre-print
Kühr only for pseudo-BCK semilattices.  ...  In this paper, we extend the notions of states and measures presented in DvPu to the case of pseudo-BCK algebras and study similar properties.  ...  In what follows, we introduce a new class of pseudo-BCK algebras which will be used in the next sections. Definition 2.22.  ... 
arXiv:0905.4789v2 fatcat:6n3onq433zbqznvxkveggp6esm

State maps on semihoops

Yu Long Fu, Xiao Long Xin, Jun Tao Wang
2018 Open Mathematics  
Then we give some examples and basic properties of (internal) state maps on semihoops. Moreover, we discuss the relations between state maps and internal states on other algebras.  ...  Then we introduce several kinds of filters by state maps on semihoops, called SM-filters, state filters and dual state filters, respectively, and discuss the relations among them.  ...  Let A be a bounded pseudo-hoop and s be a Bosbach state on A.  ... 
doi:10.1515/math-2018-0089 fatcat:6mxo3ufyobg4dmp667z5yig5h4

Fuzzy sets and formal logics

Lluís Godo, Siegfried Gottwald
2015 Fuzzy sets and systems (Print)  
The paper discusses the relationship between fuzzy sets and formal logics as well as the influences fuzzy set theory had on the development of particular formal logics.  ...  Acknowledgments The authors are grateful to an anonymous reviewer and to Carles Noguera for their useful comments and suggestions.  ...  Godo acknowledges partial support by the Spanish projects EdeTRI (TIN2012-39348-C02-01) and 2014 SGR 118.  ... 
doi:10.1016/j.fss.2015.06.021 fatcat:jstlgpnzrze3pkikat2rcbeeh4

Page 141 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
On the structure of hoops. (English summary) 2001g:03120 — (with van Alten, C. J.) On the finite embeddability property for residuated lattices, pocrims and BCK-algebras. Celani, Sergio A.  ...  O. et al., 2001j:03114 Sofronie-Stokkermans, Viorica Priestley duality for SHn-algebras and applications to the study of Kripke-style models for SHx-logics.  ... 

Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments [chapter]

Didier Dubois, Francesc Esteva, Lluís Godo, Henri Prade
2007 Handbook of the History of Logic  
This new trend has also put formal logic, originally developed in connection with the foundations of mathematics, in a completely new perspective, as a tool for processing information on computers.  ...  The idea of fuzzy sets introduced in the early sixties [Zadeh, 1965] and the development of fuzzy logic later on [Zadeh, 1975a] has brought forward a new formal framework for capturing graded imprecision  ...  The algebraic counterpart are the so-called pseudo-BL and pseudo-MTL algebras.  ... 
doi:10.1016/s1874-5857(07)80009-4 fatcat:s4i5zfomgzbxnfbuif5ffsesea