Results on equality algebras
In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, B...
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Published in | Information sciences Vol. 381; pp. 270 - 282 |
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Abstract | In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, BL-algebra, MV-algebra, Hertz-algebra, Heyting-algebra, Boolean-algebra, EQ-algebra and hoop-algebra. The aim of this paper is to find that under which conditions, equality algebras are equivalent to these logical algebras. |
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AbstractList | In this paper, by considering the notion of equality algebra, which is introduced by Jenei in [18], as a possible algebraic semantic for fuzzy type theory, we study and show that there are relations among equality algebras and some of other logical algebras such as residuated lattice, MTL-algebra, BL-algebra, MV-algebra, Hertz-algebra, Heyting-algebra, Boolean-algebra, EQ-algebra and hoop-algebra. The aim of this paper is to find that under which conditions, equality algebras are equivalent to these logical algebras. |
Author | Zebardast, F. Borzooei, R.A. Aaly Kologani, M. |
Author_xml | – sequence: 1 givenname: F. surname: Zebardast fullname: Zebardast, F. email: zebardastfathme@gmail.com organization: Department of Mathematics, Payam e Noor University, Tehran, Iran – sequence: 2 givenname: R.A. surname: Borzooei fullname: Borzooei, R.A. email: borzooei@sbu.ac.ir organization: Department of Mathematics, Shahid Beheshti University, Tehran, Iran – sequence: 3 givenname: M. surname: Aaly Kologani fullname: Aaly Kologani, M. email: mona4011@gmail.com organization: Department of Mathematics, Shahid Beheshti University, Tehran, Iran |
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Cites_doi | 10.1090/S0002-9947-1958-0094302-9 10.1007/s11225-007-9078-1 10.1023/A:1022935811257 10.1007/s00500-014-1494-3 10.1016/j.fss.2013.12.007 10.1016/j.ins.2015.03.072 10.1007/s00500-009-0491-4 10.1016/j.fss.2011.05.011 10.1016/j.fss.2004.03.027 10.1016/j.fss.2009.04.010 10.1090/S0002-9947-1939-1501995-3 10.1007/s11225-012-9457-0 10.1007/s11786-013-0157-6 10.1016/S0165-0114(01)00098-7 10.1007/s00153-014-0380-0 |
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Keywords | BL-algebra Hoop-algebra Hertz-algebra Equality algebra Residuated lattice Boolean-algebra Heyting-algebra MTL-algebra 03G25 EQ-algebra MV-algebra |
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SubjectTerms | Algebra BL-algebra Boolean-algebra EQ-algebra Equality algebra Equivalence Fuzzy logic Hertz-algebra Heyting-algebra Hoop-algebra Lattices MTL-algebra MV-algebra Residuated lattice Semantics |
Title | Results on equality algebras |
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