Involutive equality algebras
The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a ( ∼ 0 ) -involutive subalgebra. We prove that each ( ∼ 0 ) -involutive...
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| Published in | Soft computing (Berlin, Germany) Vol. 22; no. 22; pp. 7505 - 7517 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.11.2018
Springer Nature B.V |
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| Abstract | The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a
(
∼
0
)
-involutive subalgebra. We prove that each
(
∼
0
)
-involutive equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define
(
∼
0
)
-involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a
(
∼
0
)
-involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras. |
|---|---|
| AbstractList | The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a (∼0)-involutive subalgebra. We prove that each (∼0)-involutive equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define (∼0)-involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a (∼0)-involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras. The present paper aims to study a special class of equality algebras, called involutive equality algebra. We obtain some properties of this structure and prove that every linearly ordered 0-compatible equality algebra includes a ( ∼ 0 ) -involutive subalgebra. We prove that each ( ∼ 0 ) -involutive equality algebra is a lattice, while it is distributive under a suitable condition. Then, we define ( ∼ 0 ) -involutive deductive systems on bounded equality algebras and represent a condition under which the set of all dense elements of an equality algebra is a ( ∼ 0 ) -involutive deductive system. Finally, we find the relations among 0-compatible equality algebras, residuated lattices and Boolean algebras. |
| Author | Borzooei, R. A. Zahiri, O. Zarean, M. |
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| Keywords | Equality algebra Residuated lattice Involutive equality algebra Boolean algebra 03G25 06F05 06F35 |
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| References | RachůnekJŠalounováDIdeals and involutive filters in generalizations of fuzzy structuresFuzzy Sets Syst20173117085359710710.1016/j.fss.2016.03.004 CiunguLCCommutative pseudo equality algebrasSoft Comput2017214601461610.1007/s00500-016-2214-y NovákVDe BaetsBEQ-algebrasFuzzy Sets Syst200916029562978268331710.1016/j.fss.2009.04.010 CiunguLCOn pseudo-equality algebrasArch Math Log201453561570323786810.1007/s00153-014-0380-0 CiunguLavinia CorinaInternal states on equality algebrasSoft Computing201419493995310.1007/s00500-014-1494-3 MuresanCDense elements and classes of residuated latticesBull Math Soc Sci Math Roum Nouv Ser201053(101)1112426416921212.06035 WardMDilworthRPResiduated LatticesTrans Am Math Soc193945335354150199510.1090/S0002-9947-1939-1501995-3 BorzooeiRAZebardastaFAaly KologaniMSome types of filters in equality algebrasCateg Gen Algebr Struct Appl201773355368151706789591 ZareanMBorzooeiRAZahiriOOn state equality algebrasQuasigr Relat Syst2017252211220373801106854971 DvurečenskijAZahiriOPseudo equality algebras: revisionSoft Comput20162062091210110.1007/s00500-015-1888-x ZebardastaFBorzooeiRAAalyMKologani Results on equality algebrasInf Sci201738127028210.1016/j.ins.2016.11.027 JeneiSKóródiLPseudo-equality algebrasArch Math Log201352469481307277210.1007/s00153-013-0325-z BoicescuVFilipoiuAGeorgescuGRudeanuSLukasiewicz-Moisil algebras, Annals of Discrete Mathematics1991North HollandElsevier0726.06007 Novák V (2007) EQ-Algebras in progress. In: Castillo O, Melin P, Ross OM, Sepúlveda Cruz R, Pedrycz W, Kacprzyk J (eds) Theoretical advances and applications of fuzzy logic and soft computing. Advances in Soft Computing, vol 42. Springer, Berlin, Heidelberg BusneagDHertz algebras of fractions and maximal Hertz algebra of quotientsMath Jpn19933946146912788590810.06011 JeneiSEquality algebrasStud Log201210012011209300105310.1007/s11225-012-9457-0 Lavinia Corina Ciungu (3032_CR5) 2014; 19 V Novák (3032_CR12) 2009; 160 C Muresan (3032_CR10) 2010; 53(101) RA Borzooei (3032_CR2) 2017; 7 V Boicescu (3032_CR1) 1991 M Ward (3032_CR14) 1939; 45 J Rachůnek (3032_CR13) 2017; 311 LC Ciungu (3032_CR4) 2014; 53 S Jenei (3032_CR8) 2012; 100 3032_CR11 LC Ciungu (3032_CR6) 2017; 21 A Dvurečenskij (3032_CR7) 2016; 20 M Zarean (3032_CR15) 2017; 25 F Zebardasta (3032_CR16) 2017; 381 S Jenei (3032_CR9) 2013; 52 D Busneag (3032_CR3) 1993; 39 |
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| SubjectTerms | Algebra Artificial Intelligence Boolean algebra Computational Intelligence Control Engineering Equality Foundations Lattices (mathematics) Mathematical Logic and Foundations Mechatronics Robotics |
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