Applications of soft sets in hilbert algebras

The concept of soft sets, introduced by Molodtsov (20) is a math- ematical tool for dealing with uncertainties, that is free from the diculties that have troubled the traditional theoretical approaches. In this paper, we apply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras. The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras, soft abysms and soft deductive systems are introduced, and their basic proper- ties are investigated. The relations between soft Hilbert algebras, soft Hilbert abysmal algebras and soft Hilbert deductive algebras are also derived.

[1]  Young Bae Jun,et al.  Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings , 2007, Inf. Sci..

[2]  L. A. Zadeh,et al.  From Circuit Theory to System Theory , 1962, Proceedings of the IRE.

[3]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[4]  D. Molodtsov.  Soft set theory—First results , 1999 .

[5]  M. M. Zahedi,et al.  SOME RESULTS OF INTUITIONISTIC FUZZY WEAK DUAL HYPER K-IDEALS , 2008 .

[6]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[7]  Bijan Davvaz,et al.  ON ( $alpha, beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS , 2008 .

[8]  J. Bae,et al.  DEDUCTIVE SYSTEMS OF HILBERT ALGEBRAS , 1996 .

[9]  Andrzej Skowron,et al.  Rough sets and Boolean reasoning , 2007, Inf. Sci..

[10]  Bijan Davvaz,et al.  Roughness based on fuzzy ideals , 2006, Inf. Sci..

[11]  Y. Jun,et al.  INTUITIONISTIC FUZZY HYPER BCK-IDEALS OF HYPER BCK-ALGEBRAS , 2004 .

[12]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[13]  A. R. Roy,et al.  An application of soft sets in a decision making problem , 2002 .

[14]  Roh Eun Hwan,et al.  THE ABYSM OF A HILBERT ALGEBRA , 2007 .

[15]  D. A. Molodtsov,et al.  Soft sets theory-based optimization , 2007 .

[16]  A. R. Roy,et al.  Soft set theory , 2003 .

[17]  Young Bae Jun,et al.  Applications of soft sets in ideal theory of BCK/BCI-algebras , 2008, Inf. Sci..

[18]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[19]  Y. Jun,et al.  REDEFINED FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS , 2008 .

[20]  Antonio Diego,et al.  Sur les Algèbres de Hilbert , 1970 .

[21]  I. Chajda.  The Lattice of Deductive Systems on Hilbert Algebras , 2003 .

[22]  Eric C. C. Tsang,et al.  The parameterization reduction of soft sets and its applications , 2005 .

[23]  Dumitru Busneag,et al.  A note on deductive systems of a Hilbert algebra , 1985 .

[24]  Y. Jun,et al.  Annihilators and deductive systems in commutative Hilbert algebras , 2002 .

[25]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[26]  D. Busneag.  Hilbert algebras of fractions and maximal Hilbert algebras of quotients , 1988 .