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Year 2012, Volume: 1 Issue: 1, 5 - 17, 01.01.2012

Faruk Karaaslan Naim Cagman Serdar Enginoglu

Abstract

References

  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59 (11) (2010) 3458-3463.
  • M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547-1553.
  • M.I. Ali, M. Shabir, M. Naz, Comput. Math. Appl. 61 (2011) 2647-2654.
  • H. Aktas. and N. C.a˘gman, Soft sets and soft groups, Inform. Sciences. 177 (2007) 2735.
  • K.V. Babitha, J.J. Sunil, Soft set relations and functions, Comput. Math. Appl. 60 (7) (2010) 1840-1849.
  • N. C.a˘gman and S. Engino˘glu, Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2) (2010) 848-855.
  • N. Cgman and S. Engino˘glu, Soft matrix theory and its decision making, Comput. a˘ Math. Appl. 59/10 (2010) 3308-3314.
  • N. C.a˘gman, F. Cıtak and S. Engino˘glu, Fuzzy parameterized fuzzy soft set theory and its applications, Turk. J. Fuzzy Syst. 1/1 (2010) 21-35.
  • N. C.a˘gman, S. Karata¸s and S. Engino˘glu, Soft Topology, Comput. Math. Appl. 62 (2011) 351-358.
  • D. Chen, E.C.C. Tsang, D.S. Yeung and X. Wang, The parameterization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005) 757-763.
  • F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl. 56/10 (2008) 2628.
  • F. Feng, Y.B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math. 234 (1) (2010) 10-20.
  • F. Feng, C.X. Li, B. Davvaz, M. Irfan Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput. 14 (2010) 899-911.
  • F. Feng, Y.M. Li, V. Leoreanu-Fotea, Application of level soft sets in decision making based on interval-valued fuzzy soft sets, Comput. Math. Appl. 60 (2010) 1756-1767.
  • F. Feng, X.Y. Liu, V. Leoreanu-Fotea, Y.B. Jun, Soft sets and soft rough sets, Inform. Sciences, 181 (2011) 1125-1137.
  • K. Gong, Z. Xiao, X. Zhang, The bijective soft set with its operations, Comput. Math. Appl. 60 (8) (2010) 2270-2278.
  • Y. Jiang, Y. Tang, Q. Chen, J. Wang, S. Tang, Extending soft sets with description logics, Comput. Math. Appl. 59 (6) (2010) 2087-2096
  • Y.B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408-1413.
  • Y.B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI- algebras, Inform. Sciences, 178 (2008) 2466-2475.
  • Y.B. Jun, K.J. Lee and C. H. Park, Soft Set Theory Applied To Commutative Ideals In BCK-Algebras, J. Appl. Math. Inform. 26 (2008) 707-720.
  • Y.B. Jun and C. H. Park, Applications of soft sets in Hilbert algebras, Iran J. Fuzzy Syst. 6/2 (2009) 75-88.
  • Y.B. Jun, H. S. Kim and J. Neggers, Pseudo d-algebras, Inform. Sciences, 179 (2009) 1759.
  • Y.B. Jun, K.J. Lee and C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl. 57 (2009) 367-378.
  • Y.B. Jun, K.J. Lee, J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. (10)(2009) 2060-2068.
  • Y.B. Jun, K.J. Lee, A. Khan, Soft ordered semigroups, Math. Logic Quart. 56 (1) (2010) 42-50.
  • O. Kazancı, . Yılmaz, S. Yamak, Soft sets and soft BCH-algebras, Hacet. J. Math. Stat. 39 (2) (2010) 205-217.
  • F. Li, Soft Lattices, Glob. J. Sci. Front. Res. 10/4 (2010) 56-58.
  • P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9/3 (2001) 602.
  • P.K. Maji, A.R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.
  • P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 562.
  • D.A. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999) 19-31.
  • R. Nagarajan and G. Meenambigai, An Application Of Soft Sets to Lattices, Kragu- jevac J. Math. 35/1 (2011) 61-73.
  • Z. Pololak, ’Hard Set and Soft Sets’, Ics. Research Report, Institute of Computer Science, Poland, 1994.
  • K. Qin, Z. Hong, On soft equality, J. Comput. Appl. Math. 234 (5) (2010) 1347-1355.
  • A.R. Roy and P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203 (2007) 412-418.
  • M. Shabir, M. Irfan Ali, Soft ideals and generalized fuzzy ideals in semigroups, New Math. Nat. Comput. 5 (2009) 599-615.
  • Z. Xiao, K. Gong, S. Xia, Y. Zou, Exclusive disjunctive soft sets, Comput. Math. Appl. 59 (6) (2010) 2128-2137.
  • W. Xu, W. J. Ma, S. Wang and G. Hao, Vague soft sets and their properties, Comput. Math. Appl. 59 (2010) 787-794.
  • L.A. Zadeh, Fuzzy Sets, Infor. and Control, 8 (1965) 338-353.

Soft Lattices

Year 2012, Volume: 1 Issue: 1, 5 - 17, 01.01.2012

Faruk Karaaslan Naim Cagman Serdar Enginoglu

Abstract

Soft set theory was introduced by Molodtsov in 1999 as a general mathematical tool for dealing with problems that contain uncertainity. In this paper,we define concept of a soft lattice, soft sublattice, complete soft lattice, modular soft lattice, distributive soft lattice, soft chain and study their relatedproperties

Keywords

Soft sets soft sublattices complete soft lattices modular softlattices distributive soft lattices soft chain

References

  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59 (11) (2010) 3458-3463.
  • M.I. Ali, F. Feng, X. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547-1553.
  • M.I. Ali, M. Shabir, M. Naz, Comput. Math. Appl. 61 (2011) 2647-2654.
  • H. Aktas. and N. C.a˘gman, Soft sets and soft groups, Inform. Sciences. 177 (2007) 2735.
  • K.V. Babitha, J.J. Sunil, Soft set relations and functions, Comput. Math. Appl. 60 (7) (2010) 1840-1849.
  • N. C.a˘gman and S. Engino˘glu, Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2) (2010) 848-855.
  • N. Cgman and S. Engino˘glu, Soft matrix theory and its decision making, Comput. a˘ Math. Appl. 59/10 (2010) 3308-3314.
  • N. C.a˘gman, F. Cıtak and S. Engino˘glu, Fuzzy parameterized fuzzy soft set theory and its applications, Turk. J. Fuzzy Syst. 1/1 (2010) 21-35.
  • N. C.a˘gman, S. Karata¸s and S. Engino˘glu, Soft Topology, Comput. Math. Appl. 62 (2011) 351-358.
  • D. Chen, E.C.C. Tsang, D.S. Yeung and X. Wang, The parameterization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005) 757-763.
  • F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl. 56/10 (2008) 2628.
  • F. Feng, Y.B. Jun, X. Liu, L. Li, An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math. 234 (1) (2010) 10-20.
  • F. Feng, C.X. Li, B. Davvaz, M. Irfan Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Comput. 14 (2010) 899-911.
  • F. Feng, Y.M. Li, V. Leoreanu-Fotea, Application of level soft sets in decision making based on interval-valued fuzzy soft sets, Comput. Math. Appl. 60 (2010) 1756-1767.
  • F. Feng, X.Y. Liu, V. Leoreanu-Fotea, Y.B. Jun, Soft sets and soft rough sets, Inform. Sciences, 181 (2011) 1125-1137.
  • K. Gong, Z. Xiao, X. Zhang, The bijective soft set with its operations, Comput. Math. Appl. 60 (8) (2010) 2270-2278.
  • Y. Jiang, Y. Tang, Q. Chen, J. Wang, S. Tang, Extending soft sets with description logics, Comput. Math. Appl. 59 (6) (2010) 2087-2096
  • Y.B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408-1413.
  • Y.B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI- algebras, Inform. Sciences, 178 (2008) 2466-2475.
  • Y.B. Jun, K.J. Lee and C. H. Park, Soft Set Theory Applied To Commutative Ideals In BCK-Algebras, J. Appl. Math. Inform. 26 (2008) 707-720.
  • Y.B. Jun and C. H. Park, Applications of soft sets in Hilbert algebras, Iran J. Fuzzy Syst. 6/2 (2009) 75-88.
  • Y.B. Jun, H. S. Kim and J. Neggers, Pseudo d-algebras, Inform. Sciences, 179 (2009) 1759.
  • Y.B. Jun, K.J. Lee and C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl. 57 (2009) 367-378.
  • Y.B. Jun, K.J. Lee, J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. (10)(2009) 2060-2068.
  • Y.B. Jun, K.J. Lee, A. Khan, Soft ordered semigroups, Math. Logic Quart. 56 (1) (2010) 42-50.
  • O. Kazancı, . Yılmaz, S. Yamak, Soft sets and soft BCH-algebras, Hacet. J. Math. Stat. 39 (2) (2010) 205-217.
  • F. Li, Soft Lattices, Glob. J. Sci. Front. Res. 10/4 (2010) 56-58.
  • P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9/3 (2001) 602.
  • P.K. Maji, A.R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.
  • P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 562.
  • D.A. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999) 19-31.
  • R. Nagarajan and G. Meenambigai, An Application Of Soft Sets to Lattices, Kragu- jevac J. Math. 35/1 (2011) 61-73.
  • Z. Pololak, ’Hard Set and Soft Sets’, Ics. Research Report, Institute of Computer Science, Poland, 1994.
  • K. Qin, Z. Hong, On soft equality, J. Comput. Appl. Math. 234 (5) (2010) 1347-1355.
  • A.R. Roy and P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203 (2007) 412-418.
  • M. Shabir, M. Irfan Ali, Soft ideals and generalized fuzzy ideals in semigroups, New Math. Nat. Comput. 5 (2009) 599-615.
  • Z. Xiao, K. Gong, S. Xia, Y. Zou, Exclusive disjunctive soft sets, Comput. Math. Appl. 59 (6) (2010) 2128-2137.
  • W. Xu, W. J. Ma, S. Wang and G. Hao, Vague soft sets and their properties, Comput. Math. Appl. 59 (2010) 787-794.
  • L.A. Zadeh, Fuzzy Sets, Infor. and Control, 8 (1965) 338-353.
There are 39 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Faruk Karaaslan This is me

Naim Cagman This is me

Serdar Enginoglu

Publication Date January 1, 2012
Published in Issue Year 2012 Volume: 1 Issue: 1

Cite

APA Karaaslan, F., Cagman, N., & Enginoglu, S. (2012). Soft Lattices. Journal of New Results in Science, 1(1), 5-17.
AMA Karaaslan F, Cagman N, Enginoglu S. Soft Lattices. JNRS. January 2012;1(1):5-17.
Chicago Karaaslan, Faruk, Naim Cagman, and Serdar Enginoglu. “Soft Lattices”. Journal of New Results in Science 1, no. 1 (January 2012): 5-17.
EndNote Karaaslan F, Cagman N, Enginoglu S (January 1, 2012) Soft Lattices. Journal of New Results in Science 1 1 5–17.
IEEE F. Karaaslan, N. Cagman, and S. Enginoglu, “Soft Lattices”, JNRS, vol. 1, no. 1, pp. 5–17, 2012.
ISNAD Karaaslan, Faruk et al. “Soft Lattices”. Journal of New Results in Science 1/1 (January 2012), 5-17.
JAMA Karaaslan F, Cagman N, Enginoglu S. Soft Lattices. JNRS. 2012;1:5–17.
MLA Karaaslan, Faruk et al. “Soft Lattices”. Journal of New Results in Science, vol. 1, no. 1, 2012, pp. 5-17.
Vancouver Karaaslan F, Cagman N, Enginoglu S. Soft Lattices. JNRS. 2012;1(1):5-17.


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