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On Intuitionistic Fuzzy Soft Groups

Year 2013, Volume: 2 Issue: 3, 72 - 86, 01.03.2013

Faruk Karaaslan Kenan Kaygisiz Naim Çağman

Abstract

–In this paper, we give some basic properties ofintuitionistic fuzzy soft sets and (α, β)-level sets. Also we defineimage of an intuitionistic fuzzy soft set under a function, productof two intuitionistic fuzzy soft sets and obtain some results. Inaddition, we define intuitionistic fuzzy soft group and investigatetheir properties

Keywords

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References

  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computer and Mathemetics with Application, 59, 3458-3463, 2010.
  • M.I. Ali, F.Feng, X.Liu, W.K. Min, M. Shabir, On some new operations in soft set theory. Computer Mathematics with Application 57, 1547-1553, 2009.
  • H. Akta¸s, N. C¸ a˘gman, Soft sets and soft groups, Information Sciences 177, 2726- 2735, 2007.
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set and Systems, 20, 87-96, 1986.
  • K. Kaygısız, On soft int groups, Annals of Fuzzy Mathematics and Informatics. 4(2), 363-375, 2012.
  • K. Kaygısız, Normal soft int groups, arXiv.1209.3157v1 [math, GR], 14 Sep 2012.
  • A. Ayg¨unoglu, H. Ayg¨un, Introduction to fuzzy soft groups, Computer and Math- ematics with Application, 58, 1279-1286, 2009.
  • N. C¸ a˘gman, S. Engino˘glu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207, 848-855, 2010.
  • N. C¸ a˘gman, F. C¸ ıtak, S. Engino˘glu, Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy Systems, 1, 21-35, 2010.
  • N. C¸ a˘gman, S. Engino˘glu, F. C¸ ıtak Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems 8(3), 137-147, 2011.
  • N. C¸ a˘gman, F. C¸ ıtak, H. Akta¸s Soft int-group, Neural Computing and Application, 21(1), 151-158, 2012.
  • M. Fatih, A.R. Salleh, Intuitionistic fuzzy group, Asian Journal of Algebra, 2(1), 1-10, 2009.
  • F. Feng, Y.B. Jun, X. Zhao, Soft semirings, Computer and Mathematics with Applications, 56, 2621-2628, 2008.
  • F. Feng, C. Li, B. Davvaz, M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14(9), 899-911, 2010.
  • L. Flep Structure and construction of fuzzy subgroup of a group, Fuzzy Set and Systems 51, 105-109, 1992.
  • Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tang, Interval-valued intuitionistic fuzzy soft sets and their properties, Computer Mathematics with Applications, 60(3), 906- 918, 2010.
  • Y. Jiang, Y. Tang, Q. Chen, An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling, 35, 824-836, 2011.
  • Y.B. Jun, Soft BCK/BCI-algebras, Computer Mathematics with Applications, 56, 1408-1413, 2008.
  • Y.B Jun, C.H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebra Information Sciences, 178, 2466-2475, 2008.
  • Y.B. Jun, K.J Lee, A. Khan, (2010) Soft ordered semigroups. Mathematical Logic Quarterly, 56(1), 42-50, 2010.
  • P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics 9(3), 589-602, 2001.
  • P.K. Maji, R. Biswas, A.R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics 9(3), 677-692, 2001.
  • P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Computer Mathematics with Applications, 45, 555-562, 2003.
  • P. Majumdar, S.K. Samanta, Generalised fuzzy soft sets, Computer Mathematics with Application 59, 1425-1432, 2010.
  • D.A. Molodtsov, Soft set theory-first results, Computer and Mathematics with Applications 37, 19-31, 1999.
  • A. Rosenfeld, Fuzzy groups, Journal of Mathematics Analysis and Applications, 35, 512-517, 1971.
  • A. Sezgin, A.O. Atag¨un, N. C¸ a˘gman, Union soft substructures of near-rings and N-groups, Neural Computing and Applications, 21(1), 133-143, 2012.
  • N. Yaqoob, M. Akram, M. Aslam, Intuitionistic fuzzy soft groups induced by (t, s)- norm, Indian Journal of Science and Technology, 6(4), 4282-4289, 2013.
  • L.A. Zadeh, Fuzzy sets, Information Control, 8, 338-353, 1965.
  • J. Zhou, Y. Li, Y. Yin, Intuitionistic fuzzy soft semigroups, Mathematica Aeterna, 1 03, 173-183, 2011.

Year 2013, Volume: 2 Issue: 3, 72 - 86, 01.03.2013

Faruk Karaaslan Kenan Kaygisiz Naim Çağman

Abstract

References

  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computer and Mathemetics with Application, 59, 3458-3463, 2010.
  • M.I. Ali, F.Feng, X.Liu, W.K. Min, M. Shabir, On some new operations in soft set theory. Computer Mathematics with Application 57, 1547-1553, 2009.
  • H. Akta¸s, N. C¸ a˘gman, Soft sets and soft groups, Information Sciences 177, 2726- 2735, 2007.
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set and Systems, 20, 87-96, 1986.
  • K. Kaygısız, On soft int groups, Annals of Fuzzy Mathematics and Informatics. 4(2), 363-375, 2012.
  • K. Kaygısız, Normal soft int groups, arXiv.1209.3157v1 [math, GR], 14 Sep 2012.
  • A. Ayg¨unoglu, H. Ayg¨un, Introduction to fuzzy soft groups, Computer and Math- ematics with Application, 58, 1279-1286, 2009.
  • N. C¸ a˘gman, S. Engino˘glu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207, 848-855, 2010.
  • N. C¸ a˘gman, F. C¸ ıtak, S. Engino˘glu, Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy Systems, 1, 21-35, 2010.
  • N. C¸ a˘gman, S. Engino˘glu, F. C¸ ıtak Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems 8(3), 137-147, 2011.
  • N. C¸ a˘gman, F. C¸ ıtak, H. Akta¸s Soft int-group, Neural Computing and Application, 21(1), 151-158, 2012.
  • M. Fatih, A.R. Salleh, Intuitionistic fuzzy group, Asian Journal of Algebra, 2(1), 1-10, 2009.
  • F. Feng, Y.B. Jun, X. Zhao, Soft semirings, Computer and Mathematics with Applications, 56, 2621-2628, 2008.
  • F. Feng, C. Li, B. Davvaz, M.I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14(9), 899-911, 2010.
  • L. Flep Structure and construction of fuzzy subgroup of a group, Fuzzy Set and Systems 51, 105-109, 1992.
  • Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tang, Interval-valued intuitionistic fuzzy soft sets and their properties, Computer Mathematics with Applications, 60(3), 906- 918, 2010.
  • Y. Jiang, Y. Tang, Q. Chen, An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling, 35, 824-836, 2011.
  • Y.B. Jun, Soft BCK/BCI-algebras, Computer Mathematics with Applications, 56, 1408-1413, 2008.
  • Y.B Jun, C.H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebra Information Sciences, 178, 2466-2475, 2008.
  • Y.B. Jun, K.J Lee, A. Khan, (2010) Soft ordered semigroups. Mathematical Logic Quarterly, 56(1), 42-50, 2010.
  • P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics 9(3), 589-602, 2001.
  • P.K. Maji, R. Biswas, A.R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics 9(3), 677-692, 2001.
  • P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Computer Mathematics with Applications, 45, 555-562, 2003.
  • P. Majumdar, S.K. Samanta, Generalised fuzzy soft sets, Computer Mathematics with Application 59, 1425-1432, 2010.
  • D.A. Molodtsov, Soft set theory-first results, Computer and Mathematics with Applications 37, 19-31, 1999.
  • A. Rosenfeld, Fuzzy groups, Journal of Mathematics Analysis and Applications, 35, 512-517, 1971.
  • A. Sezgin, A.O. Atag¨un, N. C¸ a˘gman, Union soft substructures of near-rings and N-groups, Neural Computing and Applications, 21(1), 133-143, 2012.
  • N. Yaqoob, M. Akram, M. Aslam, Intuitionistic fuzzy soft groups induced by (t, s)- norm, Indian Journal of Science and Technology, 6(4), 4282-4289, 2013.
  • L.A. Zadeh, Fuzzy sets, Information Control, 8, 338-353, 1965.
  • J. Zhou, Y. Li, Y. Yin, Intuitionistic fuzzy soft semigroups, Mathematica Aeterna, 1 03, 173-183, 2011.
There are 30 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Faruk Karaaslan This is me

Kenan Kaygisiz This is me

Naim Çağman This is me

Publication Date March 1, 2013
Published in Issue Year 2013 Volume: 2 Issue: 3

Cite

APA Karaaslan, F., Kaygisiz, K., & Çağman, N. (2013). On Intuitionistic Fuzzy Soft Groups. Journal of New Results in Science, 2(3), 72-86.
AMA Karaaslan F, Kaygisiz K, Çağman N. On Intuitionistic Fuzzy Soft Groups. JNRS. March 2013;2(3):72-86.
Chicago Karaaslan, Faruk, Kenan Kaygisiz, and Naim Çağman. “On Intuitionistic Fuzzy Soft Groups”. Journal of New Results in Science 2, no. 3 (March 2013): 72-86.
EndNote Karaaslan F, Kaygisiz K, Çağman N (March 1, 2013) On Intuitionistic Fuzzy Soft Groups. Journal of New Results in Science 2 3 72–86.
IEEE F. Karaaslan, K. Kaygisiz, and N. Çağman, “On Intuitionistic Fuzzy Soft Groups”, JNRS, vol. 2, no. 3, pp. 72–86, 2013.
ISNAD Karaaslan, Faruk et al. “On Intuitionistic Fuzzy Soft Groups”. Journal of New Results in Science 2/3 (March 2013), 72-86.
JAMA Karaaslan F, Kaygisiz K, Çağman N. On Intuitionistic Fuzzy Soft Groups. JNRS. 2013;2:72–86.
MLA Karaaslan, Faruk et al. “On Intuitionistic Fuzzy Soft Groups”. Journal of New Results in Science, vol. 2, no. 3, 2013, pp. 72-86.
Vancouver Karaaslan F, Kaygisiz K, Çağman N. On Intuitionistic Fuzzy Soft Groups. JNRS. 2013;2(3):72-86.


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