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New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh's Logical Operators

Year 2014, Volume: 3 Issue: 4, 71 - 81, 01.04.2014

Abstract

– In this paper , we have defined First Zadeh’s implication , First Zadeh’s intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets and some their basic properties are studied with proofs and examples

References

  • K.T. Atanassov, ”Intuitionistic Fuzzy Set”. Fuzzy Sets and Systems, vol. 20(1), pp.87-86, 1986.
  • K.T. Atanassov and G. Gargov ,” Intuitionistic Fuzzy Logic “,C.R Academy of Bulgarian Society , Vol . 53, pp .9-12,1990
  • K.T. Atanassov , and G.Gargov, ,” Intuitionistic Fuzzy Prolog “,Fuzzy Sets and sSystems , Vol . 4(3), pp .121-128,1993
  • E.Szmidt and J.Kacprzyk ,” Intuitionistic Fuzzy Sets in group decision making”, Notes on IFS 2 ,pp.11-14 ,1996
  • S.K.De, R . Biswas and A.Roy ,”An Application of Intuitionstic Fuzzy set in medical diagnosis “,Fuzzy Sets and Systems, vol .117, pp 209-213 ,2001.
  • K.T. Atanassov .”Intuitionistic Fuzzy Sets “,Springer Physica-Verlag ,Heidelberg,1999.
  • K.T. Atanassov,” On Some Intuitionstic Fuzzy Implication. Comptes Rendus de l’Academie bulgare des Sciences, Tome 59 , 2006 , No .1 , 19-24
  • K.T. Atanassov. “On Zadeh’s intuitionistic Fuzzy Disjunction and Conjunction. Notes on Intuitionistic Fuzzy Sets, Vol .1,2011, No1,1-4.
  • K.T. Atanassov. “ Second Zadeh’s Intuitionistic Fuzzy Implication. Notes on Intuitionistic Fuzzy Sets, Vol .17,2011, No3 (in press)
  • D. A. Molodtsov, “Soft Set Theory - First Result”, Computers and Mathematics with Applications, Vol. 37, (1999),pp. 19-31.
  • P. K. Maji, R. Biswas and A.R. Roy, “Fuzzy Soft Sets”, Journal of Fuzzy Mathematics, Vol 9 , no.3, (2001), pp.-589-602.
  • B. Ahmad, and A. Kharal, “On Fuzzy Soft Sets”, Hindawi Publishing Corporation, Advances in Fuzzy Systems, volume Article ID 586507, (2009), 6 pages doi: 10.1155/2009/586507.
  • P. K. Maji, A. R. Roy and R. Biswas, “Fuzzy Soft Sets” ,Journal of Fuzzy Mathematics. 9 (3),(2001), pp.589-602.
  • T. J. Neog and D. K. Sut, “On Fuzzy Soft Complement and Related Properties”, Accepted for publication in International, Journal of Energy, Information and communications (IJEIC).
  • M. Borah, T. J. Neog and D. K. Sut,” A Study on some Operations of Fuzzy Soft Sets”, International Journal of Modern Engineering Research (IJMER), Vol.2, Issue. 2,(2012), pp. 157-168.
  • H. L. Yang, “Notes On Generalized Fuzzy Soft Sets”, Journal of Mathematical Research and Exposition, Vol 31, No. 3, (2011), pp.567-570.
  • P. Majumdar, S. K. Samanta, “Generalized Fuzzy Soft Sets”, Computers and Mathematics with Applications,59(2010), pp.1425-1432.
  • S. Alkhazaleh, A. R. Salleh, and N. Hassan,” Possibility Fuzzy Soft Set”, Advances in Decision Sciences,Vol 2011, Article ID 479756,18pages,doi:10.1155/2011/479756.
  • [19 ] P. K. Maji, R. Biswas, A. R. Roy, “Intuitionistic Fuzzy Soft Sets”, The journal of fuzzy mathematics 9(3)( 2001 ), pp.677-692.
  • K.V .Babitha and J. J. Sunil,” Generalized Intuitionistic Fuzzy Soft Sets and Its Applications “,Gen. Math. Notes, ISSN 2219-7184; Copyright © ICSRS Publication, (2011), Vol. 7, No. 2, (2011), pp.1-14.
  • M.Bashir, A.R. Salleh, and S. Alkhazaleh,” Possibility Intuitionistic Fuzzy Soft Set”, Advances in Decision Sciences Volume 2012 (2012), Article ID 404325, 24 pages, doi:10.1155/2012/404325.
Year 2014, Volume: 3 Issue: 4, 71 - 81, 01.04.2014

Abstract

References

  • K.T. Atanassov, ”Intuitionistic Fuzzy Set”. Fuzzy Sets and Systems, vol. 20(1), pp.87-86, 1986.
  • K.T. Atanassov and G. Gargov ,” Intuitionistic Fuzzy Logic “,C.R Academy of Bulgarian Society , Vol . 53, pp .9-12,1990
  • K.T. Atanassov , and G.Gargov, ,” Intuitionistic Fuzzy Prolog “,Fuzzy Sets and sSystems , Vol . 4(3), pp .121-128,1993
  • E.Szmidt and J.Kacprzyk ,” Intuitionistic Fuzzy Sets in group decision making”, Notes on IFS 2 ,pp.11-14 ,1996
  • S.K.De, R . Biswas and A.Roy ,”An Application of Intuitionstic Fuzzy set in medical diagnosis “,Fuzzy Sets and Systems, vol .117, pp 209-213 ,2001.
  • K.T. Atanassov .”Intuitionistic Fuzzy Sets “,Springer Physica-Verlag ,Heidelberg,1999.
  • K.T. Atanassov,” On Some Intuitionstic Fuzzy Implication. Comptes Rendus de l’Academie bulgare des Sciences, Tome 59 , 2006 , No .1 , 19-24
  • K.T. Atanassov. “On Zadeh’s intuitionistic Fuzzy Disjunction and Conjunction. Notes on Intuitionistic Fuzzy Sets, Vol .1,2011, No1,1-4.
  • K.T. Atanassov. “ Second Zadeh’s Intuitionistic Fuzzy Implication. Notes on Intuitionistic Fuzzy Sets, Vol .17,2011, No3 (in press)
  • D. A. Molodtsov, “Soft Set Theory - First Result”, Computers and Mathematics with Applications, Vol. 37, (1999),pp. 19-31.
  • P. K. Maji, R. Biswas and A.R. Roy, “Fuzzy Soft Sets”, Journal of Fuzzy Mathematics, Vol 9 , no.3, (2001), pp.-589-602.
  • B. Ahmad, and A. Kharal, “On Fuzzy Soft Sets”, Hindawi Publishing Corporation, Advances in Fuzzy Systems, volume Article ID 586507, (2009), 6 pages doi: 10.1155/2009/586507.
  • P. K. Maji, A. R. Roy and R. Biswas, “Fuzzy Soft Sets” ,Journal of Fuzzy Mathematics. 9 (3),(2001), pp.589-602.
  • T. J. Neog and D. K. Sut, “On Fuzzy Soft Complement and Related Properties”, Accepted for publication in International, Journal of Energy, Information and communications (IJEIC).
  • M. Borah, T. J. Neog and D. K. Sut,” A Study on some Operations of Fuzzy Soft Sets”, International Journal of Modern Engineering Research (IJMER), Vol.2, Issue. 2,(2012), pp. 157-168.
  • H. L. Yang, “Notes On Generalized Fuzzy Soft Sets”, Journal of Mathematical Research and Exposition, Vol 31, No. 3, (2011), pp.567-570.
  • P. Majumdar, S. K. Samanta, “Generalized Fuzzy Soft Sets”, Computers and Mathematics with Applications,59(2010), pp.1425-1432.
  • S. Alkhazaleh, A. R. Salleh, and N. Hassan,” Possibility Fuzzy Soft Set”, Advances in Decision Sciences,Vol 2011, Article ID 479756,18pages,doi:10.1155/2011/479756.
  • [19 ] P. K. Maji, R. Biswas, A. R. Roy, “Intuitionistic Fuzzy Soft Sets”, The journal of fuzzy mathematics 9(3)( 2001 ), pp.677-692.
  • K.V .Babitha and J. J. Sunil,” Generalized Intuitionistic Fuzzy Soft Sets and Its Applications “,Gen. Math. Notes, ISSN 2219-7184; Copyright © ICSRS Publication, (2011), Vol. 7, No. 2, (2011), pp.1-14.
  • M.Bashir, A.R. Salleh, and S. Alkhazaleh,” Possibility Intuitionistic Fuzzy Soft Set”, Advances in Decision Sciences Volume 2012 (2012), Article ID 404325, 24 pages, doi:10.1155/2012/404325.
There are 21 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Said Broumi This is me

Pinaki Majumdar This is me

Florentin Smarandache This is me

Publication Date April 1, 2014
Published in Issue Year 2014 Volume: 3 Issue: 4

Cite

APA Broumi, S., Majumdar, P., & Smarandache, F. (2014). New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators. Journal of New Results in Science, 3(4), 71-81.
AMA Broumi S, Majumdar P, Smarandache F. New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators. JNRS. April 2014;3(4):71-81.
Chicago Broumi, Said, Pinaki Majumdar, and Florentin Smarandache. “New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators”. Journal of New Results in Science 3, no. 4 (April 2014): 71-81.
EndNote Broumi S, Majumdar P, Smarandache F (April 1, 2014) New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators. Journal of New Results in Science 3 4 71–81.
IEEE S. Broumi, P. Majumdar, and F. Smarandache, “New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators”, JNRS, vol. 3, no. 4, pp. 71–81, 2014.
ISNAD Broumi, Said et al. “New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators”. Journal of New Results in Science 3/4 (April 2014), 71-81.
JAMA Broumi S, Majumdar P, Smarandache F. New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators. JNRS. 2014;3:71–81.
MLA Broumi, Said et al. “New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators”. Journal of New Results in Science, vol. 3, no. 4, 2014, pp. 71-81.
Vancouver Broumi S, Majumdar P, Smarandache F. New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh’s Logical Operators. JNRS. 2014;3(4):71-8.


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