BibTex RIS Kaynak Göster

NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS

Yıl 2016, Cilt: 29 Sayı: 3, 667 - 674, 30.09.2016

Öz

The concept of intuitionistic fuzzy sets and its generalizations play a vital role in modeling uncertainty and vagueness involved in deferent field of science. Recently, generalized interval valued intuitionistic fuzzy sets were presented by Baloui Jamkhaneh (2015) and defined some operations over it.  In this paper, defined arithmetic mean operation and geometric mean operation over  are proposed and few theorems were proved.  In addition, some of the basic properties of the new operations are discussed. By using these new operations, a prioritization method for generalized interval valued intuitionistic fuzzy judgment matrix is proposed.

Kaynakça

  • Atanassov, K.T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87-96.
  • Atanassov, K. T., & Gargov, G. (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343-349.
  • Atanassov, K.T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets & Systems, 61, 37-42.
  • Atanassov, K.T. (2001) Remark on two operations over intuitionistic fuzzy sets, Int. J. of Uncertainty, Fuzziness and Knowledge Syst., 9(1), 71-75.
  • Baloui Jamkhaneh E., Nadarajah S. (2015) A New generalized intuitionistic fuzzy sets, Hacettepe Journal of Mathematics and Statistics, 44 (6) , 1537 – 1551.
  • Baloui Jamkhaneh E. (2015) New generalized interval value intuitionistic fuzzy sets, Research and Communications in Mathematics and Mathematical Sciences, 5(1), 33-46.
  • Broumi S., Smarandache F. (2014) New operations over interval valued intuitionistic hesitant fuzzy set, Mathematics and Statistics 2(2): 62-71.
  • De, S. K., Biswas R. and Roy A. R. (2000) Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114 (4), 477–484.
  • Hui W. (2013) Some operations on interval-valued intuitionistic fuzzy sets", 2013 Fifth International Conference on Computational and Information Sciences (ICCIS), 832-834, doi:10.1109/ICCIS.2013.223
  • Liu Q., Ma C. and Zhou X. (2008) On properties of some IFS operators and operations, Notes on Intuitionistic Fuzzy Sets, 14(3), 17-24.
  • Riecan B. and Atanassov K. T. (2006) n-extraction operation over intuitionistic fuzzy sets, Notes in Intuitionistic Fuzzy Sets, 12(4), 9–11.
  • [`12] Riecan B. and Atanassov K. T. (2010) Operation division by n over intuitionistic fuzzy sets, Notes in Intuitionistic Fuzzy Sets, 16 (4), 1–4.
  • Parvathi R., Riecan B. and Atanassov K.(2012) Properties of some operations defined over intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 18 (1), 1–4.
  • Vasilev, T. (2008) Four equalities connected with intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 14(3), 1-4.
  • Wang W., Liu X. (2013) Some operations over Atanassovs intutionestic fuzzy sets based on Einstein t-norm and t-conorm, Int. J. Unc. Fuzz. Knowl. Based Syst. 21, 263. DOI: http://dx.doi.org/10.1142/S0218488513500141.
  • Zadeh L.A. (1965) Fuzzy sets, Information Control, 8, 338-353.
  • Zhang Z. (2013), Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision-making, Journal of Applied Mathematics, Vol. 2013, Article ID 670285, http://dx.doi.org/10.1155/2013/670285.
  • Zhang Z., Yang J., Ye Y., Zhang Q. S. (2011) A generalized interval valued intuitionistic fuzzy sets theory, Procedia Engineering 15, 2037 – 2041
  • Zhao H., Xu Z. & Yao Z. (2016) Interval-valued intuitionistic fuzzy derivative and differential operations, International Journal of Computational Intelligence Systems, 9(1), 35-56.
Yıl 2016, Cilt: 29 Sayı: 3, 667 - 674, 30.09.2016

Öz

Kaynakça

  • Atanassov, K.T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87-96.
  • Atanassov, K. T., & Gargov, G. (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343-349.
  • Atanassov, K.T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets & Systems, 61, 37-42.
  • Atanassov, K.T. (2001) Remark on two operations over intuitionistic fuzzy sets, Int. J. of Uncertainty, Fuzziness and Knowledge Syst., 9(1), 71-75.
  • Baloui Jamkhaneh E., Nadarajah S. (2015) A New generalized intuitionistic fuzzy sets, Hacettepe Journal of Mathematics and Statistics, 44 (6) , 1537 – 1551.
  • Baloui Jamkhaneh E. (2015) New generalized interval value intuitionistic fuzzy sets, Research and Communications in Mathematics and Mathematical Sciences, 5(1), 33-46.
  • Broumi S., Smarandache F. (2014) New operations over interval valued intuitionistic hesitant fuzzy set, Mathematics and Statistics 2(2): 62-71.
  • De, S. K., Biswas R. and Roy A. R. (2000) Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114 (4), 477–484.
  • Hui W. (2013) Some operations on interval-valued intuitionistic fuzzy sets", 2013 Fifth International Conference on Computational and Information Sciences (ICCIS), 832-834, doi:10.1109/ICCIS.2013.223
  • Liu Q., Ma C. and Zhou X. (2008) On properties of some IFS operators and operations, Notes on Intuitionistic Fuzzy Sets, 14(3), 17-24.
  • Riecan B. and Atanassov K. T. (2006) n-extraction operation over intuitionistic fuzzy sets, Notes in Intuitionistic Fuzzy Sets, 12(4), 9–11.
  • [`12] Riecan B. and Atanassov K. T. (2010) Operation division by n over intuitionistic fuzzy sets, Notes in Intuitionistic Fuzzy Sets, 16 (4), 1–4.
  • Parvathi R., Riecan B. and Atanassov K.(2012) Properties of some operations defined over intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 18 (1), 1–4.
  • Vasilev, T. (2008) Four equalities connected with intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 14(3), 1-4.
  • Wang W., Liu X. (2013) Some operations over Atanassovs intutionestic fuzzy sets based on Einstein t-norm and t-conorm, Int. J. Unc. Fuzz. Knowl. Based Syst. 21, 263. DOI: http://dx.doi.org/10.1142/S0218488513500141.
  • Zadeh L.A. (1965) Fuzzy sets, Information Control, 8, 338-353.
  • Zhang Z. (2013), Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision-making, Journal of Applied Mathematics, Vol. 2013, Article ID 670285, http://dx.doi.org/10.1155/2013/670285.
  • Zhang Z., Yang J., Ye Y., Zhang Q. S. (2011) A generalized interval valued intuitionistic fuzzy sets theory, Procedia Engineering 15, 2037 – 2041
  • Zhao H., Xu Z. & Yao Z. (2016) Interval-valued intuitionistic fuzzy derivative and differential operations, International Journal of Computational Intelligence Systems, 9(1), 35-56.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Bölüm Mathematics
Yazarlar

Ezzatallah Baloui Jamkhaneh

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 29 Sayı: 3

Kaynak Göster

APA Baloui Jamkhaneh, E. (2016). NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS. Gazi University Journal of Science, 29(3), 667-674.
AMA Baloui Jamkhaneh E. NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS. Gazi University Journal of Science. Eylül 2016;29(3):667-674.
Chicago Baloui Jamkhaneh, Ezzatallah. “NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS”. Gazi University Journal of Science 29, sy. 3 (Eylül 2016): 667-74.
EndNote Baloui Jamkhaneh E (01 Eylül 2016) NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS. Gazi University Journal of Science 29 3 667–674.
IEEE E. Baloui Jamkhaneh, “NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS”, Gazi University Journal of Science, c. 29, sy. 3, ss. 667–674, 2016.
ISNAD Baloui Jamkhaneh, Ezzatallah. “NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS”. Gazi University Journal of Science 29/3 (Eylül 2016), 667-674.
JAMA Baloui Jamkhaneh E. NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS. Gazi University Journal of Science. 2016;29:667–674.
MLA Baloui Jamkhaneh, Ezzatallah. “NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS”. Gazi University Journal of Science, c. 29, sy. 3, 2016, ss. 667-74.
Vancouver Baloui Jamkhaneh E. NEW OPERATIONS OVER GENERALIZED INTERVAL VALUED INTUITIONISTIC FUZZY SETS. Gazi University Journal of Science. 2016;29(3):667-74.