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Interval-Valued Fuzzy Parameterized Intuitionistic Fuzzy Soft Sets and Their Applications

Year 2019, Volume: 40 Issue: 2, 317 - 331, 30.06.2019

Hüseyin Kamacı

https://doi.org/10.17776/csj.524802
Cited By: 10

Abstract

In recent years, the fuzzy sets, interval-valued fuzzy
sets, intuitionistic fuzzy sets and soft sets, which offer different
perspectives for the structures containing the uncertainties, have attracted
the interest of many researchers. Also, the intuitionistic fuzzy soft sets
produced by combining the intuitionistic fuzzy sets with the soft sets have
been widely studied. In this work, the concept of interval-valued fuzzy
parameterized intuitionistic fuzzy soft set (IVFPIFS set) is introduced. This
set is the generalization of soft sets, fuzzy soft sets, fuzzy parameterized
(fuzzy) soft sets, interval-valued fuzzy parameterized (fuzzy) soft sets,
intuitionistic fuzzy soft sets and fuzzy parameterized intuitionistic fuzzy
soft sets. For the IVFPIFS sets, basic operations such as complement, union and
intersection are defined.  Also, the
properties of these operations are investigated in detail. Lastly, an algorithm
by using the aggregation operators based on the IVFPIFS sets is constructed.
The examples are given to verify the feasibility and validity of the proposed
algorithm.

Keywords

Fuzzy set interval valued fuzzy set intuitionistic fuzzy set intuitionistic fuzzy soft set IVFPIFS set

References

  • Zadeh, L.A., Fuzzy sets, Inform. Control 8 (1965) 338-353.
  • Sambuc, R., Fonctions Φ-floues. Application a l’aide au diagnostic en pathologie thyroidienne. Ph. D. Thesis, Univ. Marseille, France, 1975.
  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Set. Syst. 20 (1986) 87-96.
  • Atanassov, K. and Gargov, G., Interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst. 31 (1989) 343-349.
  • Molodtsov, D., Soft set theory-first results, Comput. Math. Appl. 37 (1999) 19-31.
  • Ali, M.I., Feng, F., Liu, X., Min, W.K. and Shabir, M., On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547-1553.
  • Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Comput. Math. Appl. 45 (2003) 555-562.
  • Sezgin, A. and Atagün, A.O., On operations of soft sets, Comput. Math. Appl. 61 (2011) 1457-1467.
  • Aktaş, H. and Çağman, N., Soft sets and soft groups, Inform. Sci. 177 (2007) 2726-2735.
  • Feng, F., Jun, Y.B. and Zhao, X., Soft semirings, Comput. Math. Appl. 56 (2008) 2621-2628.
  • Acar, U., Koyuncu, F. and Tanay, B., Soft sets and soft rings, Comput. Math. Appl. 59 (2010) 3458-3463.
  • Atagün, A.O. and Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl. 61 (2011) 592-601.
  • Sezgin, A., Atagün, A.O. and Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat 25 (2011) 53-68.
  • Çağman, N., Çıtak, F. and Enginoğlu, S., FP-soft set theory and its applications, Ann. Fuzzy Math. Inform. 2 (2011) 219-226.
  • Zorlutuna, I. and Atmaca, S., Notes on fuzzy parametrized soft sets, Cumhuriyet Science Journal 39 (2018) 818-827.
  • Çağman, N. and Deli, I., Products of FP-soft sets and their applications, Hacet. J. Math. Stat. 41 (2012) 365-374.
  • Çağman, N. and Deli, I., Means of FP-soft sets and their applications, Hacet. J. Math. Stat. 41 (2012) 615-625.
  • Deli, I. and Çağman, N., Relations on FP-soft sets applied to decision making problems, Journal of New Theory 3 (2015) 98-107.
  • Deli, I. and Çağman, N., Intuitionistic fuzzy parameterized soft set theory and its decision making, Appl. Soft Comput. 28 (2015) 109-113.
  • Deli, I. and Karataş, S., Interval valued intuitionistic fuzzy parameterized soft set theory and its decision making, J. Intell. Fuzzy Syst. 30 (2016) 2073-2082.
  • Çağman, N., Enginoğlu, S. and Çıtak, F., Fuzzy soft set theory and its applications, Iran. J. Fuzzy Syst. 8 (2011) 137-147.
  • Atagün, A.O., Kamacı, H. and Oktay, O., Reduced soft matrices and generalized products with applications in decision making, Neural Comput. Applic. 29 (2018) 445-456.
  • Çağman, N. and Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl. 59 (2010) 3308-3314.
  • Çağman, N. and Enginoğlu, S., Fuzzy soft matrix theory and its application in decision making, Iran. J. Fuzzy Syst. 9 (2012) 109-119.
  • Kamacı, H., Atagün, A.O. and Sönmezoğlu, A., Row-products of soft matrices with applications in multiple-disjoint decision making, Appl. Soft Comput. 62 (2018) 892-914.
  • Kamacı, H., Atagün, A.O. and Aygün, E., Difference operations of soft matrices with applications in decision making, Punjab Univ. j. math. 51 (2019) 1-21.
  • Petroudi, S.H.J., Nabati, Z. and Yaghobi, A., Some new results on fuzzy soft matrices, Turkish Journal of Fuzzy Systems 8 (2017) 52-62.
  • Maji, P.K., Biswas, R. and Roy, A.R., Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics 9 (2001) 677-692.
  • Xu, Y.-J., Sun, Y.-K. and Li, D.-F., Intuitionistic fuzzy soft set, 2nd International Workshop on Intelligent Systems and Applications IEEE, Wuhan, China, 2010.
  • Çağman, N. and Karataş, S., Intuitionistic fuzzy soft set theory and its decision making, J. Intell. Fuzzy Syst. 24 (2013) 829-836.
  • Deli, I. and Çağman, N., Similarity measure of IFS-sets and its application in medical diagnosis, Ann. Fuzzy Math. Inform. 11 (2016) 841-854.
  • Broumi, S., Majumdar, P. and Smarandache, F., New operations on intuitionistic fuzzy soft sets based on first Zadeh’s logical operators, Journal of New Results in Science, 4 (2014) 71-81.
  • Chetia, B., Das, P.K., Some results of intuitionistic fuzzy soft sets and its application in decision making, Appl. Math. Sci. 7 (2013) 4693-4712.
  • Deli, I., npn-soft sets theory and applications, Ann. Fuzzy Math. Inform. 10 (2015) 847-862.
  • Deli, I., Interval-valued neutrosophic soft sets and its decision making, Int. J. Mach. Learn. Cyber. 8 (2017) 665-676.
  • Deli, I., Eraslan, S. and Çağman, N., ivnpiv-neutrosophic soft sets and their decision making based on similarity measure, Neural Comput. Applic. 29 (2018) 187-203.
  • Dinda, B. and Samanta, T.K., Relations on intuitionistic fuzzy soft sets, General Mathematics Notes. 1 (2010) 74-83.
  • Karaaslan, F., Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making, Ann. Fuzzy Math. Inform. 11 (2016) 607-619.
  • Yin, Y., Li, H. and Jun, Y.B., On algebraic structure of intuitionistic fuzzy soft sets, Comput. Math. Appl. 64 (2012) 2896-2911.
  • Tan, C., A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS, Expert Syst. Appl. 38 (2011) 3023-3033.
  • Xu, Z., Choquet integrals of weighted intuitionistic fuzzy information, Inf. Sci., 180 (2010) 726-736.
  • Çağman, N. and Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2010) 615-625.

Aralık Değerli Bulanık Parametreli Sezgisel Bulanık Esnek Kümeler ve Uygulamaları

Year 2019, Volume: 40 Issue: 2, 317 - 331, 30.06.2019

Hüseyin Kamacı

https://doi.org/10.17776/csj.524802
Cited By: 10

Abstract

Son yıllarda, belirsizlik içeren yapılar için farklı perspektifler sunan
bulanık kümeler, aralık değerli bulanık kümeler, sezgisel bulanık kümeler ve
esnek kümeler birçok araştırmacının ilgisini çekmiştir. Ayrıca, sezgisel
bulanık kümeleri esnek kümelerle birleştirerek oluşturulan sezgisel bulanık
esnek kümeler de geniş ölçüde çalışılmıştır. Bu çalışmada, aralık değerli
bulanık parametreli sezgisel bulanık esnek küme (ADBPSBE küme) kavramı
tanıtılmıştır. Bu küme, esnek kümelerin, bulanık esnek kümelerin, bulanık
parametreli (bulanık) esnek kümelerin, aralık değerli bulanık parametreli
(bulanık) esnek kümelerin, sezgisel bulanık esnek kümelerin ve bulanık
parametreli sezgisel bulanık esnek kümelerin genelleştirilmesidir. ADBPSBE
kümeler için tümleyen, birleşim ve kesişim gibi temel işlemler tanımlanmıştır.
Ayrıca, bu işlemlerin özellikleri detaylı olarak araştırılmıştır. Son olarak,
ADBPSBE kümeler üzerine temellenmiş birleştirme operatörlerini kullanarak bir
algoritma oluşturulmuştur. Önerilen algoritmanın uygulanabilirliğini ve
geçerliliğini test etmek için örnekler verilmiştir.

References

  • Zadeh, L.A., Fuzzy sets, Inform. Control 8 (1965) 338-353.
  • Sambuc, R., Fonctions Φ-floues. Application a l’aide au diagnostic en pathologie thyroidienne. Ph. D. Thesis, Univ. Marseille, France, 1975.
  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Set. Syst. 20 (1986) 87-96.
  • Atanassov, K. and Gargov, G., Interval-valued intuitionistic fuzzy sets, Fuzzy Set. Syst. 31 (1989) 343-349.
  • Molodtsov, D., Soft set theory-first results, Comput. Math. Appl. 37 (1999) 19-31.
  • Ali, M.I., Feng, F., Liu, X., Min, W.K. and Shabir, M., On some new operations in soft set theory, Comput. Math. Appl. 57 (2009) 1547-1553.
  • Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Comput. Math. Appl. 45 (2003) 555-562.
  • Sezgin, A. and Atagün, A.O., On operations of soft sets, Comput. Math. Appl. 61 (2011) 1457-1467.
  • Aktaş, H. and Çağman, N., Soft sets and soft groups, Inform. Sci. 177 (2007) 2726-2735.
  • Feng, F., Jun, Y.B. and Zhao, X., Soft semirings, Comput. Math. Appl. 56 (2008) 2621-2628.
  • Acar, U., Koyuncu, F. and Tanay, B., Soft sets and soft rings, Comput. Math. Appl. 59 (2010) 3458-3463.
  • Atagün, A.O. and Sezgin, A., Soft substructures of rings, fields and modules, Comput. Math. Appl. 61 (2011) 592-601.
  • Sezgin, A., Atagün, A.O. and Aygün, E., A note on soft near-rings and idealistic soft near-rings, Filomat 25 (2011) 53-68.
  • Çağman, N., Çıtak, F. and Enginoğlu, S., FP-soft set theory and its applications, Ann. Fuzzy Math. Inform. 2 (2011) 219-226.
  • Zorlutuna, I. and Atmaca, S., Notes on fuzzy parametrized soft sets, Cumhuriyet Science Journal 39 (2018) 818-827.
  • Çağman, N. and Deli, I., Products of FP-soft sets and their applications, Hacet. J. Math. Stat. 41 (2012) 365-374.
  • Çağman, N. and Deli, I., Means of FP-soft sets and their applications, Hacet. J. Math. Stat. 41 (2012) 615-625.
  • Deli, I. and Çağman, N., Relations on FP-soft sets applied to decision making problems, Journal of New Theory 3 (2015) 98-107.
  • Deli, I. and Çağman, N., Intuitionistic fuzzy parameterized soft set theory and its decision making, Appl. Soft Comput. 28 (2015) 109-113.
  • Deli, I. and Karataş, S., Interval valued intuitionistic fuzzy parameterized soft set theory and its decision making, J. Intell. Fuzzy Syst. 30 (2016) 2073-2082.
  • Çağman, N., Enginoğlu, S. and Çıtak, F., Fuzzy soft set theory and its applications, Iran. J. Fuzzy Syst. 8 (2011) 137-147.
  • Atagün, A.O., Kamacı, H. and Oktay, O., Reduced soft matrices and generalized products with applications in decision making, Neural Comput. Applic. 29 (2018) 445-456.
  • Çağman, N. and Enginoğlu, S., Soft matrix theory and its decision making, Comput. Math. Appl. 59 (2010) 3308-3314.
  • Çağman, N. and Enginoğlu, S., Fuzzy soft matrix theory and its application in decision making, Iran. J. Fuzzy Syst. 9 (2012) 109-119.
  • Kamacı, H., Atagün, A.O. and Sönmezoğlu, A., Row-products of soft matrices with applications in multiple-disjoint decision making, Appl. Soft Comput. 62 (2018) 892-914.
  • Kamacı, H., Atagün, A.O. and Aygün, E., Difference operations of soft matrices with applications in decision making, Punjab Univ. j. math. 51 (2019) 1-21.
  • Petroudi, S.H.J., Nabati, Z. and Yaghobi, A., Some new results on fuzzy soft matrices, Turkish Journal of Fuzzy Systems 8 (2017) 52-62.
  • Maji, P.K., Biswas, R. and Roy, A.R., Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics 9 (2001) 677-692.
  • Xu, Y.-J., Sun, Y.-K. and Li, D.-F., Intuitionistic fuzzy soft set, 2nd International Workshop on Intelligent Systems and Applications IEEE, Wuhan, China, 2010.
  • Çağman, N. and Karataş, S., Intuitionistic fuzzy soft set theory and its decision making, J. Intell. Fuzzy Syst. 24 (2013) 829-836.
  • Deli, I. and Çağman, N., Similarity measure of IFS-sets and its application in medical diagnosis, Ann. Fuzzy Math. Inform. 11 (2016) 841-854.
  • Broumi, S., Majumdar, P. and Smarandache, F., New operations on intuitionistic fuzzy soft sets based on first Zadeh’s logical operators, Journal of New Results in Science, 4 (2014) 71-81.
  • Chetia, B., Das, P.K., Some results of intuitionistic fuzzy soft sets and its application in decision making, Appl. Math. Sci. 7 (2013) 4693-4712.
  • Deli, I., npn-soft sets theory and applications, Ann. Fuzzy Math. Inform. 10 (2015) 847-862.
  • Deli, I., Interval-valued neutrosophic soft sets and its decision making, Int. J. Mach. Learn. Cyber. 8 (2017) 665-676.
  • Deli, I., Eraslan, S. and Çağman, N., ivnpiv-neutrosophic soft sets and their decision making based on similarity measure, Neural Comput. Applic. 29 (2018) 187-203.
  • Dinda, B. and Samanta, T.K., Relations on intuitionistic fuzzy soft sets, General Mathematics Notes. 1 (2010) 74-83.
  • Karaaslan, F., Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making, Ann. Fuzzy Math. Inform. 11 (2016) 607-619.
  • Yin, Y., Li, H. and Jun, Y.B., On algebraic structure of intuitionistic fuzzy soft sets, Comput. Math. Appl. 64 (2012) 2896-2911.
  • Tan, C., A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS, Expert Syst. Appl. 38 (2011) 3023-3033.
  • Xu, Z., Choquet integrals of weighted intuitionistic fuzzy information, Inf. Sci., 180 (2010) 726-736.
  • Çağman, N. and Enginoğlu, S., Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2010) 615-625.
There are 42 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Hüseyin Kamacı 0000-0002-0429-6713

Publication Date June 30, 2019
Submission Date February 8, 2019
Acceptance Date May 31, 2019
Published in Issue Year 2019Volume: 40 Issue: 2

Cite

APA Kamacı, H. (2019). Interval-Valued Fuzzy Parameterized Intuitionistic Fuzzy Soft Sets and Their Applications. Cumhuriyet Science Journal, 40(2), 317-331. https://doi.org/10.17776/csj.524802

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