Research Article
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Year 2021, Volume: 70 Issue: 2, 582 - 599, 31.12.2021

Orhan Dalkılıç

https://doi.org/10.31801/cfsuasmas.770623
Cited By: 1

Abstract

References

  • Zadeh, L. A., Fuzzy sets, Inf. Control. 8 (1965), 338-353.
  • Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  • Sun Z., Han, J., Inverse alpha-Cuts and Interval [a; b)-Cuts, Proceedings of the International Conference on Innovative Computing, Information and Control (ICICIC2006), 30 August-1 September, Beijing, IEEE Press, (2006), 441-444. Doi:10.1109/ICICIC.2006.105
  • Shabir, M., Naz, M., On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344, 2013.
  • Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003), 555-562. Doi:10.1016/S0898-1221(03)00016-6
  • Ozturk, T. Y., On bipolar soft topological spaces, Journal of New Theory, 20 (2018), 64-75.
  • Mordeson, J. N., Malik, D. S., Fuzzy Commutative Algebra, World Scientific Publishing, Singapore, 1998.
  • Mordeson, J. N., Bhutani, K. R., Rosenfeld, A., Fuzzy Group Theory, Springer, New York, 2005.
  • Dubois, D., Hullermeier, E., Prade, H., On the representation of fuzzy rules in terms of crisp rules, Information Sciences, 151 (2003), 301-326. Doi:10.1016/S00200255(02)00403-6
  • Luo, C. Z., Wang, P. Z., Representation of compositional relations in fuzzy reasoning, Fuzzy Sets and Systems, 36 (1990), 327-337. Doi:10.1016/0165-0114(90)90080-P
  • Bertoluzza, C., Solci, M., Caodieci, M. L., Measure of a fuzzy set: The approach in the finite case, Fuzzy Sets and Systems, 123 (2001), 93-102. Doi:10.1016/S0165-0114(00)00074-9
  • Garcia, J. N., Kutalik, Z., Cho, K. H., Wolkenhauer, O., Level sets and the minimum volume sets of probability density function, International Journal of Approximate Reasoning, 34 (2003), 25-47. Doi:10.1016/S0888-613X(03)00052-5
  • Pap, E., Surla, D., Lebesgue measure of approach for finding the height of the membership function, Fuzzy Sets and Systems, 111 (2000), 341-350. Doi:10.1016/S0165-0114(98)00162-6
  • Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980.
  • Yuan, X. H., Li, H. X., Stanley Lee, E., Three new cut sets of fuzzy sets and new theories of fuzzy sets, Computer and Mathematics with Applications, 57 (2009), 691-701. Doi:10.1016/j.camwa.2008.05.044
  • Atanassov, K., Intuitionistic fuzzy sets, International Journal Bioautomation, 20(1) (2016), 1-6.
  • Zadeh, L., The concept of a linguistic variable and its application to approximate reasoning, Part 1, Inform. Sci., 8 (1975), 199-249. Doi:10.1016/0020-0255(75)90036-5
  • Gau, W. L., Buehrer, D. J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics, 23 (1993), 610-614. Doi:10.1109/21.229476
  • Lee, K. M., Bipolar-valued fuzzy sets and their basic operations, Proceeding International Conference, Bangkok, Thailand, (2000), 307-317.
  • Abdullah, S., Aslam, M., Ullah, K., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent and Fuzzy Systems, 27(2) (2014), 729-742. Doi:10.3233/IFS-131031
  • Karaaslan, F., Karatas, S., A new approach to bipolar soft sets and its applications. Discrete Mathematics, Algorithms and Applications, 7(4) (2015), 1550054. Doi:10.1142/S1793830915500548
  • Demirtas, N., Hussain, S., Dalkılıç, O., New approaches of inverse soft rough sets and their applications in a decision making problem, Journal of applied mathematics and informatics, 38(3-4) (2020), 335-349. Doi:10.14317/jami.2020.335
  • Dalkılıç, O., Demirtas, N., VFP-soft Sets and its application on decision making problems, Journal of Polytechnic, (2021). https://doi.org/10.2339/politeknik.685634
  • Garg, H., Arora, R., Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set, Journal of Ambient Intelligence and Humanized Computing, 11 (1) (2020), 375-410. Doi:10.1007/s12652-019-01238-w
  • Zhang, W. R., Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, In Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. 18-21 Dec., San Antonio, TX, USA, 1994. Doi:10.1109/IJCF.1994.375115
  • Zhang, W. R., Bipolar fuzzy sets, In Proceedings of the 1998 IEEE International Conference on Fuzzy Systems, Anchorage, AK, USA, 1998.
  • Öztürk, T. Y., On bipolar soft points, TWMS J. App. and Eng. Math., 10(4) (2020), 877-885.
  • Dizman, T. S., Ozturk, T. Y., Fuzzy Bipolar soft topological spaces, TWMS J. App. and Eng. Math., 11(1) (2021), 151-159.

(α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets

Year 2021, Volume: 70 Issue: 2, 582 - 599, 31.12.2021

Orhan Dalkılıç

https://doi.org/10.31801/cfsuasmas.770623
Cited By: 1

Abstract

Bipolar fuzzy soft set theory, which is a very useful hybrid set in decision making problems, is a mathematical model that has been emphasized especially recently. In this paper, the concepts of (α,β)-cuts, first type semi-strong (α,β)-cuts, second type semi-strong (α,β)-cuts, strong (α,β)-cuts, inverse (α,β)-cuts, first type semi-weak inverse (α,β)-cuts, second type semi-weak inverse (α,β)-cuts and weak inverse (α,β)-cuts of bipolar fuzzy soft sets were introduced together with some of their properties. In addition, some distinctive properties between (α,β)-cuts and inverse (α,β)-cuts were established. Moreover, some related theorems were formulated and proved. It is further demonstrated that both (α,β)-cuts and inverse (α,β)-cuts of bipolar fuzzy soft sets were useful tools in decision making.

Keywords

Bipolar soft set bipolar fuzzy soft set (α,β)-cut inverse(α,β)-cut

References

  • Zadeh, L. A., Fuzzy sets, Inf. Control. 8 (1965), 338-353.
  • Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
  • Sun Z., Han, J., Inverse alpha-Cuts and Interval [a; b)-Cuts, Proceedings of the International Conference on Innovative Computing, Information and Control (ICICIC2006), 30 August-1 September, Beijing, IEEE Press, (2006), 441-444. Doi:10.1109/ICICIC.2006.105
  • Shabir, M., Naz, M., On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344, 2013.
  • Maji, P. K., Biswas, R., Roy, A. R., Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003), 555-562. Doi:10.1016/S0898-1221(03)00016-6
  • Ozturk, T. Y., On bipolar soft topological spaces, Journal of New Theory, 20 (2018), 64-75.
  • Mordeson, J. N., Malik, D. S., Fuzzy Commutative Algebra, World Scientific Publishing, Singapore, 1998.
  • Mordeson, J. N., Bhutani, K. R., Rosenfeld, A., Fuzzy Group Theory, Springer, New York, 2005.
  • Dubois, D., Hullermeier, E., Prade, H., On the representation of fuzzy rules in terms of crisp rules, Information Sciences, 151 (2003), 301-326. Doi:10.1016/S00200255(02)00403-6
  • Luo, C. Z., Wang, P. Z., Representation of compositional relations in fuzzy reasoning, Fuzzy Sets and Systems, 36 (1990), 327-337. Doi:10.1016/0165-0114(90)90080-P
  • Bertoluzza, C., Solci, M., Caodieci, M. L., Measure of a fuzzy set: The approach in the finite case, Fuzzy Sets and Systems, 123 (2001), 93-102. Doi:10.1016/S0165-0114(00)00074-9
  • Garcia, J. N., Kutalik, Z., Cho, K. H., Wolkenhauer, O., Level sets and the minimum volume sets of probability density function, International Journal of Approximate Reasoning, 34 (2003), 25-47. Doi:10.1016/S0888-613X(03)00052-5
  • Pap, E., Surla, D., Lebesgue measure of approach for finding the height of the membership function, Fuzzy Sets and Systems, 111 (2000), 341-350. Doi:10.1016/S0165-0114(98)00162-6
  • Dubois, D., Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980.
  • Yuan, X. H., Li, H. X., Stanley Lee, E., Three new cut sets of fuzzy sets and new theories of fuzzy sets, Computer and Mathematics with Applications, 57 (2009), 691-701. Doi:10.1016/j.camwa.2008.05.044
  • Atanassov, K., Intuitionistic fuzzy sets, International Journal Bioautomation, 20(1) (2016), 1-6.
  • Zadeh, L., The concept of a linguistic variable and its application to approximate reasoning, Part 1, Inform. Sci., 8 (1975), 199-249. Doi:10.1016/0020-0255(75)90036-5
  • Gau, W. L., Buehrer, D. J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics, 23 (1993), 610-614. Doi:10.1109/21.229476
  • Lee, K. M., Bipolar-valued fuzzy sets and their basic operations, Proceeding International Conference, Bangkok, Thailand, (2000), 307-317.
  • Abdullah, S., Aslam, M., Ullah, K., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent and Fuzzy Systems, 27(2) (2014), 729-742. Doi:10.3233/IFS-131031
  • Karaaslan, F., Karatas, S., A new approach to bipolar soft sets and its applications. Discrete Mathematics, Algorithms and Applications, 7(4) (2015), 1550054. Doi:10.1142/S1793830915500548
  • Demirtas, N., Hussain, S., Dalkılıç, O., New approaches of inverse soft rough sets and their applications in a decision making problem, Journal of applied mathematics and informatics, 38(3-4) (2020), 335-349. Doi:10.14317/jami.2020.335
  • Dalkılıç, O., Demirtas, N., VFP-soft Sets and its application on decision making problems, Journal of Polytechnic, (2021). https://doi.org/10.2339/politeknik.685634
  • Garg, H., Arora, R., Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set, Journal of Ambient Intelligence and Humanized Computing, 11 (1) (2020), 375-410. Doi:10.1007/s12652-019-01238-w
  • Zhang, W. R., Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, In Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. 18-21 Dec., San Antonio, TX, USA, 1994. Doi:10.1109/IJCF.1994.375115
  • Zhang, W. R., Bipolar fuzzy sets, In Proceedings of the 1998 IEEE International Conference on Fuzzy Systems, Anchorage, AK, USA, 1998.
  • Öztürk, T. Y., On bipolar soft points, TWMS J. App. and Eng. Math., 10(4) (2020), 877-885.
  • Dizman, T. S., Ozturk, T. Y., Fuzzy Bipolar soft topological spaces, TWMS J. App. and Eng. Math., 11(1) (2021), 151-159.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Applied Mathematics
Journal Section Research Articles
Authors

Orhan Dalkılıç 0000-0003-3875-1398

Publication Date December 31, 2021
Submission Date July 16, 2020
Acceptance Date January 30, 2021
Published in Issue Year 2021 Volume: 70 Issue: 2

Cite

APA Dalkılıç, O. (2021). (α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 582-599. https://doi.org/10.31801/cfsuasmas.770623
AMA Dalkılıç O. (α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):582-599. doi:10.31801/cfsuasmas.770623
Chicago Dalkılıç, Orhan. “(α, β)-Cuts and Inverse (α, β)-Cuts in Bipolar Fuzzy Soft Sets”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 582-99. https://doi.org/10.31801/cfsuasmas.770623.
EndNote Dalkılıç O (December 1, 2021) (α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 582–599.
IEEE O. Dalkılıç, “(α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 582–599, 2021, doi: 10.31801/cfsuasmas.770623.
ISNAD Dalkılıç, Orhan. “(α, β)-Cuts and Inverse (α, β)-Cuts in Bipolar Fuzzy Soft Sets”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 582-599. https://doi.org/10.31801/cfsuasmas.770623.
JAMA Dalkılıç O. (α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:582–599.
MLA Dalkılıç, Orhan. “(α, β)-Cuts and Inverse (α, β)-Cuts in Bipolar Fuzzy Soft Sets”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 582-99, doi:10.31801/cfsuasmas.770623.
Vancouver Dalkılıç O. (α, β)-cuts and inverse (α, β)-cuts in bipolar fuzzy soft sets. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):582-99.

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