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RP-T-Fuzzy Soft Subrings and Ideals of Soft Rings

Year 2020, Volume: 41 Issue: 4, 832 - 844, 29.12.2020

Canan Akın , Ertuğrul Akçay

https://doi.org/10.17776/csj.623545

Abstract

 In this paper we introduce a concept which is called RP-T-fuzzy

soft subring and examine some properties of the restricted intersection, the

restricted union, the ∧-intersection and the product of their families. A con-

dition to make the restricted union of RP-T-fuzzy soft subrings of a soft ring

to be RP-T-fuzzy soft subring of this soft ring is determined. A correlation

between the RP-T-fuzzy soft subring of a soft ring and α-level sets of this soft

ring is demonstrated. The RP-T-fuzzy soft subrings under some binary opera-

tions are investigated. Moreover, the image and pre-image of RP-T-fuzzy soft

subrings under fuzzy soft homomorphisms is examined. Finally, we present the

concept of RP-T-fuzzy soft ideal and we investigate the analogue properties

for them.

Keywords

Fuzzy soft set UP-fuzzy soft subset RP-T-fuzzy soft subring

References

  • [1] Zadeh L. A., Fuzzy Sets, Inf. Control, 8 (1965) 338–353.
  • [2] Rosenfeld A., Fuzzy Groups, Journal of Mathematical Analysis and Applications, 35(3) (1971) 512–517.
  • [3] Liu W. , Fuzzy Invariant Subgroups and Fuzzy Ideals, Fuzzy Sets and Systems, 8 (1982) 133–139.
  • [4] Dixit V. N., Kumar R., and Ajmal N., On fuzzy rings, Fuzzy Sets and Systems, 49 (1992) 205–213.
  • [5] Molodtsov D., Soft Set Theory First Results, Computers and Mathematics with Applications, 37 (1999) 19–31.
  • [6] Maji P.K., Biswas R. and Roy A.R., . Soft Set Theory, Computers and Mathematics with Applications, 45 (2003) 555–562.
  • [7] Ali M. I., Feng F., Liu -X., Min -W.K. and Shabir M., On Some New Operations in Soft Set Theory, Computers and Mathematics with Applications, 57 (2009) 1547–1553.
  • [8] Aktaş H. and Çağman N., Soft Sets and Soft Groups, Inform. Sci., 177 (2007) 2726–2735.
  • [9] Acar U., Koyuncu F. and Tanay B., Soft Sets and Soft Rings, Computers and Mathematics with Applications, 59 (2010) 3458–3463.
  • [10] Atagün A. O. and Sezgin A., Soft Substructures of Rings, Fields and Modules, Computers and Mathematics with Applications, 61(3) (2011) 592–601.
  • [11] Maji P.K., Biswas R. and Roy, A.R., Fuzzy Soft Sets, J. Fuzzy Math., 9 (2001) 589–602.
  • [12] Aygünoğlu A. and Aygün H., Introduction to fuzzy soft groups, Comput. Math. Appl., 58 (2009) 1279–1286.
  • [13] Pazar Varol B., Aygünoğlu A. and Aygün H., On Fuzzy Soft Rings, Journal of Hyperstructures, 1(2) (2012) 1–15.
  • [14] İnan E. and Öztürk M. A., Fuzzy Soft Rings and Fuzzy Soft Ideals, Neural Comput. Appl., 21(1) (2012) 1–8.
  • [15] Çelik Y., Ekiz C. and Yamak S., Applications of fuzzy soft sets in ring theory, Annals Fuzzy Mathematics and Informatics, 5 (2013) 451–462.
  • [16] Akın C. and Karakaya Ü., SP-fuzzy Soft Ideals in Semigroups, Turk. J. Math. Comput. Sci., 10 (2018) 22–32.
  • [17] Akın C., GP-Fuzzy Soft Groups, Erzincan University Journal of Science and Technology, 12(2) (2019) 759–770.
  • [18] Al-Qudah Y. and Hassan N., Complex Multi-Fuzzy Soft Expert Set and Its Application, International Journal of Mathematics and Computer Science, 14(1) (2019) 149–176.
  • [19] Fatimah F., Rosadi D., Hakim RB. F. and Alcantud J. C. R., Probabilistic Soft Sets and Dual Probabilistic Soft Sets In Decision-Making, Neural Comput and Applic., 31 (2019) 397–407.
  • [20] Hayat K., Ali M. I., Cao B.-Y., Karaaslan F. and Yang X.-P., Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods, Symmetry, 10(12) (2018) 753.
  • [21] Karaaslan F., Çağman N., Bipolar Soft Rough Sets and Their Applications in Decision Making, Afrika Matematika, 29 (2018) 823–839.
  • [22] Malik N. and Shabir M., Rough Fuzzy Bipolar Soft Sets and Application in Decision-Making Problems, Soft Computing, 23 (2019) 1603–1614.
  • [23] Riaz M., Çağman N., Zareef I. and Aslam M., N-soft Topology And Its Applications to Multi-Criteria Group Decision Making, Journal of Intelligent and Fuzzy Systems, 36(6) (2019) 6521–6536.
  • [24] Sezgin A., Çağman N. and Çıtak F., α-Inclusions Applied to Group Theory Via Soft Set and Logic, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019) 334–352.
  • [25] Ullah A., Karaaslan F. and Ahmad I., Soft Uni-Abel-Grassmann’s Groups, European Journal of Pure And Applied Mathematics, 11 (2018) 517–536.
  • [26] Zorlutuna İ. and Atmaca S., Notes on Fuzzy Parametrized Soft Sets, Cumhuriyet Science Journal, 39 (2018) 818–827.
  • [27] Mordeson, J. N. and Malik, D. S., Fuzzy Commutative Algebra, World Scientific Publishing Co., Singapure, 1998.
  • [28] Baczynski M. and Jayaram B., Fuzzy implications Studies in Fuzziness and Soft Computing, Springer, Berlin Heidelberg: Vol. 231, 2008.
  • [29] Fodor J. C. and Roubens M., Fuzzy Preference Modelling and Multicriteria Decision Support, Dordrecht: Kluwer, 1994.
  • [30] Klement E.P., Mesiar R. and Pap E., Triangular Norms, Dordrecht: Kluwer Academic Publishers, 2000.
  • [31] De Baets B., and Mesiar R., Triangular Norms on Product Lattices, Fuzzy Sets and Systems, 17 (1999) 191–208.
  • [32] Wang Z. and Yu Y., Pseudo-t-norms and Implication Operators on Acomplete Brouwerian Lattice, Fuzzy Sets and Systems, 132 (2002) 113–124.
  • [33] Bhakat S. K. and Das P., Fuzzy Subrings and Ideals Redefined, Fuzzy Sets Syst, 81 (1996) 383–393.
  • [34] Yu Y. and Wang Z., TL-subrings and TL-ideals, Fuzzy Sets and Systems, 68(1) (1994), 93–103.
  • [35] Kharal A. and Ahmad B.. Mappings on soft classes, New Mathematics and Natural Computation, 7 (2011) 471–481.
  • [36] Feng F., Jun Y. B. and Zhao, X., Soft Semirings, Computers and Mathematics with Applications, 56 (2008) 2621–2628.
  • [37] Çelik Y., Ekiz C. and Yamak S., A New View on Soft Rings, Hacettepe Journal of Mathematics and Statistics, 40 (2011) 273–286.
  • [38] Kazancı O., Yılmaz Ş. and Yamak S., Soft Sets and Soft Bch-algebras, Hacettepe Journal of Mathematics and Statistics, 39 (2010) 205–217.
  • [39] Pei D. and Miao D., From Soft Sets to Information Systems, In: 2005 IEEE International Conference on Granular Computing, (2) (2005) 617–621.
  • [40] Ahmad B. and Kharal A., On Fuzzy Soft Sets, Advances in Fuzzy Systems, 2009 (2009) 586–507.

Year 2020, Volume: 41 Issue: 4, 832 - 844, 29.12.2020

Canan Akın , Ertuğrul Akçay

https://doi.org/10.17776/csj.623545

Abstract

References

  • [1] Zadeh L. A., Fuzzy Sets, Inf. Control, 8 (1965) 338–353.
  • [2] Rosenfeld A., Fuzzy Groups, Journal of Mathematical Analysis and Applications, 35(3) (1971) 512–517.
  • [3] Liu W. , Fuzzy Invariant Subgroups and Fuzzy Ideals, Fuzzy Sets and Systems, 8 (1982) 133–139.
  • [4] Dixit V. N., Kumar R., and Ajmal N., On fuzzy rings, Fuzzy Sets and Systems, 49 (1992) 205–213.
  • [5] Molodtsov D., Soft Set Theory First Results, Computers and Mathematics with Applications, 37 (1999) 19–31.
  • [6] Maji P.K., Biswas R. and Roy A.R., . Soft Set Theory, Computers and Mathematics with Applications, 45 (2003) 555–562.
  • [7] Ali M. I., Feng F., Liu -X., Min -W.K. and Shabir M., On Some New Operations in Soft Set Theory, Computers and Mathematics with Applications, 57 (2009) 1547–1553.
  • [8] Aktaş H. and Çağman N., Soft Sets and Soft Groups, Inform. Sci., 177 (2007) 2726–2735.
  • [9] Acar U., Koyuncu F. and Tanay B., Soft Sets and Soft Rings, Computers and Mathematics with Applications, 59 (2010) 3458–3463.
  • [10] Atagün A. O. and Sezgin A., Soft Substructures of Rings, Fields and Modules, Computers and Mathematics with Applications, 61(3) (2011) 592–601.
  • [11] Maji P.K., Biswas R. and Roy, A.R., Fuzzy Soft Sets, J. Fuzzy Math., 9 (2001) 589–602.
  • [12] Aygünoğlu A. and Aygün H., Introduction to fuzzy soft groups, Comput. Math. Appl., 58 (2009) 1279–1286.
  • [13] Pazar Varol B., Aygünoğlu A. and Aygün H., On Fuzzy Soft Rings, Journal of Hyperstructures, 1(2) (2012) 1–15.
  • [14] İnan E. and Öztürk M. A., Fuzzy Soft Rings and Fuzzy Soft Ideals, Neural Comput. Appl., 21(1) (2012) 1–8.
  • [15] Çelik Y., Ekiz C. and Yamak S., Applications of fuzzy soft sets in ring theory, Annals Fuzzy Mathematics and Informatics, 5 (2013) 451–462.
  • [16] Akın C. and Karakaya Ü., SP-fuzzy Soft Ideals in Semigroups, Turk. J. Math. Comput. Sci., 10 (2018) 22–32.
  • [17] Akın C., GP-Fuzzy Soft Groups, Erzincan University Journal of Science and Technology, 12(2) (2019) 759–770.
  • [18] Al-Qudah Y. and Hassan N., Complex Multi-Fuzzy Soft Expert Set and Its Application, International Journal of Mathematics and Computer Science, 14(1) (2019) 149–176.
  • [19] Fatimah F., Rosadi D., Hakim RB. F. and Alcantud J. C. R., Probabilistic Soft Sets and Dual Probabilistic Soft Sets In Decision-Making, Neural Comput and Applic., 31 (2019) 397–407.
  • [20] Hayat K., Ali M. I., Cao B.-Y., Karaaslan F. and Yang X.-P., Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods, Symmetry, 10(12) (2018) 753.
  • [21] Karaaslan F., Çağman N., Bipolar Soft Rough Sets and Their Applications in Decision Making, Afrika Matematika, 29 (2018) 823–839.
  • [22] Malik N. and Shabir M., Rough Fuzzy Bipolar Soft Sets and Application in Decision-Making Problems, Soft Computing, 23 (2019) 1603–1614.
  • [23] Riaz M., Çağman N., Zareef I. and Aslam M., N-soft Topology And Its Applications to Multi-Criteria Group Decision Making, Journal of Intelligent and Fuzzy Systems, 36(6) (2019) 6521–6536.
  • [24] Sezgin A., Çağman N. and Çıtak F., α-Inclusions Applied to Group Theory Via Soft Set and Logic, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019) 334–352.
  • [25] Ullah A., Karaaslan F. and Ahmad I., Soft Uni-Abel-Grassmann’s Groups, European Journal of Pure And Applied Mathematics, 11 (2018) 517–536.
  • [26] Zorlutuna İ. and Atmaca S., Notes on Fuzzy Parametrized Soft Sets, Cumhuriyet Science Journal, 39 (2018) 818–827.
  • [27] Mordeson, J. N. and Malik, D. S., Fuzzy Commutative Algebra, World Scientific Publishing Co., Singapure, 1998.
  • [28] Baczynski M. and Jayaram B., Fuzzy implications Studies in Fuzziness and Soft Computing, Springer, Berlin Heidelberg: Vol. 231, 2008.
  • [29] Fodor J. C. and Roubens M., Fuzzy Preference Modelling and Multicriteria Decision Support, Dordrecht: Kluwer, 1994.
  • [30] Klement E.P., Mesiar R. and Pap E., Triangular Norms, Dordrecht: Kluwer Academic Publishers, 2000.
  • [31] De Baets B., and Mesiar R., Triangular Norms on Product Lattices, Fuzzy Sets and Systems, 17 (1999) 191–208.
  • [32] Wang Z. and Yu Y., Pseudo-t-norms and Implication Operators on Acomplete Brouwerian Lattice, Fuzzy Sets and Systems, 132 (2002) 113–124.
  • [33] Bhakat S. K. and Das P., Fuzzy Subrings and Ideals Redefined, Fuzzy Sets Syst, 81 (1996) 383–393.
  • [34] Yu Y. and Wang Z., TL-subrings and TL-ideals, Fuzzy Sets and Systems, 68(1) (1994), 93–103.
  • [35] Kharal A. and Ahmad B.. Mappings on soft classes, New Mathematics and Natural Computation, 7 (2011) 471–481.
  • [36] Feng F., Jun Y. B. and Zhao, X., Soft Semirings, Computers and Mathematics with Applications, 56 (2008) 2621–2628.
  • [37] Çelik Y., Ekiz C. and Yamak S., A New View on Soft Rings, Hacettepe Journal of Mathematics and Statistics, 40 (2011) 273–286.
  • [38] Kazancı O., Yılmaz Ş. and Yamak S., Soft Sets and Soft Bch-algebras, Hacettepe Journal of Mathematics and Statistics, 39 (2010) 205–217.
  • [39] Pei D. and Miao D., From Soft Sets to Information Systems, In: 2005 IEEE International Conference on Granular Computing, (2) (2005) 617–621.
  • [40] Ahmad B. and Kharal A., On Fuzzy Soft Sets, Advances in Fuzzy Systems, 2009 (2009) 586–507.
There are 40 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Canan Akın 0000-0002-8922-3272

Ertuğrul Akçay 0000-0002-4515-9344

Publication Date December 29, 2020
Submission Date September 23, 2019
Acceptance Date September 16, 2020
Published in Issue Year 2020 Volume: 41 Issue: 4

Cite

APA Akın, C., & Akçay, E. (2020). RP-T-Fuzzy Soft Subrings and Ideals of Soft Rings. Cumhuriyet Science Journal, 41(4), 832-844. https://doi.org/10.17776/csj.623545