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BIPOLAR SOFT ROUGH RELATIONS

Year 2016, Volume: 65 Issue: 1, 105 - 126, 01.02.2016

Faruk Karaaslan

https://doi.org/10.1501/Commua1_0000000747
Cited By: 7

Abstract

In this study, Cartesian products of bipolar soft P-lower and Pupper approximations of two bipolar soft rough sets are defined and based
on the these cartesian products, concepts of bipolar soft rough P-upper and
P-lower relations are introduced, and some properties existing in the classical
relations are obtained for bipolar soft rough relations. Also, some new concepts
such as equivalence bipolar soft rough relation, inverse bipolar soft rough relation, bipolar equivalence class of an element in universal set and partition of
bipolar soft rough set under equivalence bipolar soft rough relation are defined
and supported by examples.

Keywords

Rough set soft set bipolar soft set bipolar soft rough set cartesianproduct relation

References

  • Abdullah, S., Aslam, M. and Ullah, K., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent and Fuzzy Systems (2014), 27(2), 729-742.
  • Akta¸s H. and Ça¼gman, N., Soft sets and soft groups, Information Sciences (2007), 177, 2726-2735.
  • Ali, M. I., A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing Journal (2011), 11(4), 3329-3332.
  • 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 Application (2009), 57, 1547-1553.
  • Atagün, A.O. and Aygün, E., Groups of soft sets, Journal of Intelligent and Fuzzy Systems (2016), 30(2), 729-733.
  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems (1986), 20, 87-96.
  • Babitha, K.V. and Sunil, J.J., Soft set relations and functions, Computers and Mathematics with Applications (2010), 60, 1840-1849.
  • Ça¼gman, N. and Engino¼glu, S., Soft set theory and uni-int decision making, European Journal of Operational Research (2010), 207, 848-855.
  • Ça¼gman, N. and Engino¼glu, S., Fuzzy soft set theory and its applications, Iranian journal of fuzzy systems (2011), 8(3), 137-147.
  • Ça¼gman, N. and Karata¸s, S., Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems (2013), 24, 829-836.
  • Ça¼gman, N., Contributions to the theory of soft sets, Journal of New Results in Science (2014), 4, 33-41.
  • Dubois, D., Prade, H., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems (1990), 17, 191-209.
  • Feng F. and Liu, X., Soft rough sets with applications to demand analysis, Intelligent Systems and Applications (2009), DOI:10.1109/IWISA.2009.5073114.
  • Feng, F., Li, C., Davvaz, B. and Ali, M. I., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing (2010), 14(9), 899-911.
  • Feng, F., Liu, X., Leoreanu-Fotea, V. and Jun, Y. B., Soft sets and soft rough sets, Informa- tion Sciences (2011), 181(6), 1125-1137.
  • Feng, F., Soft rough sets applied to multicriteria group decision making, Annals of Fuzzy Mathematics and Informatics (2011), 2(1), 69-80.
  • Gau, W.L., Buehrer, D.J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics (1993), 23(2), 610-614.
  • Gong, K., Xiao, Z. and Zhang, X., The bijective soft set with its operations, Computers and Mathematics with Applications (2010), 60, 2270-2278.
  • Herawan, T. and Deris, M.M., A Direct Proof of Every Rough Set is a Soft Set, Third Asia International Conference on Modelling and Simulation (2009), DOI 10.1109/AMS.2009.148.
  • Ibrahim, A. M., Dauda, M. K. and Singh, D., Composition of Soft Set Relations and Con- struction of Transitive, Mathematical Theory and Modeling (2012), 2(7), 98-107.
  • Jiang, Y., Tang, Y., Chen, Q., Liu, H. and Tang, J., Intervalvalued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications (2010), 60, 906-918.
  • Karaaslan, F. and Karata¸s, S., A new approach bipolar soft sets and its applications, Discrete Mathematics, Algorithm and Applications (2015), 7(4), 1550054.
  • Karaaslan, F., Soft classes and soft rough classes with application in decision making, Math- ematical Problem in Engineering, In press.
  • Karaaslan, F. and Ça¼gman, N., Bipolar soft rough sets and their applications in decision making, Submitted.
  • Kima, Y. K. and Minb, W. K., Full soft sets and full soft decision systems, Journal of Intelligent and Fuzzy Systems, DOI:10.3233/IFS-130783.
  • Li, Z., Qin, B. and Cai, Z., Soft Rough Approximation Operators and Related Results, Journal of Applied Mathematics, doi.org/10.1155/2013/241485.
  • Maji, P.K., Biswas, R. and Roy, A.R., Fuzzy soft sets, Journal of Fuzzy Mathematics (2001), 9(3),589-602.
  • Maji, P.K., Biswas, R. and Roy, A.R., Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathe- matics (2001), 9(3), 677-692.
  • Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Computers and Mathematics with Applications (2003), 45, 555-562.
  • Maji, P.K., Roy, A.R. and Biswas, R., On intuitionistic fuzzy soft sets, Computers and Mathematics with Applications (2004), 12(3), 669-683.
  • Majumdar, P. and Samanta, S.K., Generalised fuzzy soft sets, Computers and Mathematics with Applications (2010), 59, 1425-1432.
  • Meng, D., Zhang, X. H. and Qin, K. Y., Soft rough fuzzy sets and soft fuzzy rough sets, Computers and Mathematics With Applications (2011), 62(12), 4635-4645.
  • Molodtsov, D., Soft set theory …rst results, Computers and Mathematics with Applications (1999), 37, 19-31.
  • Naz, M. and Shabir, M., On bipolar fuzzy soft sets, their algebaraic structures and applica- tions, Journal of Intelligent and Fuzzy Systems (2014), 26(4) 1645-1656.
  • Park, J.H., Kima, O.H. and Kwun, Y. C., Some properties of equivalence soft set relations, Computers and Mathematics with Applications (2012), 63, 1079-1088.
  • Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences (1982), 11(5), 341-356.
  • Pawlak, Z., Skowron, A. Rudiments of rough sets, Information Sciences (2007), 177, 3–27.
  • Qin, K., Liu, Q. and Xu, Y., Rede…ned soft relations and soft functions, International journal of Computational Intelligence Systems (2015), 8(5), 819-828.
  • Qin, K.Y. and Hong, Z.Y. On soft equality, Journal of Computational and Applied Mathe- matics (2010), 234, 1347-1355.
  • Sezgin, A. and Atagün, A.O., Soft groups and normalistic soft groups, Computers and Math- ematics with Applications (2011), 62(2), 685-698.
  • Sezgin, A. and Atagün, A.O., On operations of soft sets, Computers and Mathematics with Applications (2011), 61, 1457-1467.
  • Shabir, M. and Naz, M., On bipolar soft sets, arXiv:1303.1344v1 [math.LO] (2013)
  • Shabir, M., Ali, M.I. and Shaheen, T., Another approach to soft rough sets, Know ledge-Based Systems (2013), 61, 72-80.
  • Sun, B. and Ma, W., Soft fuzzy rough sets and its application in decision making, Arti…cial Intelligence Review (2014), 41(1), 67-68.
  • Xiao, Z., Gong, K., Xia, S. and Zou, Y., Exclusive disjunctive soft sets, Computers and Mathematics with Applications (2010), 59, 2128-2137.
  • Xu, W., Ma, J., Wang, S. and Hao, G., Vague soft sets and their properties, Computers and Mathematics with Applications (2010), 59, 787-794.
  • Yang, X.B., Lin, T.Y., Yang, J.Y., Li, Y. and Yu, D.J., Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications (2009), 58, 521-527.
  • Yang, H.L, and Guoa, Z.L., Kernels and closures of soft set relations, and soft set relation mappings, Computers and Mathematics with Applications (2011), 61 651-662.
  • Zadeh, L. A., Fuzzy sets, Information and Control (1965), 8, 338-353.
  • Zhang, Z., A rough set approach to intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling, (2011), DOI: 10.1016/j.apm.2011.11.071.
  • Zhang, Z., The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets, Advances in Fuzzy Systems (2013), doi.org/10.1155/2013/197435, .
  • Zhang, W.-R., Bipolar fuzzy set and relations: a computational framework for cognitive modeling and multiagent decision analysis, Proceeding of IEEE Conference (1994), 305-309.
  • Zhang, W.-R., Bipolar fuzzy sets, Proceeding of FUZZY-IEEE (1994), 835-840.
  • Current address : Department of Mathematics, Faculty of Sciences, ÇankırıKaratekin Univer sity, 18100, Çankırı, Turkey

Year 2016, Volume: 65 Issue: 1, 105 - 126, 01.02.2016

Faruk Karaaslan

https://doi.org/10.1501/Commua1_0000000747
Cited By: 7

Abstract

References

  • Abdullah, S., Aslam, M. and Ullah, K., Bipolar fuzzy soft sets and its applications in decision making problem, Journal of Intelligent and Fuzzy Systems (2014), 27(2), 729-742.
  • Akta¸s H. and Ça¼gman, N., Soft sets and soft groups, Information Sciences (2007), 177, 2726-2735.
  • Ali, M. I., A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing Journal (2011), 11(4), 3329-3332.
  • 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 Application (2009), 57, 1547-1553.
  • Atagün, A.O. and Aygün, E., Groups of soft sets, Journal of Intelligent and Fuzzy Systems (2016), 30(2), 729-733.
  • Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems (1986), 20, 87-96.
  • Babitha, K.V. and Sunil, J.J., Soft set relations and functions, Computers and Mathematics with Applications (2010), 60, 1840-1849.
  • Ça¼gman, N. and Engino¼glu, S., Soft set theory and uni-int decision making, European Journal of Operational Research (2010), 207, 848-855.
  • Ça¼gman, N. and Engino¼glu, S., Fuzzy soft set theory and its applications, Iranian journal of fuzzy systems (2011), 8(3), 137-147.
  • Ça¼gman, N. and Karata¸s, S., Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems (2013), 24, 829-836.
  • Ça¼gman, N., Contributions to the theory of soft sets, Journal of New Results in Science (2014), 4, 33-41.
  • Dubois, D., Prade, H., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems (1990), 17, 191-209.
  • Feng F. and Liu, X., Soft rough sets with applications to demand analysis, Intelligent Systems and Applications (2009), DOI:10.1109/IWISA.2009.5073114.
  • Feng, F., Li, C., Davvaz, B. and Ali, M. I., Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing (2010), 14(9), 899-911.
  • Feng, F., Liu, X., Leoreanu-Fotea, V. and Jun, Y. B., Soft sets and soft rough sets, Informa- tion Sciences (2011), 181(6), 1125-1137.
  • Feng, F., Soft rough sets applied to multicriteria group decision making, Annals of Fuzzy Mathematics and Informatics (2011), 2(1), 69-80.
  • Gau, W.L., Buehrer, D.J., Vague sets, IEEE Transactions on Systems, Man and Cybernetics (1993), 23(2), 610-614.
  • Gong, K., Xiao, Z. and Zhang, X., The bijective soft set with its operations, Computers and Mathematics with Applications (2010), 60, 2270-2278.
  • Herawan, T. and Deris, M.M., A Direct Proof of Every Rough Set is a Soft Set, Third Asia International Conference on Modelling and Simulation (2009), DOI 10.1109/AMS.2009.148.
  • Ibrahim, A. M., Dauda, M. K. and Singh, D., Composition of Soft Set Relations and Con- struction of Transitive, Mathematical Theory and Modeling (2012), 2(7), 98-107.
  • Jiang, Y., Tang, Y., Chen, Q., Liu, H. and Tang, J., Intervalvalued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications (2010), 60, 906-918.
  • Karaaslan, F. and Karata¸s, S., A new approach bipolar soft sets and its applications, Discrete Mathematics, Algorithm and Applications (2015), 7(4), 1550054.
  • Karaaslan, F., Soft classes and soft rough classes with application in decision making, Math- ematical Problem in Engineering, In press.
  • Karaaslan, F. and Ça¼gman, N., Bipolar soft rough sets and their applications in decision making, Submitted.
  • Kima, Y. K. and Minb, W. K., Full soft sets and full soft decision systems, Journal of Intelligent and Fuzzy Systems, DOI:10.3233/IFS-130783.
  • Li, Z., Qin, B. and Cai, Z., Soft Rough Approximation Operators and Related Results, Journal of Applied Mathematics, doi.org/10.1155/2013/241485.
  • Maji, P.K., Biswas, R. and Roy, A.R., Fuzzy soft sets, Journal of Fuzzy Mathematics (2001), 9(3),589-602.
  • Maji, P.K., Biswas, R. and Roy, A.R., Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathe- matics (2001), 9(3), 677-692.
  • Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Computers and Mathematics with Applications (2003), 45, 555-562.
  • Maji, P.K., Roy, A.R. and Biswas, R., On intuitionistic fuzzy soft sets, Computers and Mathematics with Applications (2004), 12(3), 669-683.
  • Majumdar, P. and Samanta, S.K., Generalised fuzzy soft sets, Computers and Mathematics with Applications (2010), 59, 1425-1432.
  • Meng, D., Zhang, X. H. and Qin, K. Y., Soft rough fuzzy sets and soft fuzzy rough sets, Computers and Mathematics With Applications (2011), 62(12), 4635-4645.
  • Molodtsov, D., Soft set theory …rst results, Computers and Mathematics with Applications (1999), 37, 19-31.
  • Naz, M. and Shabir, M., On bipolar fuzzy soft sets, their algebaraic structures and applica- tions, Journal of Intelligent and Fuzzy Systems (2014), 26(4) 1645-1656.
  • Park, J.H., Kima, O.H. and Kwun, Y. C., Some properties of equivalence soft set relations, Computers and Mathematics with Applications (2012), 63, 1079-1088.
  • Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences (1982), 11(5), 341-356.
  • Pawlak, Z., Skowron, A. Rudiments of rough sets, Information Sciences (2007), 177, 3–27.
  • Qin, K., Liu, Q. and Xu, Y., Rede…ned soft relations and soft functions, International journal of Computational Intelligence Systems (2015), 8(5), 819-828.
  • Qin, K.Y. and Hong, Z.Y. On soft equality, Journal of Computational and Applied Mathe- matics (2010), 234, 1347-1355.
  • Sezgin, A. and Atagün, A.O., Soft groups and normalistic soft groups, Computers and Math- ematics with Applications (2011), 62(2), 685-698.
  • Sezgin, A. and Atagün, A.O., On operations of soft sets, Computers and Mathematics with Applications (2011), 61, 1457-1467.
  • Shabir, M. and Naz, M., On bipolar soft sets, arXiv:1303.1344v1 [math.LO] (2013)
  • Shabir, M., Ali, M.I. and Shaheen, T., Another approach to soft rough sets, Know ledge-Based Systems (2013), 61, 72-80.
  • Sun, B. and Ma, W., Soft fuzzy rough sets and its application in decision making, Arti…cial Intelligence Review (2014), 41(1), 67-68.
  • Xiao, Z., Gong, K., Xia, S. and Zou, Y., Exclusive disjunctive soft sets, Computers and Mathematics with Applications (2010), 59, 2128-2137.
  • Xu, W., Ma, J., Wang, S. and Hao, G., Vague soft sets and their properties, Computers and Mathematics with Applications (2010), 59, 787-794.
  • Yang, X.B., Lin, T.Y., Yang, J.Y., Li, Y. and Yu, D.J., Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications (2009), 58, 521-527.
  • Yang, H.L, and Guoa, Z.L., Kernels and closures of soft set relations, and soft set relation mappings, Computers and Mathematics with Applications (2011), 61 651-662.
  • Zadeh, L. A., Fuzzy sets, Information and Control (1965), 8, 338-353.
  • Zhang, Z., A rough set approach to intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling, (2011), DOI: 10.1016/j.apm.2011.11.071.
  • Zhang, Z., The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets, Advances in Fuzzy Systems (2013), doi.org/10.1155/2013/197435, .
  • Zhang, W.-R., Bipolar fuzzy set and relations: a computational framework for cognitive modeling and multiagent decision analysis, Proceeding of IEEE Conference (1994), 305-309.
  • Zhang, W.-R., Bipolar fuzzy sets, Proceeding of FUZZY-IEEE (1994), 835-840.
  • Current address : Department of Mathematics, Faculty of Sciences, ÇankırıKaratekin Univer sity, 18100, Çankırı, Turkey
There are 54 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Faruk Karaaslan This is me

Publication Date February 1, 2016
Published in Issue Year 2016 Volume: 65 Issue: 1

Cite

APA Karaaslan, F. (2016). BIPOLAR SOFT ROUGH RELATIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 65(1), 105-126. https://doi.org/10.1501/Commua1_0000000747
AMA Karaaslan F. BIPOLAR SOFT ROUGH RELATIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2016;65(1):105-126. doi:10.1501/Commua1_0000000747
Chicago Karaaslan, Faruk. “BIPOLAR SOFT ROUGH RELATIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65, no. 1 (February 2016): 105-26. https://doi.org/10.1501/Commua1_0000000747.
EndNote Karaaslan F (February 1, 2016) BIPOLAR SOFT ROUGH RELATIONS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65 1 105–126.
IEEE F. Karaaslan, “BIPOLAR SOFT ROUGH RELATIONS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 65, no. 1, pp. 105–126, 2016, doi: 10.1501/Commua1_0000000747.
ISNAD Karaaslan, Faruk. “BIPOLAR SOFT ROUGH RELATIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65/1 (February2016), 105-126. https://doi.org/10.1501/Commua1_0000000747.
JAMA Karaaslan F. BIPOLAR SOFT ROUGH RELATIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65:105–126.
MLA Karaaslan, Faruk. “BIPOLAR SOFT ROUGH RELATIONS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 65, no. 1, 2016, pp. 105-26, doi:10.1501/Commua1_0000000747.
Vancouver Karaaslan F. BIPOLAR SOFT ROUGH RELATIONS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2016;65(1):105-26.

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