Research Article
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Year 2025, Volume: 11 Issue: 1, 12 - 22, 29.06.2025
https://doi.org/10.51477/mejs.1677824

Abstract

References

  • Zadeh, L.A., “Fuzzy sets”, Information and Control, 8(3), 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  • Atanassov, K., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20(1), 87–96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  • Gau, W.L., Buehrer, D.J., “Vague sets”, IEEE Trans. Syst. Man. Cybern., 23(2), 610–614, 1993. DOI: 10.1109/21.229476
  • Pawlak, Z., “Rough sets”, International Journal of Computer & Information Sciences, 11(5), 341–356, 1982. https://doi.org/10.1007/BF01001956
  • Molodtsov, D., “Soft set theory – First results”, Computers and Mathematics with Applications, 37( 4-5), 19–31, 1999. https://doi.org/10.1016/S0898-1221(99)00056-5
  • Maji, P.K., Biswas, R., Roy, A.R., “Soft set theory”, Computers and Mathematics with Applications, 45(4-5), 555–562, 2003. https://doi.org/10.1016/S0898-1221(03)00016-6
  • Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabira, M., “On some new operations in soft set theory”, Computers and Mathematics with Applications, 57(9), 1547-1553, 2009. https://doi.org/10.1016/j.camwa.2008.11.009
  • Maji, P.K., Roy, A.R., Biswas, R., “An application of soft sets in a decision making problem”, Computers and Mathematics with Applications, 44(8-9), 1077–1083, 2002. https://doi.org/10.1016/S0898-1221(02)00216-X
  • Chen, D., Tsang, E.C.C., Yeung, D.S., Wang, X., “The parameterization reduction of soft sets and its applications”, Computers and Mathematics with Applications, 49(5-6), 757-763, 2005. https://doi.org/10.1016/j.camwa.2004.10.036
  • Gong, K., Xiao, Z., Zhang, X., “The bijective soft set with its operations”, Computers and Mathematics with Applications, 60(8), 2270–2278, 2010. https://doi.org/10.1016/j.camwa.2010.08.017
  • Aktaş, H., “ Some algebraic applications of soft sets”, Applied Soft Computing, 28, 327-331, 2015. https://doi.org/10.1016/j.asoc.2014.11.045
  • Koyuncu, F., “Bijective soft rings with applications”, Journal of New Results in Science, 13(1), 47-60, 2024. https://doi.org/10.54187/jnrs.1464556
  • Gong, K., Wang, P., Peng, Y. “Fault-tolerant enhanced bijective soft set with applications”, Applied Soft Computing, 54, 431-439, 2017. https://doi.org/10.1016/j.asoc.2016.06.009
  • Tiwari, V., Jain, P.K., Tandon, P., “A bijective soft set theoretic approach for concept selection in design process”, Journal of Engineering Design, 28(2), 100-117, 2017. https://doi.org/10.1080/09544828.2016.1274718
  • Pawlak, Z., Skowron, A., “Rough sets and Boolean reasoning”, Information Sciences, 177(1), 41–73, 2007. https://doi.org/10.1016/j.ins.2006.06.007
  • Pawlak, Z., “Rough sets and intelligent data analysis”, Information Sciences, 147(1-4), 1-12, 2002. https://doi.org/10.1016/S0020-0255(02)00197-4
  • Pawlak, Z., Skowron, A., “Rudiments of rough sets”, Information Sciences, 177(1), 3-27, 2007. https://doi.org/10.1016/j.ins.2006.06.003
  • Polkowski, L., Skowron, A., “Rough mereology: a new paradigm for approximate reasoning”, International Journal of Approximate Reasoning, 15(4), 333–365, 1997. https://doi.org/10.1016/S0888-613X(96)00072-2
  • Peters, J.F., Pal, S.K., Cantor, Fuzzy, Near, and Rough Sets in Image Analysis, in: Rough Fuzzy Image Analysis: Foundations and Methodologies, (Eds: Pal, S.K. and Peters, J. F.) CRC Pres, Taylor and Francis Group, Boca Raton, U.S.A, pp. 1.1-1.16., 2010.
  • Herawan, T., Deris, M.M., “A direct proof of every rough set is a soft set”, Third Asia International Conference on Modelling & Simulation, Bali, Indonesia, 2009, pp. 119 -124.
  • Feng, F., Li, C., Davvaz, B., Ali, M.I., “Soft sets combined with fuzzy sets and rough sets: A tentative approach”, Soft Computing, 14(9), 899–911, 2010. https://doi.org/10.1007/s00500-009-0465-6
  • Feng, F., Liu, X., Leoreanu-Fotea, V., Jun, Y.B., “Soft sets and soft rough sets”, Information Sciences, 181(6), 125–1137, 2011. https://doi.org/10.1016/j.ins.2010.11.004
  • Pan, W., Zhan, J., “Soft Rough Groups and Corresponding Decision Making”, Italian Journal of Pure and Applied Mathematics, 38, 158-171, 2017.
  • Zhan, J., Liu, Q., Herawan, T., “A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making”, Applied Soft Computing, 54, 393-402, 2017. https://doi.org/10.1016/j.asoc.2016.09.012
  • Wang, Q., Zhan, J., Borzooei, R.A., “A study on soft rough semigroups and corresponding decision making applications”, Open Mathematics, 15(1), 1400–1413, 2017. https://doi.org/10.1515/math-2017-0119
  • Bağırmaz, N., Bijective Soft Rough Sets, in: Unified Perspectives in Mathematics and Geometry (Ed. İ. Eryılmaz). BIDGE Publications, Ankara, pp. 142-161, 2024.

DECISION MAKING WITH BIJECTIVE SOFT ROUGH SET MODEL

Year 2025, Volume: 11 Issue: 1, 12 - 22, 29.06.2025
https://doi.org/10.51477/mejs.1677824

Abstract

Rough sets and soft sets are two important mathematical tools for dealing with uncertainty. Methods that combine properties of both sets can provide more effective solutions in certain applications. This paper aims to present an application of one such method, bijective soft rough sets. Subsequently, an algorithm based on bijective soft rough sets for decision making is developed and a real-life application of the proposed method is presented.

References

  • Zadeh, L.A., “Fuzzy sets”, Information and Control, 8(3), 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  • Atanassov, K., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20(1), 87–96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  • Gau, W.L., Buehrer, D.J., “Vague sets”, IEEE Trans. Syst. Man. Cybern., 23(2), 610–614, 1993. DOI: 10.1109/21.229476
  • Pawlak, Z., “Rough sets”, International Journal of Computer & Information Sciences, 11(5), 341–356, 1982. https://doi.org/10.1007/BF01001956
  • Molodtsov, D., “Soft set theory – First results”, Computers and Mathematics with Applications, 37( 4-5), 19–31, 1999. https://doi.org/10.1016/S0898-1221(99)00056-5
  • Maji, P.K., Biswas, R., Roy, A.R., “Soft set theory”, Computers and Mathematics with Applications, 45(4-5), 555–562, 2003. https://doi.org/10.1016/S0898-1221(03)00016-6
  • Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabira, M., “On some new operations in soft set theory”, Computers and Mathematics with Applications, 57(9), 1547-1553, 2009. https://doi.org/10.1016/j.camwa.2008.11.009
  • Maji, P.K., Roy, A.R., Biswas, R., “An application of soft sets in a decision making problem”, Computers and Mathematics with Applications, 44(8-9), 1077–1083, 2002. https://doi.org/10.1016/S0898-1221(02)00216-X
  • Chen, D., Tsang, E.C.C., Yeung, D.S., Wang, X., “The parameterization reduction of soft sets and its applications”, Computers and Mathematics with Applications, 49(5-6), 757-763, 2005. https://doi.org/10.1016/j.camwa.2004.10.036
  • Gong, K., Xiao, Z., Zhang, X., “The bijective soft set with its operations”, Computers and Mathematics with Applications, 60(8), 2270–2278, 2010. https://doi.org/10.1016/j.camwa.2010.08.017
  • Aktaş, H., “ Some algebraic applications of soft sets”, Applied Soft Computing, 28, 327-331, 2015. https://doi.org/10.1016/j.asoc.2014.11.045
  • Koyuncu, F., “Bijective soft rings with applications”, Journal of New Results in Science, 13(1), 47-60, 2024. https://doi.org/10.54187/jnrs.1464556
  • Gong, K., Wang, P., Peng, Y. “Fault-tolerant enhanced bijective soft set with applications”, Applied Soft Computing, 54, 431-439, 2017. https://doi.org/10.1016/j.asoc.2016.06.009
  • Tiwari, V., Jain, P.K., Tandon, P., “A bijective soft set theoretic approach for concept selection in design process”, Journal of Engineering Design, 28(2), 100-117, 2017. https://doi.org/10.1080/09544828.2016.1274718
  • Pawlak, Z., Skowron, A., “Rough sets and Boolean reasoning”, Information Sciences, 177(1), 41–73, 2007. https://doi.org/10.1016/j.ins.2006.06.007
  • Pawlak, Z., “Rough sets and intelligent data analysis”, Information Sciences, 147(1-4), 1-12, 2002. https://doi.org/10.1016/S0020-0255(02)00197-4
  • Pawlak, Z., Skowron, A., “Rudiments of rough sets”, Information Sciences, 177(1), 3-27, 2007. https://doi.org/10.1016/j.ins.2006.06.003
  • Polkowski, L., Skowron, A., “Rough mereology: a new paradigm for approximate reasoning”, International Journal of Approximate Reasoning, 15(4), 333–365, 1997. https://doi.org/10.1016/S0888-613X(96)00072-2
  • Peters, J.F., Pal, S.K., Cantor, Fuzzy, Near, and Rough Sets in Image Analysis, in: Rough Fuzzy Image Analysis: Foundations and Methodologies, (Eds: Pal, S.K. and Peters, J. F.) CRC Pres, Taylor and Francis Group, Boca Raton, U.S.A, pp. 1.1-1.16., 2010.
  • Herawan, T., Deris, M.M., “A direct proof of every rough set is a soft set”, Third Asia International Conference on Modelling & Simulation, Bali, Indonesia, 2009, pp. 119 -124.
  • Feng, F., Li, C., Davvaz, B., Ali, M.I., “Soft sets combined with fuzzy sets and rough sets: A tentative approach”, Soft Computing, 14(9), 899–911, 2010. https://doi.org/10.1007/s00500-009-0465-6
  • Feng, F., Liu, X., Leoreanu-Fotea, V., Jun, Y.B., “Soft sets and soft rough sets”, Information Sciences, 181(6), 125–1137, 2011. https://doi.org/10.1016/j.ins.2010.11.004
  • Pan, W., Zhan, J., “Soft Rough Groups and Corresponding Decision Making”, Italian Journal of Pure and Applied Mathematics, 38, 158-171, 2017.
  • Zhan, J., Liu, Q., Herawan, T., “A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making”, Applied Soft Computing, 54, 393-402, 2017. https://doi.org/10.1016/j.asoc.2016.09.012
  • Wang, Q., Zhan, J., Borzooei, R.A., “A study on soft rough semigroups and corresponding decision making applications”, Open Mathematics, 15(1), 1400–1413, 2017. https://doi.org/10.1515/math-2017-0119
  • Bağırmaz, N., Bijective Soft Rough Sets, in: Unified Perspectives in Mathematics and Geometry (Ed. İ. Eryılmaz). BIDGE Publications, Ankara, pp. 142-161, 2024.
There are 26 citations in total.

Details

Primary Language English
Subjects Quantitative Decision Methods , Pure Mathematics (Other)
Journal Section Research Article
Authors

Nurettin Bağırmaz 0000-0002-7663-3002

Early Pub Date June 26, 2025
Publication Date June 29, 2025
Submission Date April 16, 2025
Acceptance Date June 12, 2025
Published in Issue Year 2025 Volume: 11 Issue: 1

Cite

IEEE N. Bağırmaz, “DECISION MAKING WITH BIJECTIVE SOFT ROUGH SET MODEL”, MEJS, vol. 11, no. 1, pp. 12–22, 2025, doi: 10.51477/mejs.1677824.

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