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Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem

Year 2022, Volume: 11 Issue: 1, 26 - 47, 30.04.2022
https://doi.org/10.54187/jnrs.1031222

Abstract

Molodtsov introduced a soft set (SS) to model uncertainty parametrically, and Chaterjee et al. proposed the notion of quadripartitioned neutrosophic set (QNS) by dividing indeterminacy into two independent components, namely contradiction (C) and unknown (U). Afterwards, by combining the SS and QNS, a new concept known as quadripartitioned neutrosophic soft set (QNSS) is introduced. In relation to the concept of QNSS, another concept called interval-valued intuitionistic quadripartitioned neutrosophic soft set (in short IVIQNSS) is established to handle more complex indeterminate information parametrically with the restricted conditions. This paper aims to further generalize the existing soft models by introducing an IVIQNSS to explore another kind of imprecise knowledge. The IVIQNSS model can be viewed as a more flexible and powerful framework to encounter indeterminacy parametrically with T,F,C, and U as dependent interval quadripartitioned neutrosophic components where T,F,C,U⊆[0,1] such that sup⁡T+sup⁡F≤1, and sup⁡C+sup⁡U≤1. So, by using the IVIQNSS framework we are capable to address the indeterminate, inconsistent, and incomplete information more accurately. Different operations such as complement, AND, OR, union, intersection, etc. are defined on IVIQNSSs. Furthermore, an algorithm is constructed to solve decision-making (DM) problems based on IVIQNSS. Finally, an illustrative example is executed to validate the proposed study.

Supporting Institution

Tripura University(Central), Suryamaninagar-799022, Tripura, India

Project Number

NA

References

  • L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965) 338–353.
  • D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4–5), (1999) 19–31.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45(4–5), (2003) 555–562.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57(9), (2009) 1547–1553.
  • K. V. Babitha, J. Sunil, Soft set relations and functions, Computers and Mathematics with Applications, 60(7), (2010) 1840–1849.
  • N. Çağman, S. Enginoğlu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207(2), (2010) 848–855.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision-making problem, Computers and Mathematics with Applications, 44(8–9), (2002) 1077–1083.
  • Y. Jun, C. Park, Applications of soft sets in ideal theory of BCK/BCI algebras, Information Sciences, 178(11), (2008) 2466–2475.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications, 49(5–6), (2005) 757–763.
  • A. Sezgin, A. O. Atagün, On operations of soft sets, Computers and Mathematics with Applications, 61(5), (2011) 1457–1467.
  • H. Aktaş, N. Çağman, Soft sets and soft groups, Information Sciences, 177(13), (2007) 2726–2735.
  • N. Çağman, S. Enginoğlu, Soft matrix theory and its decision making, Computers and Mathematics with Applications, 59(10), (2010) 3308–3314.
  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications, 59(11), (2010) 3458–3463.
  • M. K. Tahat, F. Sidky, M. Abo Elhamayel, Soft topological rings, Journal of King Saud University Science, 31(4), (2019) 1127–1136.
  • A. R. Roy, P. K. Maji, A fuzzy soft set-theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, 203(2), (2007) 412–418.
  • P. Majumdar, S. K. Samanta, Generalized fuzzy soft sets, Computers and Mathematics with Applications, 59(4), (2010) 1425–1432.
  • Z. Xiao, S. Xia, K. Gong, D. Li, The trapezoidal fuzzy soft set and its application in MCDM, Applied Mathematical Modelling, 36(12), (2012) 5844–5855.
  • Y. Yang, X. Tan, C. Meng, The multi fuzzy soft set and its application in decision making, Applied Mathematical Modelling, 37(7), (2013) 4915–4923.
  • N. Çağman, S. Karataş, Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems, 24(4), (2013) 829–836.
  • B. Said, F. Smarandache, Intuitionistic neutrosophic soft set, Journal of Information and Computing Science, 8(2), (2013) 130–140.
  • M. Bashir, A. R. Salleh, S. Alkhazaleh, Possibility intuitionistic fuzzy soft set, Advances in Decision Sciences, 2012, (2012) Article ID: 404325, 1–24.
  • Y. Jiang, Y. Tang, H. Liu, Z. Chen, Entropy on intuitionistic fuzzy soft sets and interval valued fuzzy soft sets, Information Sciences, 240(10), (2013) 95–114.
  • X. Yang, T. Y. Lin, J. Yang, Y. Li, D. Yu, Combination of interval valued fuzzy set and soft set, Computers and Mathematics with Applications, 58(3), (2009) 521–527.
  • F. Feng, Y. Li, V. LeoreanuFotea, Application of level soft sets in decision making based on interval valued fuzzy soft sets, Computers and Mathematics with Applications, 60(6), (2010) 1756–1767.
  • X. Peng, H. Garg, Algorithms for interval valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure, Computers and Industrial Engineering, 119, (2018) 439–452.
  • B. K. Tripathy, T. R. Sooraj, R. K. Mohanty, A new approach to interval valued fuzzy soft sets and its application in decision making, Advances in Computational Intelligence, Springer, Singapore, 509, (2016) 3–10.
  • Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tang, Interval valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60(3), (2010) 906–918.
  • A. Khalid, M. Abbas, Distance measures, and operations in intuitionistic and interval valued intuitionistic fuzzy soft set theory, International Journal of Fuzzy Systems, 17(3), (2015) 490–497.
  • Z. Zhang, C. Wang, D. Tian, K. Li, A novel approach to interval valued intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling, 38(4), (2014) 1255–1270.
  • H. Garg, R. Arora, A nonlinear programming methodology for multiattribute decision making problem with interval valued intuitionistic fuzzy soft sets information, Applied Intelligence, 48(8), (2018) 2031–2046.
  • M. J. Khan, P. Kumam, P. Liu, W. Kumam, Another view on generalized interval valued intuitionistic fuzzy soft set and its applications in decision support system, Journal of Intelligent and Fuzzy Systems, 38(4), (2020) 4327–4341.
  • R. M. Zulqarnain, X. L. Xin, M. Saqlain, W. A. Khan, TOPSIS method based on the correlation coefficient of interval valued intuitionistic fuzzy soft sets and aggregation operators with their application in decision making, Journal of Mathematics, 2021, (2021) Article ID: 6656858, 1–16.
  • T. Aydın, S. Enginoğlu, Interval valued intuitionistic fuzzy parameterized interval valued intuitionistic fuzzy soft sets and their application in decision making, Journal of Ambient Intelligence and Humanized Computing, 12(1), (2021) 1541–1558.
  • V. Chinnadurai, A. Swaminathan, A. Bobin, B. KatharKani, Generalized interval valued intuitionistic fuzzy soft matrices and their application to multicriteria decision making, Recent Trends in Pure and Applied Mathematics, 2177, (2019) 020019.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87–96.
  • F. Smarandache, Neutrosophic set - A Generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics, 24(3), (2005) 287–297.
  • H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets, Technical Sciences and Applied Mathematics, 1, (2010) 10–14.
  • P. K. Maji, A Neutrosophic soft set approach to a decision-making problem, Annals of Fuzzy Mathematics and Informatics, 3, (2012) 313–319.
  • S. Broumi, R. Şahin, F. Smarandache, Generalized interval neutrosophic soft set and its decision-making problem, Journal of New Results in Science, (7), (2014) 29–47.
  • İ. Deli, Interval valued neutrosophic soft sets and its decision making, International Journal of Machine Learning and Cybernetics, 8(2), (2017) 665–676.
  • C. Veerappan, B. Albert, Interval valued intuitionistic neutrosophic soft set and its application on diagnosing psychiatric disorder by using similarity measure, Neutrosophic Sets and Systems, 41, (2021) 215–245.
  • A. Fahmi, F. Amin, S. B. Shah, Geometric operators based on linguistic interval valued intuitionistic neutrosophic fuzzy number and their application in decision making, Annals of Optimization Theory and Practice, 3(1), (2020) 47–71.
  • S. Broumi, I. Deli, F. Smarandache, Distance and similarity measures of interval neutrosophic soft sets, In Proceedings of the 17th International Conference on Information Fusion, Salamanca, Spain, 2014, pp. 79–96.
  • İ. Deli, S. Eraslan, N. Çağman, ivnpiv-neutrosophic soft sets and their decision making based on similarity measure, Neural Computing and Applications, 29(1), (2018) 187–203.
  • İ. Deli, S. Broumi, Neutrosophic soft matrices and NSM-decision making, Journal of Intelligent and Fuzzy Systems, 28(5), (2015) 2233–2241.
  • R. Chatterjee, P. Majumdar, S. K. Samanta, On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets, Journal of Intelligent and Fuzzy Systems, 30(4), (2016) 2475–2485.
  • R. Chatterjee, P. Majumder, S. K. Samanta, A multicriteria group decision making algorithm with quadripartitioned neutrosophic weighted aggregation operators using quadripartitioned neutrosophic numbers in IPQSVNSS environment, Soft Computing, 24(1), (2020) 8857–8880.
  • S. Roy, J. G. Lee, A. Pal, S. K. Samanta, Similarity measures of quadripartitioned single valued bipolar neutrosophic sets and its application in multicriteria decision making problem, Symmetry, 12(6), (2020) 1–16.
  • M. Mohanasundari, K. Mohana, Quadripartitioned single valued neutrosophic dombi weighted aggregation operators for multiple attribute decision making, Neutrosophic Sets and Systems, 32, (2020) 107–122.
  • K. Sinha, P. Majumdar, Bipolar quadripartitioned single valued neutrosophic sets, Journal of Mathematics, 39(6), (2020) 1597–1614.
  • S. A. Mary, Quadripartitioned neutrosophic soft set, International Research Journal on Advanced Science Hub, 3(2), (2021) 106–112.
  • R. Chatterjee, P. Majumdar, S. K. Samanta, Interval valued possibility quadripartitioned single valued neutrosophic soft sets and some uncertainty-based measures on them, Neutrosophic Sets and Systems, 14, (2016) 35–43.
  • K. T. Atanassov, Interval valued intuitionistic fuzzy sets, in intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, Physica, Heidelberg, 35, (1999) 139–177.
  • M. Bhowmik, M. Pal, Intuitionistic neutrosophic set, Journal of Information and Computing Science, 4(2), (2009) 142–152.
  • H. Wang, F. Smarandache, YQ. Zhang, R. Sunderraman, Interval neutrosophic sets, and logic: theory and applications in computing, Neutrosophic Book Series, 5 (2005) Hexis, Arizona.
Year 2022, Volume: 11 Issue: 1, 26 - 47, 30.04.2022
https://doi.org/10.54187/jnrs.1031222

Abstract

Project Number

NA

References

  • L. A. Zadeh, Fuzzy sets, Information and Control, 8(3), (1965) 338–353.
  • D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37(4–5), (1999) 19–31.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications, 45(4–5), (2003) 555–562.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57(9), (2009) 1547–1553.
  • K. V. Babitha, J. Sunil, Soft set relations and functions, Computers and Mathematics with Applications, 60(7), (2010) 1840–1849.
  • N. Çağman, S. Enginoğlu, Soft set theory and uni-int decision making, European Journal of Operational Research, 207(2), (2010) 848–855.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision-making problem, Computers and Mathematics with Applications, 44(8–9), (2002) 1077–1083.
  • Y. Jun, C. Park, Applications of soft sets in ideal theory of BCK/BCI algebras, Information Sciences, 178(11), (2008) 2466–2475.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications, 49(5–6), (2005) 757–763.
  • A. Sezgin, A. O. Atagün, On operations of soft sets, Computers and Mathematics with Applications, 61(5), (2011) 1457–1467.
  • H. Aktaş, N. Çağman, Soft sets and soft groups, Information Sciences, 177(13), (2007) 2726–2735.
  • N. Çağman, S. Enginoğlu, Soft matrix theory and its decision making, Computers and Mathematics with Applications, 59(10), (2010) 3308–3314.
  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications, 59(11), (2010) 3458–3463.
  • M. K. Tahat, F. Sidky, M. Abo Elhamayel, Soft topological rings, Journal of King Saud University Science, 31(4), (2019) 1127–1136.
  • A. R. Roy, P. K. Maji, A fuzzy soft set-theoretic approach to decision making problems, Journal of Computational and Applied Mathematics, 203(2), (2007) 412–418.
  • P. Majumdar, S. K. Samanta, Generalized fuzzy soft sets, Computers and Mathematics with Applications, 59(4), (2010) 1425–1432.
  • Z. Xiao, S. Xia, K. Gong, D. Li, The trapezoidal fuzzy soft set and its application in MCDM, Applied Mathematical Modelling, 36(12), (2012) 5844–5855.
  • Y. Yang, X. Tan, C. Meng, The multi fuzzy soft set and its application in decision making, Applied Mathematical Modelling, 37(7), (2013) 4915–4923.
  • N. Çağman, S. Karataş, Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems, 24(4), (2013) 829–836.
  • B. Said, F. Smarandache, Intuitionistic neutrosophic soft set, Journal of Information and Computing Science, 8(2), (2013) 130–140.
  • M. Bashir, A. R. Salleh, S. Alkhazaleh, Possibility intuitionistic fuzzy soft set, Advances in Decision Sciences, 2012, (2012) Article ID: 404325, 1–24.
  • Y. Jiang, Y. Tang, H. Liu, Z. Chen, Entropy on intuitionistic fuzzy soft sets and interval valued fuzzy soft sets, Information Sciences, 240(10), (2013) 95–114.
  • X. Yang, T. Y. Lin, J. Yang, Y. Li, D. Yu, Combination of interval valued fuzzy set and soft set, Computers and Mathematics with Applications, 58(3), (2009) 521–527.
  • F. Feng, Y. Li, V. LeoreanuFotea, Application of level soft sets in decision making based on interval valued fuzzy soft sets, Computers and Mathematics with Applications, 60(6), (2010) 1756–1767.
  • X. Peng, H. Garg, Algorithms for interval valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure, Computers and Industrial Engineering, 119, (2018) 439–452.
  • B. K. Tripathy, T. R. Sooraj, R. K. Mohanty, A new approach to interval valued fuzzy soft sets and its application in decision making, Advances in Computational Intelligence, Springer, Singapore, 509, (2016) 3–10.
  • Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tang, Interval valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60(3), (2010) 906–918.
  • A. Khalid, M. Abbas, Distance measures, and operations in intuitionistic and interval valued intuitionistic fuzzy soft set theory, International Journal of Fuzzy Systems, 17(3), (2015) 490–497.
  • Z. Zhang, C. Wang, D. Tian, K. Li, A novel approach to interval valued intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling, 38(4), (2014) 1255–1270.
  • H. Garg, R. Arora, A nonlinear programming methodology for multiattribute decision making problem with interval valued intuitionistic fuzzy soft sets information, Applied Intelligence, 48(8), (2018) 2031–2046.
  • M. J. Khan, P. Kumam, P. Liu, W. Kumam, Another view on generalized interval valued intuitionistic fuzzy soft set and its applications in decision support system, Journal of Intelligent and Fuzzy Systems, 38(4), (2020) 4327–4341.
  • R. M. Zulqarnain, X. L. Xin, M. Saqlain, W. A. Khan, TOPSIS method based on the correlation coefficient of interval valued intuitionistic fuzzy soft sets and aggregation operators with their application in decision making, Journal of Mathematics, 2021, (2021) Article ID: 6656858, 1–16.
  • T. Aydın, S. Enginoğlu, Interval valued intuitionistic fuzzy parameterized interval valued intuitionistic fuzzy soft sets and their application in decision making, Journal of Ambient Intelligence and Humanized Computing, 12(1), (2021) 1541–1558.
  • V. Chinnadurai, A. Swaminathan, A. Bobin, B. KatharKani, Generalized interval valued intuitionistic fuzzy soft matrices and their application to multicriteria decision making, Recent Trends in Pure and Applied Mathematics, 2177, (2019) 020019.
  • K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), (1986) 87–96.
  • F. Smarandache, Neutrosophic set - A Generalization of the intuitionistic fuzzy set, International Journal of Pure and Applied Mathematics, 24(3), (2005) 287–297.
  • H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single valued neutrosophic sets, Technical Sciences and Applied Mathematics, 1, (2010) 10–14.
  • P. K. Maji, A Neutrosophic soft set approach to a decision-making problem, Annals of Fuzzy Mathematics and Informatics, 3, (2012) 313–319.
  • S. Broumi, R. Şahin, F. Smarandache, Generalized interval neutrosophic soft set and its decision-making problem, Journal of New Results in Science, (7), (2014) 29–47.
  • İ. Deli, Interval valued neutrosophic soft sets and its decision making, International Journal of Machine Learning and Cybernetics, 8(2), (2017) 665–676.
  • C. Veerappan, B. Albert, Interval valued intuitionistic neutrosophic soft set and its application on diagnosing psychiatric disorder by using similarity measure, Neutrosophic Sets and Systems, 41, (2021) 215–245.
  • A. Fahmi, F. Amin, S. B. Shah, Geometric operators based on linguistic interval valued intuitionistic neutrosophic fuzzy number and their application in decision making, Annals of Optimization Theory and Practice, 3(1), (2020) 47–71.
  • S. Broumi, I. Deli, F. Smarandache, Distance and similarity measures of interval neutrosophic soft sets, In Proceedings of the 17th International Conference on Information Fusion, Salamanca, Spain, 2014, pp. 79–96.
  • İ. Deli, S. Eraslan, N. Çağman, ivnpiv-neutrosophic soft sets and their decision making based on similarity measure, Neural Computing and Applications, 29(1), (2018) 187–203.
  • İ. Deli, S. Broumi, Neutrosophic soft matrices and NSM-decision making, Journal of Intelligent and Fuzzy Systems, 28(5), (2015) 2233–2241.
  • R. Chatterjee, P. Majumdar, S. K. Samanta, On some similarity measures and entropy on quadripartitioned single valued neutrosophic sets, Journal of Intelligent and Fuzzy Systems, 30(4), (2016) 2475–2485.
  • R. Chatterjee, P. Majumder, S. K. Samanta, A multicriteria group decision making algorithm with quadripartitioned neutrosophic weighted aggregation operators using quadripartitioned neutrosophic numbers in IPQSVNSS environment, Soft Computing, 24(1), (2020) 8857–8880.
  • S. Roy, J. G. Lee, A. Pal, S. K. Samanta, Similarity measures of quadripartitioned single valued bipolar neutrosophic sets and its application in multicriteria decision making problem, Symmetry, 12(6), (2020) 1–16.
  • M. Mohanasundari, K. Mohana, Quadripartitioned single valued neutrosophic dombi weighted aggregation operators for multiple attribute decision making, Neutrosophic Sets and Systems, 32, (2020) 107–122.
  • K. Sinha, P. Majumdar, Bipolar quadripartitioned single valued neutrosophic sets, Journal of Mathematics, 39(6), (2020) 1597–1614.
  • S. A. Mary, Quadripartitioned neutrosophic soft set, International Research Journal on Advanced Science Hub, 3(2), (2021) 106–112.
  • R. Chatterjee, P. Majumdar, S. K. Samanta, Interval valued possibility quadripartitioned single valued neutrosophic soft sets and some uncertainty-based measures on them, Neutrosophic Sets and Systems, 14, (2016) 35–43.
  • K. T. Atanassov, Interval valued intuitionistic fuzzy sets, in intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, Physica, Heidelberg, 35, (1999) 139–177.
  • M. Bhowmik, M. Pal, Intuitionistic neutrosophic set, Journal of Information and Computing Science, 4(2), (2009) 142–152.
  • H. Wang, F. Smarandache, YQ. Zhang, R. Sunderraman, Interval neutrosophic sets, and logic: theory and applications in computing, Neutrosophic Book Series, 5 (2005) Hexis, Arizona.
There are 55 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Articles
Authors

Somen Debnath 0000-0003-3585-0868

Project Number NA
Early Pub Date April 30, 2022
Publication Date April 30, 2022
Published in Issue Year 2022 Volume: 11 Issue: 1

Cite

APA Debnath, S. (2022). Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem. Journal of New Results in Science, 11(1), 26-47. https://doi.org/10.54187/jnrs.1031222
AMA Debnath S. Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem. JNRS. April 2022;11(1):26-47. doi:10.54187/jnrs.1031222
Chicago Debnath, Somen. “Interval-Valued Intuitionistic Quadripartitioned Neutrosophic Soft Sets With T, F, C, and U As Dependent Neutrosophic Components and Their Application in Decision-Making Problem”. Journal of New Results in Science 11, no. 1 (April 2022): 26-47. https://doi.org/10.54187/jnrs.1031222.
EndNote Debnath S (April 1, 2022) Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem. Journal of New Results in Science 11 1 26–47.
IEEE S. Debnath, “Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem”, JNRS, vol. 11, no. 1, pp. 26–47, 2022, doi: 10.54187/jnrs.1031222.
ISNAD Debnath, Somen. “Interval-Valued Intuitionistic Quadripartitioned Neutrosophic Soft Sets With T, F, C, and U As Dependent Neutrosophic Components and Their Application in Decision-Making Problem”. Journal of New Results in Science 11/1 (April 2022), 26-47. https://doi.org/10.54187/jnrs.1031222.
JAMA Debnath S. Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem. JNRS. 2022;11:26–47.
MLA Debnath, Somen. “Interval-Valued Intuitionistic Quadripartitioned Neutrosophic Soft Sets With T, F, C, and U As Dependent Neutrosophic Components and Their Application in Decision-Making Problem”. Journal of New Results in Science, vol. 11, no. 1, 2022, pp. 26-47, doi:10.54187/jnrs.1031222.
Vancouver Debnath S. Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem. JNRS. 2022;11(1):26-47.


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