A MATLAB TOOLBOX FOR INTERVAL VALUED NEUTROSOPHIC MATRICES FOR COMPUTER APPLICATIONS
Year 2017,
Volume: 1 Issue: 1, 1 - 21, 29.12.2017
Said Broumi
,
Assia Bakalı
Mohamed Talea
Florentin Smarandache
Abstract
The
concept of interval valued neutrosophic matrices is a generalized structure of
fuzzy matrices, intuitionistic fuzzy matrices, interval fuzzy matrices and
single valued neutrosophic matrices. Recently many studies have focused on
interval valued neutrosophic matrices, In this paper, a variety of operations
on interval valued neutrosophic matrices are presented using a new Matlab’
package. This package contains some essential functions which could help the
researchers to do computations on interval valued neutrosophic matrices quickly.
References
- Anand, M.C.J. and Anand, M.E.,(2015) Eigenvaluesand eigen vectors for fuzzy matrix, International Journal of Engineering Research and General Science Volume 3, Issue 1, 2015, pp.878- 890
- Bausys, R., & Zavadskas, E. K. (2015). Multıcrıterıa Decısıon Makıng Approach By Vıkor Under Interval Neutrosophıc Set Envıronment. Economic Computation & Economic Cybernetics Studies & Research, 49(4).
- Broumi, S. , M. Talea, A. Bakali, F. Smarandache, (2016). Interval Valued Neutrosophic Graphs, Critical Review, XII, 2016. pp.5-33.
- Broumi, S., A.Bakali, M.Talea, F.Smarandache, R.Verma,(2017) Computing Minimum Spanning Tree In Interval Valued Bipolar Neutrosophic Environment,International Journal of Modeling and Optimization, Vol. 7, No. 5, 2017, pp300-304.
- Broumi, S., Le Hoang, F. Smarandache, A. Bakali, M.Talea, G.Selvachandran, Kishore Kumar.P.K, Computing Operational Matrices in Neutrosophic Environments: A Matlab toolbox, submitted
- Broumi, S., Smarandache, F., Talea, M., & Bakali, A. (2016). Operations on interval valued neutrosophic graphs. Infinite Study. Graphs, chapter in book- New Trends in Neutrosophic Theory and Applications- FlorentinSmarandache and SurpatiPramanik (Editors), pp. 231-254. ISBN 978-1-59973-498-9
- Broumi, S., Talea, M., Smarandache, F., & Bakali, A. (2016, December). Decision-making method based on the interval valued neutrosophic graph. In Future Technologies Conference (FTC) (pp. 44-50). IEEE.
- C.Jaisankar, S.Arunvasan and R.Mani.,(2016) On Hessenberg of Triangular fuzzy matrices, IJSRET, V-5(12), 2016,pp.586-591
- Deli, I. (2017). Interval-valued neutrosophic soft sets and its decision making. International Journal of Machine Learning and Cybernetics, 8(2), 665-676.
- Dinagar, D. S., & Latha, K. (2013). Some types of type-2 triangular fuzzy matrices. International Journal of Pure and Applied Mathematics, 82(1), 21-32.
- Garg, H. (2016). An improved score function for ranking neutrosophic sets and its application to decision-making process. International Journal for Uncertainty Quantification, 6(5).
- Garg, H. (2017). Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Applied Intelligence, 1-15.
- Huang, Y. H., Wei, G. W., & Wei, C. (2017). VIKOR method for interval neutrosophic multiple attribute group decision-making. Information, 8(4), 144. doi:10.3390/info8040144
- Jaisankar, C., and Mani, R., (2017) Some Properties of Determinant of Trapezoidal Fuzzy Number Matrices, International Journal Of Modern Engineering Research, Vol. 7 ,Iss. 1 , 2017 ,pp70-78
- Karaşan, A., & Kahraman, C. (2017). Interval-Valued Neutrosophic Extension of EDAS Method. In Advances in Fuzzy Logic and Technology 2017 (pp. 343-357). Springer, Cham. DOI 10.1007/978-3-319-66824-6_3
- Karunambigai, M. G., and Kalaivani, O. K., (2016). Software development in intuitionistic Fuzzy Relational Calculus. International Journal of Scientific and research Publication, 6(7), 2016,pp.311-331.
- Ma, Y. X., Wang, J. Q., Wang, J., & Wu, X. H. (2017). An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options. Neural Computing and Applications, 28(9), 2745-2765. DOI 10.1007/s00521-016-2203-1.
- Pal, A., & Pal, M. (2010, December). Some results on interval-valued fuzzy matrices. In The 2010 International Conference on E-Business Intelligence, Org. by Tsinghua University, Kunming, China, Atlantis Press (pp. 554-559).
- Pal, M., Khan, S. K., & Shyamal, A. K. (2002). Intuitionistic fuzzy matrices. Notes on Intuitionistic fuzzy sets, 8(2), 51-62.
- Peeva, K., & Kyosev, Y. (2004) Solving problems in intuitionistic fuzzy relational calculus with fuzzy relational calculus toolbox. In Eight International Conference on IFSs, Varna (pp. 37-43).
- Pushpalatha, V.,(2017). α-Cuts Of Interval-Valued Fuzzy Matrices With Interval-Valued Fuzzy Rows And Columns, IOSR Journal of Mathematics, Volume 13, Issue 3 Ver. II ,2017, pp.55-62
- Reddy, R., Reddy, D., & Krishnaiah, G. (2016). Lean Supplier Selection based on Hybrid MCGDM Approach using Interval Valued Neutrosophic Sets: A Case Study. International Journal of Innovative Research and Development, 5(4). pp.291-296.
- Smarandache, F. (1998). Neutrosophy. neutrosophic probability, set, and logic, ProQuest information and learning. Ann Arbor, Michigan, USA, 105.
- Sun, H. X., Yang, H. X., Wu, J. Z., & Ouyang, Y. (2015). Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making. Journal of Intelligent & Fuzzy Systems, 28(6), 2443-2455.
- Şahin, M., Ulucay V., and Menekşe, M., (2017). (α,β,ϒ) Interval Cut Set Of Interval Valued Neutrosophic Sets, International Conference on Mathematics and Mathematics Education (ICMME-2017), Harran University, Şanlıurfa, 11-13 May 2017
- Şahin, R. (2017). Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Computing and Applications, 28(5), 1177-1187
- Tian, Z. P., Zhang, H. Y., Wang, J., Wang, J. Q., & Chen, X. H. (2016). Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. International Journal of Systems Science, 47(15), 3598-3608.
- Venkatesan, D. and Sriram, S. (2017). Multiplicative Operations of Intuitionistic Fuzzy Matrices, Annals of Pure and Applied Mathematics Vol. 14, No. 1, 2017, pp.173-181
- Venkatesan, D. and Sriram, S. (2017). Multiplicative Operations of Intuitionistic Fuzzy Matrices, Annals of Pure and Applied Mathematics Vol. 14, No. 1, 2017, pp.173-181
- Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Review of the Air Force Academy, (1), 10. pp. 410-413.
- Ye, J. (2014a). Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. Journal of Intelligent & Fuzzy Systems, 26(1), 165-172.
- Ye, J. (2014b). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 26(5), 2459-2466.
- Ye, J. (2015). Multiple attribute decision-making method based on the possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers. Journal of Intelligent & Fuzzy Systems, 28(3), 1307-1317.
- Ye, J. (2016a). Interval neutrosophic multiple attribute decision-making method with credibility information. International Journal of Fuzzy Systems, 18(5), 914-923. DOI 10.1007/s40815-015-0122-4.
- Ye, J. (2016b). Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods. SpringerPlus, 5(1), 1488.
- Zahariev, Z. (2009, November). Software package and API in MATLAB for working with fuzzy algebras. In AIP Conference Proceedings (Vol. 1184, No. 1, pp. 341-348). AIP.
- Zhang, H. Y., Wang, J. Q., & Chen, X. H. (2014). Interval neutrosophic sets and their application in multicriteria decision making problems. The Scientific World Journal, 2014. doi:10.1155/2014/645953.
A MATLAB TOOLBOX FOR INTERVAL VALUED NEUTROSOPHIC MATRICES FOR COMPUTER APPLICATIONS
Year 2017,
Volume: 1 Issue: 1, 1 - 21, 29.12.2017
Said Broumi
,
Assia Bakalı
Mohamed Talea
Florentin Smarandache
Abstract
The
concept of interval valued neutrosophic matrices is a generalized structure of
fuzzy matrices, intuitionistic fuzzy matrices, interval fuzzy matrices and
single valued neutrosophic matrices. Recently many studies have focused on
interval valued neutrosophic matrices, In this paper, a variety of operations
on interval valued neutrosophic matrices are presented using a new Matlab’
package. This package contains some essential functions which could help the
researchers to do computations on interval valued neutrosophic matrices quickly.
References
- Anand, M.C.J. and Anand, M.E.,(2015) Eigenvaluesand eigen vectors for fuzzy matrix, International Journal of Engineering Research and General Science Volume 3, Issue 1, 2015, pp.878- 890
- Bausys, R., & Zavadskas, E. K. (2015). Multıcrıterıa Decısıon Makıng Approach By Vıkor Under Interval Neutrosophıc Set Envıronment. Economic Computation & Economic Cybernetics Studies & Research, 49(4).
- Broumi, S. , M. Talea, A. Bakali, F. Smarandache, (2016). Interval Valued Neutrosophic Graphs, Critical Review, XII, 2016. pp.5-33.
- Broumi, S., A.Bakali, M.Talea, F.Smarandache, R.Verma,(2017) Computing Minimum Spanning Tree In Interval Valued Bipolar Neutrosophic Environment,International Journal of Modeling and Optimization, Vol. 7, No. 5, 2017, pp300-304.
- Broumi, S., Le Hoang, F. Smarandache, A. Bakali, M.Talea, G.Selvachandran, Kishore Kumar.P.K, Computing Operational Matrices in Neutrosophic Environments: A Matlab toolbox, submitted
- Broumi, S., Smarandache, F., Talea, M., & Bakali, A. (2016). Operations on interval valued neutrosophic graphs. Infinite Study. Graphs, chapter in book- New Trends in Neutrosophic Theory and Applications- FlorentinSmarandache and SurpatiPramanik (Editors), pp. 231-254. ISBN 978-1-59973-498-9
- Broumi, S., Talea, M., Smarandache, F., & Bakali, A. (2016, December). Decision-making method based on the interval valued neutrosophic graph. In Future Technologies Conference (FTC) (pp. 44-50). IEEE.
- C.Jaisankar, S.Arunvasan and R.Mani.,(2016) On Hessenberg of Triangular fuzzy matrices, IJSRET, V-5(12), 2016,pp.586-591
- Deli, I. (2017). Interval-valued neutrosophic soft sets and its decision making. International Journal of Machine Learning and Cybernetics, 8(2), 665-676.
- Dinagar, D. S., & Latha, K. (2013). Some types of type-2 triangular fuzzy matrices. International Journal of Pure and Applied Mathematics, 82(1), 21-32.
- Garg, H. (2016). An improved score function for ranking neutrosophic sets and its application to decision-making process. International Journal for Uncertainty Quantification, 6(5).
- Garg, H. (2017). Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment. Applied Intelligence, 1-15.
- Huang, Y. H., Wei, G. W., & Wei, C. (2017). VIKOR method for interval neutrosophic multiple attribute group decision-making. Information, 8(4), 144. doi:10.3390/info8040144
- Jaisankar, C., and Mani, R., (2017) Some Properties of Determinant of Trapezoidal Fuzzy Number Matrices, International Journal Of Modern Engineering Research, Vol. 7 ,Iss. 1 , 2017 ,pp70-78
- Karaşan, A., & Kahraman, C. (2017). Interval-Valued Neutrosophic Extension of EDAS Method. In Advances in Fuzzy Logic and Technology 2017 (pp. 343-357). Springer, Cham. DOI 10.1007/978-3-319-66824-6_3
- Karunambigai, M. G., and Kalaivani, O. K., (2016). Software development in intuitionistic Fuzzy Relational Calculus. International Journal of Scientific and research Publication, 6(7), 2016,pp.311-331.
- Ma, Y. X., Wang, J. Q., Wang, J., & Wu, X. H. (2017). An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options. Neural Computing and Applications, 28(9), 2745-2765. DOI 10.1007/s00521-016-2203-1.
- Pal, A., & Pal, M. (2010, December). Some results on interval-valued fuzzy matrices. In The 2010 International Conference on E-Business Intelligence, Org. by Tsinghua University, Kunming, China, Atlantis Press (pp. 554-559).
- Pal, M., Khan, S. K., & Shyamal, A. K. (2002). Intuitionistic fuzzy matrices. Notes on Intuitionistic fuzzy sets, 8(2), 51-62.
- Peeva, K., & Kyosev, Y. (2004) Solving problems in intuitionistic fuzzy relational calculus with fuzzy relational calculus toolbox. In Eight International Conference on IFSs, Varna (pp. 37-43).
- Pushpalatha, V.,(2017). α-Cuts Of Interval-Valued Fuzzy Matrices With Interval-Valued Fuzzy Rows And Columns, IOSR Journal of Mathematics, Volume 13, Issue 3 Ver. II ,2017, pp.55-62
- Reddy, R., Reddy, D., & Krishnaiah, G. (2016). Lean Supplier Selection based on Hybrid MCGDM Approach using Interval Valued Neutrosophic Sets: A Case Study. International Journal of Innovative Research and Development, 5(4). pp.291-296.
- Smarandache, F. (1998). Neutrosophy. neutrosophic probability, set, and logic, ProQuest information and learning. Ann Arbor, Michigan, USA, 105.
- Sun, H. X., Yang, H. X., Wu, J. Z., & Ouyang, Y. (2015). Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making. Journal of Intelligent & Fuzzy Systems, 28(6), 2443-2455.
- Şahin, M., Ulucay V., and Menekşe, M., (2017). (α,β,ϒ) Interval Cut Set Of Interval Valued Neutrosophic Sets, International Conference on Mathematics and Mathematics Education (ICMME-2017), Harran University, Şanlıurfa, 11-13 May 2017
- Şahin, R. (2017). Cross-entropy measure on interval neutrosophic sets and its applications in multicriteria decision making. Neural Computing and Applications, 28(5), 1177-1187
- Tian, Z. P., Zhang, H. Y., Wang, J., Wang, J. Q., & Chen, X. H. (2016). Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. International Journal of Systems Science, 47(15), 3598-3608.
- Venkatesan, D. and Sriram, S. (2017). Multiplicative Operations of Intuitionistic Fuzzy Matrices, Annals of Pure and Applied Mathematics Vol. 14, No. 1, 2017, pp.173-181
- Venkatesan, D. and Sriram, S. (2017). Multiplicative Operations of Intuitionistic Fuzzy Matrices, Annals of Pure and Applied Mathematics Vol. 14, No. 1, 2017, pp.173-181
- Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Review of the Air Force Academy, (1), 10. pp. 410-413.
- Ye, J. (2014a). Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making. Journal of Intelligent & Fuzzy Systems, 26(1), 165-172.
- Ye, J. (2014b). A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets. Journal of Intelligent & Fuzzy Systems, 26(5), 2459-2466.
- Ye, J. (2015). Multiple attribute decision-making method based on the possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers. Journal of Intelligent & Fuzzy Systems, 28(3), 1307-1317.
- Ye, J. (2016a). Interval neutrosophic multiple attribute decision-making method with credibility information. International Journal of Fuzzy Systems, 18(5), 914-923. DOI 10.1007/s40815-015-0122-4.
- Ye, J. (2016b). Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods. SpringerPlus, 5(1), 1488.
- Zahariev, Z. (2009, November). Software package and API in MATLAB for working with fuzzy algebras. In AIP Conference Proceedings (Vol. 1184, No. 1, pp. 341-348). AIP.
- Zhang, H. Y., Wang, J. Q., & Chen, X. H. (2014). Interval neutrosophic sets and their application in multicriteria decision making problems. The Scientific World Journal, 2014. doi:10.1155/2014/645953.