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COMPUTATION OF SHORTEST PATH PROBLEM IN A NETWORK WITH SV-TRIANGULAR NEUTROSOPHIC NUMBERS

Year 2019, Volume 3, Issue 2, 41 - 51, 29.12.2019
https://doi.org/10.33461/uybisbbd.588290

Abstract

In this article, we present an algorithm method for finding the shortest path length between a paired nodes on a network where  the edge weights are characterized by single valued triangular neutrosophic numbers. The proposed algorithm gives the shortest path length from source node to destination node based on a ranking method. Finally, a numerical example is also presented to illustrate the efficiency of the proposed approach.

References

  • Abdel-Baset M., Chang V., & Gamal A. (2019). “Evaluation of the green supply chain management practices: A novel neutrosophic approach”. Computers in Industry 108, 210-220
  • Abdel-Basset M., Saleh M., Gamal A., & Smarandache F. (2019a).”An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number”. Applied Soft Computing 77, 438-452.
  • Anuuya V.and Sathya R. (2013). “Shortest Path with Complement of Type -2 Fuzzy Number”. Malya Journal of Matematik, S(1), 71-76.
  • Atanassov K. (1986). “Intuitionistic Fuzzy Sets”. Fuzzy Sets and Systems 20, 87-96.
  • Atanassov K. and Gargov G. (1989). “Interval Valued Intuitionisitic Fuzzy Sets”. Fuzzy Sets and Systems 31, 343-349.
  • Biswas P., Parmanik S. and Giri B. C. (2014). “Cosine Similarity Measure Based Multi-attribute Decision- Making With Trapezoidal Fuzzy Neutrosophic Numbers”.Neutrosophic sets and systems 8, 47-57.
  • Broumi S. and Talea M. and Bakali A. and Smarandache F. and Khan M. (2017). “A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited”. International Journal of New Computer Architectures and their Applications (IJNCAA) 7(3), 89-94
  • Broumi S. , Talea M., Bakali A. , Smarandache F. , Nagarajan D., Lathamaheswari M. and Parimala M. (2019e). “Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview”. Complex & Intelligent Systems , ,1-8, https://doi.org/10.1007/s40747-019-0098-z
  • Broumi S., Bakali A., Talea M., Smarandache F., Ali M. (2016f). “Shortest Path Problem Under Bipolar Neutrosophic Setting”.Applied Mechanics and Materials 859, 59-66
  • Broumi S., A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari and Ranjan Kumar (2019d), “Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment”.Complex & Intelligent Systems ,1-8, https://doi.org/10.1007/s40747-019-0101-8,
  • Broumi S., Bakali A., Talea M. and Smarandache F. (2016b). “Isolated Single Valued Neutrosophic Graphs”. Neutrosophic Sets and Systems 11, 74-78.
  • Broumi S., Bakali A., Talea M. and Smarandache F., “Shortest Path Problem on Single Valued Neutrosophic Graphs”, 2017 International Symposium on Networks, Computers and Communications (ISNCC): Wireless and Mobile Communications and Networking - Wireless and Mobile Communications and Networking, 978-1-5090-4260-9/17/$31.00 ©2017 IEEE .
  • Broumi S., Bakali A., Talea M. and Smarandache F., Şahin R., Krishnan Kishore K. P., (2019a).”Shortest Path Problem Under Interval Valued Neutrosophic Setting” .International Journal of Advanced Trends in Computer Science and Engineering 8, No.1.1, 216-222.
  • Broumi S., Bakali A., Talea M., Smarandache F. (2017a). “A Matlab Toolbox for interval valued neutrosophic matrices for computer applications”. Uluslararası Yönetim Bilişim Sistemlerive Bilgisayar Bilimleri Dergisi, 1(1),1-21
  • Broumi S., Bakali A., Talea M., Smarandache F., and Singh P. K.(2019b). “Properties of Interval-Valued Neutrosophic Graphs”, in :C. Kahraman and ˙ I. Otay (eds.), Fuzzy Multicriteria Decision MakingUsingNeutrosophic Sets, Studies in Fuzziness and Soft Computing 369,https://doi.org/10.1007/978-3-030-00045-5_8
  • Broumi S., Bakali A., Talea M., Smarandache F., Uluçay V., Sahin M., Dey A., Dhar M., Tan R.P., Bahnasse A., Pramanik S. (2018). “Neutrosophic Sets: An Overview”, In book: New Trends in Neutrosophic Theory and Applications, Edition: Volume 2, Publisher: pons edition, Editors: FlorentinSmarandache, SurapatiPramanik, 403-434
  • Broumi S., Nagarajan D. , Bakali A. , Talea M. , Smarandache F. , Lathamaheswari M.(2019f).”The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment”. Complex & Intelligent Systems,1-12, https://doi.org/10.1007/s40747-019-0092-5.
  • Broumi S., Smarandache F., Talea M. and Bakali A. (2016b).”An Introduction to Bipolar Single Valued Neutrosophic Graph Theory”. Applied Mechanics and Materials 841, 184-191.
  • Broumi S., Smarandache F., Talea M. and Bakali A. (2016d). “Decision-Making Method Based On the Interval Valued Neutrosophic Graph”. Future Technologie, IEEE, 44-50.
  • Broumi S., Son L.H., Bakali A., Talea M., Smarandache F., Selvachandran G. (2017b). “Computing Operational Matrices in Neutrosophic Environments: A Matlab Toolbox”.Neutrosophic Sets and Systems18, 58-66
  • Broumi S., Talea M., Bakali A. and Smarandache F. (2016a).On Bipolar Single Valued Neutrosophic Graphs”.Journal Of New Theory 11, 84-102.
  • Broumi S., Talea M., Bakali A., Smarandache F. (2016). “Single Valued Neutrosophic Graphs. Journal of New Theory 10, 86-101.
  • Broumi S., Talea M., Bakali A., Singh P. K., Smarandache F. (2019c). “Energy and Spectrum Analysis of Interval Valued Neutrosophic Graph using MATLAB”. Neutrosophic Sets and Systems 24, 46-60.
  • Broumi S., Talea M., Smarandache F. and Bakali A.(2016e).”Single Valued Neutrosophic Graphs: Degree, Order and Size”. IEEE International Conference on Fuzzy Systems (FUZZ), 2444-2451.
  • Deli I. and Subas Y. (2016). “A Ranking methods of single valued neutrosophic numbers and its application to multi-attribute decision making problems”. International Journal of Machine Learning and Cybernetics, 1-14. http://fs.gallup.unm.edu/NSS.
  • Jayagowri P. and Ramani G.G(2014). “Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network”, Volume 2014. Advances in Fuzzy Systems, 6 pages.
  • Kumar A. and Kaur M. (2011a). “Solution of fuzzy maximal flow problems using fuzzy linear programming”. World Academy of Science and Technology87, 28-31.
  • Kumar A. and Kaur M. (2011). “A New Algorithm for Solving Shortest Path Problem on a Network with Imprecise Edge Weight”. Applications and Applied Mathematics 6( 2), 602-619.
  • Majumdaer S. and Pal A. (2013). “Shortest Path Problem on Intuitionistic Fuzzy Network”. Annals of Pure and Applied Mathematics 5, No.1, 26-36.
  • Nagarajan D., Lathamaheswari M., Broumi S., Kavikumar J. (2019). “A new perspective on traffic control management using triangular interval type-2 fuzzy sets and interval neutrosophic sets”. Operations Research Perspectives, https://doi.org/10.1016/j.orp.2019.100099.
  • Porchelvi R. S. and Sudha G. (2013). “A modified a algorithm for solving shortest path problem with intuitionistic fuzzy arc length”.International Journal and Engineering Research 4,issue 10, 884-847.
  • Smarandache F. (2005). A unifying field in logic. Neutrosophy: Neutrosophic probability, set, logic, American Research Press, Rehoboth, fourth edition,
  • Smarandache F., Neutrosophic set- a generalization of the intuitionistic fuzzy set, Granular Computing. 2006 IEEE International Conference, 2006, 38-42.
  • Smarandache F., (2015a) “symbolic Neutrosophic Theory”, Europanova asbl, Brussels, , 195p.
  • Smarandache F., “Types of Neutrosophic Graphs and neutrosophic Algebraic Structures together with their Applications in Technology,” seminar, Universitatea Transilvania din
  • Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania 06 June 2015
  • Subas Y., “Neutrosophic numbers and their application to multi-attribute decision making problems”,( in Turkish) ( master Thesis, 7 Aralk university. Graduate School of Natural and Applied Science, 2015.
  • ŞAHİN R., Peide Liu, “Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information”, Neural Computing and Applications
  • Turksen I., “Interval Valued Fuzzy Sets based on Normal Forms”. Fuzzy Sets and Systems20, 191-210.
  • Wang H., Smarandache F., Zhang Y.and Sunderraman R. (2010). “Single Valued Neutrosophic Sets”. Multispace and Multisrtucture 4, pp.410-413.
  • Zadeh L. (1965). “Fuzzy Sets”. Information and Control 8, 338-353.

COMPUTATION OF SHORTEST PATH PROBLEM IN A NETWORK WITH SV-TRIANGULAR NEUTROSOPHIC NUMBERS

Year 2019, Volume 3, Issue 2, 41 - 51, 29.12.2019
https://doi.org/10.33461/uybisbbd.588290

Abstract

In this article, we present an algorithm method for finding the shortest path length between a paired nodes on a network where  the edge weights are characterized by single valued triangular neutrosophic numbers. The proposed algorithm gives the shortest path length from source node to destination node based on a ranking method. Finally, a numerical example is also presented to illustrate the efficiency of the proposed approach.

References

  • Abdel-Baset M., Chang V., & Gamal A. (2019). “Evaluation of the green supply chain management practices: A novel neutrosophic approach”. Computers in Industry 108, 210-220
  • Abdel-Basset M., Saleh M., Gamal A., & Smarandache F. (2019a).”An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number”. Applied Soft Computing 77, 438-452.
  • Anuuya V.and Sathya R. (2013). “Shortest Path with Complement of Type -2 Fuzzy Number”. Malya Journal of Matematik, S(1), 71-76.
  • Atanassov K. (1986). “Intuitionistic Fuzzy Sets”. Fuzzy Sets and Systems 20, 87-96.
  • Atanassov K. and Gargov G. (1989). “Interval Valued Intuitionisitic Fuzzy Sets”. Fuzzy Sets and Systems 31, 343-349.
  • Biswas P., Parmanik S. and Giri B. C. (2014). “Cosine Similarity Measure Based Multi-attribute Decision- Making With Trapezoidal Fuzzy Neutrosophic Numbers”.Neutrosophic sets and systems 8, 47-57.
  • Broumi S. and Talea M. and Bakali A. and Smarandache F. and Khan M. (2017). “A Bipolar Single Valued Neutrosophic Isolated Graphs: Revisited”. International Journal of New Computer Architectures and their Applications (IJNCAA) 7(3), 89-94
  • Broumi S. , Talea M., Bakali A. , Smarandache F. , Nagarajan D., Lathamaheswari M. and Parimala M. (2019e). “Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview”. Complex & Intelligent Systems , ,1-8, https://doi.org/10.1007/s40747-019-0098-z
  • Broumi S., Bakali A., Talea M., Smarandache F., Ali M. (2016f). “Shortest Path Problem Under Bipolar Neutrosophic Setting”.Applied Mechanics and Materials 859, 59-66
  • Broumi S., A. Dey, M. Talea, A. Bakali, F. Smarandache, D. Nagarajan, M. Lathamaheswari and Ranjan Kumar (2019d), “Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment”.Complex & Intelligent Systems ,1-8, https://doi.org/10.1007/s40747-019-0101-8,
  • Broumi S., Bakali A., Talea M. and Smarandache F. (2016b). “Isolated Single Valued Neutrosophic Graphs”. Neutrosophic Sets and Systems 11, 74-78.
  • Broumi S., Bakali A., Talea M. and Smarandache F., “Shortest Path Problem on Single Valued Neutrosophic Graphs”, 2017 International Symposium on Networks, Computers and Communications (ISNCC): Wireless and Mobile Communications and Networking - Wireless and Mobile Communications and Networking, 978-1-5090-4260-9/17/$31.00 ©2017 IEEE .
  • Broumi S., Bakali A., Talea M. and Smarandache F., Şahin R., Krishnan Kishore K. P., (2019a).”Shortest Path Problem Under Interval Valued Neutrosophic Setting” .International Journal of Advanced Trends in Computer Science and Engineering 8, No.1.1, 216-222.
  • Broumi S., Bakali A., Talea M., Smarandache F. (2017a). “A Matlab Toolbox for interval valued neutrosophic matrices for computer applications”. Uluslararası Yönetim Bilişim Sistemlerive Bilgisayar Bilimleri Dergisi, 1(1),1-21
  • Broumi S., Bakali A., Talea M., Smarandache F., and Singh P. K.(2019b). “Properties of Interval-Valued Neutrosophic Graphs”, in :C. Kahraman and ˙ I. Otay (eds.), Fuzzy Multicriteria Decision MakingUsingNeutrosophic Sets, Studies in Fuzziness and Soft Computing 369,https://doi.org/10.1007/978-3-030-00045-5_8
  • Broumi S., Bakali A., Talea M., Smarandache F., Uluçay V., Sahin M., Dey A., Dhar M., Tan R.P., Bahnasse A., Pramanik S. (2018). “Neutrosophic Sets: An Overview”, In book: New Trends in Neutrosophic Theory and Applications, Edition: Volume 2, Publisher: pons edition, Editors: FlorentinSmarandache, SurapatiPramanik, 403-434
  • Broumi S., Nagarajan D. , Bakali A. , Talea M. , Smarandache F. , Lathamaheswari M.(2019f).”The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment”. Complex & Intelligent Systems,1-12, https://doi.org/10.1007/s40747-019-0092-5.
  • Broumi S., Smarandache F., Talea M. and Bakali A. (2016b).”An Introduction to Bipolar Single Valued Neutrosophic Graph Theory”. Applied Mechanics and Materials 841, 184-191.
  • Broumi S., Smarandache F., Talea M. and Bakali A. (2016d). “Decision-Making Method Based On the Interval Valued Neutrosophic Graph”. Future Technologie, IEEE, 44-50.
  • Broumi S., Son L.H., Bakali A., Talea M., Smarandache F., Selvachandran G. (2017b). “Computing Operational Matrices in Neutrosophic Environments: A Matlab Toolbox”.Neutrosophic Sets and Systems18, 58-66
  • Broumi S., Talea M., Bakali A. and Smarandache F. (2016a).On Bipolar Single Valued Neutrosophic Graphs”.Journal Of New Theory 11, 84-102.
  • Broumi S., Talea M., Bakali A., Smarandache F. (2016). “Single Valued Neutrosophic Graphs. Journal of New Theory 10, 86-101.
  • Broumi S., Talea M., Bakali A., Singh P. K., Smarandache F. (2019c). “Energy and Spectrum Analysis of Interval Valued Neutrosophic Graph using MATLAB”. Neutrosophic Sets and Systems 24, 46-60.
  • Broumi S., Talea M., Smarandache F. and Bakali A.(2016e).”Single Valued Neutrosophic Graphs: Degree, Order and Size”. IEEE International Conference on Fuzzy Systems (FUZZ), 2444-2451.
  • Deli I. and Subas Y. (2016). “A Ranking methods of single valued neutrosophic numbers and its application to multi-attribute decision making problems”. International Journal of Machine Learning and Cybernetics, 1-14. http://fs.gallup.unm.edu/NSS.
  • Jayagowri P. and Ramani G.G(2014). “Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network”, Volume 2014. Advances in Fuzzy Systems, 6 pages.
  • Kumar A. and Kaur M. (2011a). “Solution of fuzzy maximal flow problems using fuzzy linear programming”. World Academy of Science and Technology87, 28-31.
  • Kumar A. and Kaur M. (2011). “A New Algorithm for Solving Shortest Path Problem on a Network with Imprecise Edge Weight”. Applications and Applied Mathematics 6( 2), 602-619.
  • Majumdaer S. and Pal A. (2013). “Shortest Path Problem on Intuitionistic Fuzzy Network”. Annals of Pure and Applied Mathematics 5, No.1, 26-36.
  • Nagarajan D., Lathamaheswari M., Broumi S., Kavikumar J. (2019). “A new perspective on traffic control management using triangular interval type-2 fuzzy sets and interval neutrosophic sets”. Operations Research Perspectives, https://doi.org/10.1016/j.orp.2019.100099.
  • Porchelvi R. S. and Sudha G. (2013). “A modified a algorithm for solving shortest path problem with intuitionistic fuzzy arc length”.International Journal and Engineering Research 4,issue 10, 884-847.
  • Smarandache F. (2005). A unifying field in logic. Neutrosophy: Neutrosophic probability, set, logic, American Research Press, Rehoboth, fourth edition,
  • Smarandache F., Neutrosophic set- a generalization of the intuitionistic fuzzy set, Granular Computing. 2006 IEEE International Conference, 2006, 38-42.
  • Smarandache F., (2015a) “symbolic Neutrosophic Theory”, Europanova asbl, Brussels, , 195p.
  • Smarandache F., “Types of Neutrosophic Graphs and neutrosophic Algebraic Structures together with their Applications in Technology,” seminar, Universitatea Transilvania din
  • Brasov, Facultatea de Design de Produs si Mediu, Brasov, Romania 06 June 2015
  • Subas Y., “Neutrosophic numbers and their application to multi-attribute decision making problems”,( in Turkish) ( master Thesis, 7 Aralk university. Graduate School of Natural and Applied Science, 2015.
  • ŞAHİN R., Peide Liu, “Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information”, Neural Computing and Applications
  • Turksen I., “Interval Valued Fuzzy Sets based on Normal Forms”. Fuzzy Sets and Systems20, 191-210.
  • Wang H., Smarandache F., Zhang Y.and Sunderraman R. (2010). “Single Valued Neutrosophic Sets”. Multispace and Multisrtucture 4, pp.410-413.
  • Zadeh L. (1965). “Fuzzy Sets”. Information and Control 8, 338-353.

Details

Primary Language English
Subjects Computer Science, Artifical Intelligence, Engineering, Multidisciplinary
Journal Section Articles
Authors

Said BROUMİ>

0000-0001-8099-9413
Türkiye


Assia BAKALİ This is me

0000-0001-8099-9413


Mohamed TALEA This is me

0000-0001-8099-9413


Florentin SMARANDACHE>

0000-0001-8099-9413

Publication Date December 29, 2019
Published in Issue Year 2019, Volume 3, Issue 2

Cite

APA Broumi, S. , Bakali, A. , Talea, M. & Smarandache, F. (2019). COMPUTATION OF SHORTEST PATH PROBLEM IN A NETWORK WITH SV-TRIANGULAR NEUTROSOPHIC NUMBERS . Uluslararası Yönetim Bilişim Sistemleri ve Bilgisayar Bilimleri Dergisi , 3 (2) , 41-51 . DOI: 10.33461/uybisbbd.588290