Volume 6 • Issue 1 • PP: 21-28 • 2023
Neutrosophic Pythagorean Fuzzy Shortest Path in a Network
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© 2023 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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We began a novel technique to dealing with the Neutrosophic Pythagorean shortest route problem in a network in this paper by representing each edge weight as a triangular fuzzy Pythagorean number with dependent Neutrosophic components and Pythagorean fuzzy graph condition.0≤μ_1 (v_i^' )^2+β_1 (v_i^' )^2+σ_1 (v_i^' )^2≤2. The main purpose of this article is to show how to use Neutrosophic Pythagorean fuzzy graphs. As a result, we created the proposed method, which also delivers the shortest path length from the source node (SN) to the destination node by using a ranking function for the Neutrosophic Pythagorean fuzzy Triangular number. Finally, an illustrative instance is supplied for validation.
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References
[1] Nagoor Gani, M. Mohammed Jabarulla, On Searching Intuitionistic Fuzzy Shortest path in a Network, Applied Mathematical Sciences, Vol.4, no.69,3447-3454, 2010.
[2] D. Ajay, P. Chellamani, International Journal of Neutrosophic Science, Vol 11, No. 2, PP. 108 – 114, 2020.
[3] Deng Y, Chen Y, Zhang Y, Mahadevan S, Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment. Appl Soft Comput: 12:1231–1237, 2012.
[4] F. Smarandache, “A geometric interpretation of the neutrosophic set — A generalization of the intuitionistic fuzzy set,” Granular Computing, IEEE International Conference, pp.602 – 606, 2011.
[5] Geetharamani G, Jayagowri P, Using similarity degree approach for shortest path in Intuitionistic fuzzy network, In: International conference on computing, communication and applications (ICCCA), IEEE, Dindigul, Tamilnadu, India, pp 1–6, 2012.
[6] H. Garg (ed.), (2021). Pythagorean Fuzzy Sets, Theory and Applications, under exclusive license to Springer Nature Singapore Ptr Ltd.
[7] K.T. Atanassov (2019). Intuitionistic Fuzzy Sets, Springer.
[8] Karunambigai MG, Ranagasmy P, Atanassov K, Palaniappan N, an intuitionistic fuzzy graph method for finding the shortest paths in networks. Advances in soft Computing: 42:3 – 10, 2007.
[9] Keshavarz E, Khorram E, A fuzzy shortest path with the highest reliability. J Comput Appl Math: 230:204–212, 2009.
[10] Kumar A., Kaur M, A new algorithm for solving network flow with fuzzy arc lenths. An official Journal of Turkish Fuzzy systems Association: 2(1); 1 – 13, 2011.
[11] L.A. Zadeh, Fuzzy Sets, Information and Control 8(3), 338-353, 1965.
[12] Lazim Abdullah, Pinxin Goh, Decision making method based on Pythagorean fuzzy sets and its application to solid waste management, Complex and Intelligent System, 5:185-198, 2019.
[13] L. Sujatha, Hyacinta JD, The Shortest Path Problem on Networks with Intuitionistic Fuzzy Edge Weights, Global Journal of Pure and Applied Mathematics, Vol 13, No.7, PP. 3285-3300, 2017.
[14] M. Muhammad Akram, Farwa Ilyasa and Arsham Borumand Saeid, Certain Notions of Pythagorean Fuzzy Graphs, Journal of Intelligent and Fuzzy Systems 36, 5857-5874, 2019.
[15] M. Muhammad Akram, W.A. Dudek, F Ilyas (2019). Group decision-making based on Pythagorean fuzzy TOPSIS method. International Journal of Intelligent system.
[16] Okada S, Fuzzy Shortest path problems incorporating among paths. Fuzzy sets and Systems: 142:335 – 357, 2004.
[17] P. Jayagowri and G. Geetha Ramani, (2014). Using Trapezoidal Intuitionistic Fuzzy Number to Find Optimized Path in a Network, Hindawi Publishing Corporation, Advances in Fuzzy Systems, Article ID 183607.
[18] P. Biswas, S. Pramanik and B. C. Giri, Aggregation of Triangular Fuzzy Neutrosophic Set Information and its Application to Multiattribute Decision Making, Neutrosophic sets and systems, 12, pp.20-40, 2016.
[19] R.R. Yager, Pythagorean fuzzy subsets, In: Proc Joint IFSA world congress and NAFIPS Annual Meeting, Edmonton, Canada, PP.57-61, 2013.
[20] R.R. Yager, Pythagorean membership grades in decision making, IEEE Transactions on Fuzzy Systems 22(4), 958-965, 2014.
[21] S. Broumi, A. Bakali, M. Talea, F. Smarandache and L. Vladareanu, Shortest path problem under triangular fuzzy neutrosophic information, 10th International Conference on software, Knowledge, Information Management & Applications, PP. 169 – 174, 2016.
[22] S. Broumi, M. Talea, A. Bakali, F. Smarandache, “On Bipolar Single Valued Neutrosophic Graphs,” Journal of New Theory, N11, pp.84-102, 2016.
[23] S. Broumi, F. Smarandache, M. Talea and A. Bakali, An Introduction to Bipolar Single Valued Neutrosophic Graph Theory. Applied Mechanics and Materials, vol.841, 184-191, 2016.
[24] S. Broumi, M. Talea, A. Bakali, F. Smarandache, “Single Valued Neutrosophic Graphs,” Journal of New Theory, N 10, pp. 86-101, 2016.
[25] S. Broumi, M. Talea, F. Smarandache and A. Bakali, Single Valued Neutrosophic Graphs: Degree, Order and Size. IEEE World Congress on Computational Intelligence, 2016, pp.2444-2451, 2016.
[26] S. Broumi, A. Bakali, M, Talea, and F, Smarandache, Isolated Single Valued Neutrosophic Graphs. Neutrosophic Sets and Systems, Vol. 11, pp.74-78, 2016.
[27] Sujatha L, Hyacinta JD, The SPP on Networks with Intui Fuzzy Edge Weights, Global Journal of Pure and Applied Mathematics: Vol 13, No.7, PP. 3285-3300, 2017.
[28] X. Zhang and Z. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, International Journal of Intelligent Systems 29(12), 1061-1078, 2014.
[29] Xin Zhang, Peide Liu, Method for Aggregating Triangular Fuzzy Intuitionistic Fuzzy Information and its Application to Decision Making, Baltic Journal on Sustainability, 16(2); 280-290, 2010.
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