Interval-Valued Bipolar Trapezoidal Neutrosophic Number Approach in Distribution Planning Problem

Authors

  • Chhavi Jain Research Scholar, School of Business Studies, Sharda University, Greater Noida,Uttar Pradesh, India
  • R K Saini Department of Mathematical Sciences and Computer Applications, Bundelkhand University, Jhansi, Uttar Pradesh, India https://orcid.org/0000-0003-2620-774X
  • Atul Sangal School of Business Studies, Sharda University, Greater Noida, Uttar Pradesh, India
  • Ashik Ahirwar Department of Mathematical Sciences and Computer Applications, Bundelkhand University, Jhansi, Uttar Pradesh, India

Keywords:

Interval Valued Bipolar Trapezoidal Neutrosophic Number, Fully Neutrosophic Transportation Problem, Interval Valued Fuzzy Numbers

Abstract

An interval valued bipolar trapezoidal neutrosophic set [IVBTrNS] is a special neutrosophic set on the set of real numbers R, is a new generalization of bipolar fuzzy sets, neutrosophic sets, interval valued neutrosophic set, and bipolar neutrosophic sets, so that it can handle uncertain information more flexibly in the optimization. Distribution planning is a process in which we study the way to get materials and distribute the product from delivery point to the consuming point after production planning in supply chain. In the present research article, we propose concept of interval valued bipolar trapezoidal neutrosophic number [IVBTrNN] and its operations in the fully neutrosophic transportation problem [FNTP], where neutrosophic variable are required to be equal either 0 or 1. During the covid-19 pandemic, to maintain physical distance among, human, used & unused equipments and researchers, in place of crisp numbers, the interval-valued fuzzy numbers [IVFNs] are much effective to address the uncertainty & hesitation in real world situations. To save the human lives in a covid-19 pandemic, the crisp cost, demand, and crisp supply in transportation problem are not so effective in compression of neutrosophic numbers. The use of IVBTrNN in place of crisp number, are more suitable to distribute the necessary equipments, medicines, food products, and other relevant items from one place to another. To understand the practical applications of interval-valued neutrosophic numbers [IVNNs], a numerical of FNTP and conclusion also the part of this paper for better execution in support of our proposed result & methodology with IVBTrNNs.

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References

Hitchcock F.L., The distribution of a product from several sources to numerous localities, Journal of Mathematical Physics, 20(2), (1941), 224–230.

http://dx.doi.org/10.1002/sapm1941201224.

Zadeh L. A., “Fuzzy sets,” Information and Control, vol. 8, no. 3, (1965), 338–353.

DOI: https://doi.org/ 10.2307/2272014.

Ebrahimnejad A. and Verdegay, J.L., An efficient computational approach for solving type-2 intuitionistic fuzzy numbers based transportation problems, International Journal of Computational Intelligence Systems, 9(6), (2016), 1154– 1173., https://doi.org/10.1080/18756891.2016.1256576.

Ebrahimnejad A. and Verdegay J.L., A new approach for solving fully intuitionistic fuzzy transportation problems, Fuzzy Optimization and Decision Making, 17(4), (2018), 447–474, doi: 10.1007/s10700-017-9280-1.

Atanassov K. T., Intuitionistic fuzzy sets, Fuzzy Sets System, vol. 20, no. 1, (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3.

Atanassov K. T., Intuitionistic Fuzzy Sets: Theory and Appl., Physica, Heidelberg, Germany (1999).

https://doi.org/10.1007/978-3-7908-1870-3_1.

Chen S. M. and Han W.H., An improved MADM method using interval-valued intuitionistic fuzzy values, Information Sciences, 467 (2018), 489-505.

Roy S.K., Ebrahimnejad A., Verdegay J.L. and Das, S., New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana 43(1), 3 (2018), 1-12.https://doi.org/10.1007/s12046-017-0777-7.

Wan S. P. and Dong J. Y. Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision, Expert Systems with Applications, 31(10), (2016), 1908-1914.

Xu Z., Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Control and Decision, 22 (2) (2007), 215-219.

Goar, . V. K. ., and N. S. . Yadav. “Business Decision Making by Big Data Analytics”. International Journal on Recent and Innovation Trends in Computing and Communication, vol. 10, no. 5, May 2022, pp. 22-35, doi:10.17762/ijritcc.v10i5.5550.

Zeng S., Chen S.M. and Fan K.Y., Interval-valued intuitionistic fuzzy multiple attribute decision making based on nonlinear programming methodology and TOPSIS method, Information Sciences 506 (2020), 424-442. https://doi.org/10.1016/j.ins.2019.08.027.

Atanassov K.T., Gargov, An interval-valued intuitionistic fuzzy sets, Fuzzy Sets System, 31, (1989), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4.

Smarandache F., “Neutrosophic set, a generalization of the intuitionistic fuzzy set,” International Journal of Pure and Applied Mathematics, vol. 24, no. 3, (2005) 287–297.

Smarandache F., A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic, American Research Press, Rehoboth, NM, USA, 1998.

Garg, D. K. . (2022). Understanding the Purpose of Object Detection, Models to Detect Objects, Application Use and Benefits. International Journal on Future Revolution in Computer Science &Amp; Communication Engineering, 8(2), 01–04. https://doi.org/10.17762/ijfrcsce.v8i2.2066

Smarandache F., Neutrosophic Theory and its Applications, Collected Papers, EuropaNova, Brussels, Belgium, Vol. 1, (2014), 480 p.

Wang H, Smarandache F., Zhang Y. Q. and Sunderraman R., “Single valued neutrosophic sets,” multi-space and multi-structure, vol. 4, (2010), 410–413.

Smarandache F., Interval-Valued Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets, Int. Jl. of Science and Engg. Investi., vol. 5, issue 54, (2016), 2251-8843. https://hal.archives-ouvertes.fr/hal-01340831

Ye J. and Smarandache F., Similarity Measure of Refined Single-Valued Neutrosophic Sets and Its Multicriteria Decision Making, Neutrosophic Sets and Systems, Vol. 12, (2016), 41-44.

Bharati S.K. and Singh S.R., A new interval-valued intuitionistic fuzzy numbers: ranking methodology and application, New Mathematics and Natural Computation, 14(03), (2018), 363–381.

https://doi.org/10.1142/S1793005718500229

Chen S. M. and Huang Z.C., Multiattribute decision making based on interval-valued intuitionistic fuzzy values and linear programming methodology, Information Sciences, 381 (2017) 341-351. https://doi.org/10.1016/j.ins.2016.11.010

Kour D., Mukherjee S. and Basu K., Solving intuitionistic fuzzy transportation problem using linear programming, Int. Jl. of Syst. Assurance Engg. and Management, 8(2), (2017), 1090–1101. DOI: 10.1007/s13198-017-0575-y

Khatter K., Neutrosophic linear programming using possibilistic mean, Soft Computing 24 (22), (2020), 16847-16867.https://doi.org/10.1007/s00500-020-04980-y

Rani D., Gulati T.R. and Garg H., Multi-objective non-linear programming problem in intuitionistic fuzzy environment, Expert Systems with Applications, 64, (2016), 228–238.https://doi.org/10.1016/j.eswa.2016.07.034

Yu V. F., Hu K.-J and Chang A.-Y, An interactive approach for the multi-objective transportation problem with interval parameters, Inter. Journal of Production Res., Vol. 53, no. 4, (2015), 1051–1064.

https://doi.org/10.1080/00207543.2014.939236

Kose, O., & Oktay, T. (2022). Hexarotor Yaw Flight Control with SPSA, PID Algorithm and Morphing. International Journal of Intelligent Systems and Applications in Engineering, 10(2), 216–221. Retrieved from https://ijisae.org/index.php/IJISAE/article/view/1879

Zimmerman H.J., Fuzzy programming and linear programming with several objective functions. Fuzzy Sets System, 1, (1978), 45–55. https://doi.org/10.1016/0165-0114(78)90031-3

Lee K. M., Bipolar-valued fuzzy sets and their operations. Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand (2000), 307-312.

Bosc P. and Pivert O., On a fuzzy bipolar relational algebra, Information Sciences, 219 (2013) 1–16. DOI:10.1016/j.ins.2012.07.018

Chen J., Li, S., Ma S. and Wang X., bi-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets, The Scientific World Journal, (2014) http://dx.doi.org/ 10.1155/2014/416530.

Deli I. “Interval-valued neutrosophic soft sets and its decision making, International Journal of Machine Learning and Cybernetics, volume 8, (2017), 665–676.

DOI: 10.1007/s13042-015-0461-3.

Kang M. K. and Kang J. G., Bipolar fuzzy set theory applied to sub semi groups with operators in semi groups. J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 19/1 (2012) 23-35. doi.org/10.7468/jksmeb.2012.19.1.23

Lee K. J., Bipolar fuzzy sub algebras and bipolar fuzzy ideals of BCK/BCI-algebras, Bull. Malays. Math. Sci. Soc., 32/3 (2009) 361-373, www.springer.com/journal/40840.

Manemaran S. K. and Chellappa B., Structures on Bipolar Fuzzy Groups and Bipolar Fuzzy D-Ideals under (T, S) Norms, International Journal of Computer Applications, 9/12, 7-10, doi=10.1.1.206.4101

André Sanches Fonseca Sobrinho. (2020). An Embedded Systems Remote Course. Journal of Online Engineering Education, 11(2), 01–07. Retrieved from http://onlineengineeringeducation.com/index.php/joee/article/view/39

Ye J., Vector Similarity Measures of Simplified Neutrosophic Sets and Their Application in Multi-criteria Decision Making, International Journal of Fuzzy Systems, 16/2 (2014) 204-211, ijfs16-2-r-8-20140604145108_v2.pdf

Zhou M. and Li S., Application of Bipolar Fuzzy Sets in Semi rings, Journal of Mathematical Research with Applications, Vol. 34/ 1 (2014) 61-72.

Deli I, Ali M. and Smarandache F., Bipolar Neutrosophic Sets and Their Application Based on Multi-Criteria Decision Making Problems, Proceedings of the 2015 International Conference on Advanced Mechatronic Systems, 22-24 August, 2015, Beijing, China. DOI:10.5281/zenodo.49119

Deli I., Subas Y., Smarandache F. and Ali M., Interval Valued Bipolar Fuzzy Weighted Neutrosophic Sets and Their Application, 2016 IEEE International Conference on Fuzzy Systems (FUZZ), 2460-2467.

IVBTrNN

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Published

01.10.2022

How to Cite

Jain, C. ., Saini, R. K. ., Sangal, A. ., & Ahirwar, A. . (2022). Interval-Valued Bipolar Trapezoidal Neutrosophic Number Approach in Distribution Planning Problem. International Journal of Intelligent Systems and Applications in Engineering, 10(3), 390–402. Retrieved from https://ijisae.org/index.php/IJISAE/article/view/2180

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Research Article