Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

S Samuel Nirmalsingh; P John Robinson

doi:10.17485/IJST/v16iSP3.icrtam297

Article

Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

VIEWS 250
PDF 71

Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16iSP3.icrtam297

Year: 2023, Volume: 16, Issue: Special Issue 3, Pages: 75-83

Original Article

Triangular Intuitionistic Fuzzy Linear Programming Problem with a New Ranking Method based on Correlation Coefficient

S Samuel Nirmalsingh^1*, P John Robinson¹

¹PG and Research Department of Mathematics, Bishop Heber College, Affiliated to Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:06 February 2023, Accepted Date:11 August 2023, Published Date:04 December 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The study discusses solving Triangular Intuitionistic Fuzzy Linear Programming Problem (TIFLPP) with triangular intuitionistic fuzzy coefficients and variables using triangular intuitionistic fuzzy simplex method. Method: The triangular intuitionistic fuzzy information given for the linear programming problem is preserved and not converted to crisp values while solving the problem which will represent the complete information of the decision problem. Findings: Several definitions and theorems are given to justify the stability of the triangular intuitionistic fuzzy simplex method. In addition to the existing ratio ranking method for finding the minimum ratio a new method of correlation coefficient is proposed for finding the minimum ratio in the simplex method. The procedure of the simplex method is explained through a numerical illustration. Novelty: The proposed new correlation coefficient of triangular intuitionistic fuzzy with graded mean integration representation and triangular intuitionistic fuzzy simplex method with defuzzification method are compared and suggestions are given based on the results obtained.

Keywords: Triangular Intuitionistic Fuzzy Sets, Linear Programming Problem, Ratio Ranking, Intuitionistic Fuzzy Simplex Method, Correlation Coefficient of Triangular Intuitionistic Fuzzy Sets 1

References

Pérez-Cañedo B, Concepción-Morales ER. On LR-type fully intuitionistic fuzzy linear programming with inequality constraints: Solutions with unique optimal values. Expert Systems with Applications. 2019;128:246–255. Available from: https://doi.org/10.1016/j.eswa.2019.03.035
Jayalakshmi M, Anuradha D, Sujatha V, Deepa G. A simple mathematical approach to solve intuitionistic fuzzy linear programming problems. In: Recent Trends in Pure and Applied Mathematics, AIP Conference Proceedings. Vellore, India, 13–15 December 2018. AIP Publishing. 2177:20025–20026.
Kabiraj A, Nayak PK, Raha S. Solving Intuitionistic Fuzzy Linear Programming Problem—II. International Journal of Intelligence Science. 2019;9(4):93–110. Available from: https://www.scirp.org/journal/paperinformation.aspx?paperid=95264
Mohan S, Kannusamy AP, Sidhu SK. Solution of intuitionistic fuzzy linear programming problem by dual simplex algorithm and sensitivity analysis. Computational Intelligence. 2021;37(2):852–872. Available from: https://doi.org/10.1111/coin.12435
Kousar S, Zafar A, Kausar N, Pamucar D, Kattel P. Fruit Production Planning in Semiarid Zones: A Novel Triangular Intuitionistic Fuzzy Linear Programming Approach. Mathematical Problems in Engineering. 2022;2022:1–13. Available from: https://doi.org/10.1155/2022/3705244
Abinaya B, Amirtharaj ECH. Application of Multiple Attribute Group Decision Making to Solve Fuzzy Time Cost Trade off Problems. Journal of Algebraic Statistics. 2022;13(2):153–163. Available from: https://doi.org/10.52783/jas.v13i2.150
Augustine EP. Novel Correlation Coefficient for Intuitionistic Fuzzy Sets and Its Application to Multi-Criteria Decision-Making Problems. International Journal of Fuzzy System Applications. 2021;10(2):39–58. Available from: https://doi.org/10.4018/IJFSA.2021040103
Li P, Ji Y, Wu Z, Qu SJJ. A New Multi-Attribute Emergency Decision-Making Algorithm Based on Intuitionistic Fuzzy Cross-Entropy and Comprehensive Grey Correlation Analysis. Entropy. 2020;22(7):1–21. Available from: https://doi.org/10.3390/e22070768
Robinson PJ, Li DF, Nirmalsingh SS. An Automated Decision Support Systems Miner for Intuitionistic Trapezoidal Fuzzy Multiple Attribute Group Decision-Making Modeling with Constraint Matrix Games. In: Artificial Intelligence and Technologies, Lecture Notes in Electrical Engineering . (Vol. 806, pp. 343-351) Singapore. Springer . 2021.
Li DF. A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Computers & Mathematics with Applications. 2010;60(6):1557–1570. Available from: https://doi.org/10.1016/j.camwa.2010.06.039

Copyright

© 2023 Nirmalsingh & Robinson. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)