Analysis the Barrier of E-Learning in Mathematics Using Type-2 Fuzzy Data

Authors

  • Rahul Kar Springdale high school, Kalyani, India Author
  • Ashok Kumar Shaw Regent Education and Research Foundation, Kolkata Author

DOI:

https://doi.org/10.37303/jelmar.v1i2.73

Keywords:

Triangular intuitionistic Type 2 fuzzy number (TIT2FN), System reliability, Parallel system, Series system, e-learning, e-learning mathematics

Abstract

E-Learning is mean to learn all round educational subjects taking assist of modern technology of the online. E-learning is also a big platform to learn mathematics. But in the current public health crisis, we are all working quickly to move our classes out of the classroom. Fortunately, even if online teaching and learning are new to all of us, some uncertainties are there exists. According to modern view uncertainty is considered essential to science and technology, it is not only the unavoidable plague but also it has impact a great utility. Generally, fuzzy sets are used to analyse fuzzy system reliability. To analyse the fuzzy system reliability, the reliability of each component of the system is considered as a Triangular intuitionistic Type 2 fuzzy number (TIT2FN).

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References

Alefeld, G., & Herzberger, J. (1983). Introduction to interval computation. Academic Press.

Cai, K. Y., & Wen, C. Y. (1990). Street-lighting lamps replacement: A fuzzy viewpoint. Fuzzy Sets and Systems, 37, 161–172.

Cai, K. Y., Wen, C. Y., & Zhang, M. L. (1991). Fuzzy reliability modelling of gracefully degradable computing systems. Reliability Engineering and System Safety, 33, 141–157.

Cai, K. Y., Wen, C. Y., & Zhang, M. L. (1991). Survival index for CCNs: A measure of fuzzy reliability computing systems. Reliability Engineering and System Safety, 33, 141–157.

Chakraborty, A., Mondal, S. P., Ahmadian, A., Senu, N., Alam, S., & Salahshour, S. (2018). Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications. Symmetry, 10(8), 327.

Chakraborty, A., Mondal, S. P., Alam, S., Ahmadian, A., Senu, N., De, D., & Salahshour, S. (2019). Disjunctive representation of triangular bipolar neutrosophic numbers, de-bipolarization technique and application in multi-criteria decision-making problems. Symmetry, 11(7), 932.

Chakraborty, A., Mondal, S. P., Alam, S., Ahmadian, A., Senu, N., De, D., & Salahshour, S. (2019). The pentagonal fuzzy number: Its different representations, properties, ranking, defuzzification and application in game problems. Symmetry, 11(2), 248.

Chen, S. H. (1985). Operations on fuzzy numbers with function principle. Tamkang Journal of Management Sciences, 6(1), 13–26.

Chen, S. M., & Jong, W. T. (1996). Analyzing fuzzy system reliability using interval of confidence. International Journal of Information Management and Engineering, 2, 16–23.

Cheng, C. H., & Mon, D. L. (1993). Fuzzy system reliability analysis by interval of confidence. Fuzzy Sets and Systems, 56, 29–35.

Delgado, M., Verdegay, J. L., & Vila, M. A. (1989). A general model for fuzzy linear programming. Fuzzy Sets and Systems, 29, 21–29.

Dubois, D., & Prade, H. (1978). Operations of fuzzy numbers. International Journal of Systems Science, 9(6), 613–626.

Dubois, D., & Prade, H. (1980). Fuzzy sets and systems: Theory and applications. Academic Press.

Dwyer, P. S. (1951). Linear computation. Wiley.

Dwyer, P. S. (1964). Matrix inversion with the square root method. Technometrics, 6(2).

Fang, S. C., Hu, C. F., Wu, S. Y., & Wang, H. F. (1999). Linear programming with fuzzy coefficients in constraint. Computers and Mathematics with Applications, 37, 63–76.

Hansen, E. R. (1965). Interval arithmetic in matrix computations. SIAM Journal, Series B, 2(2).

Hansen, E. R. (1969). On the solutions of linear algebraic equations with interval coefficients. Linear Algebra and Its Applications, 2, 153–165.

Hansen, E. R. (1992). Global optimization using interval analysis. Marcel Dekker.

Hansen, E. R., & Smith, R. R. (1967). Interval arithmetic in matrix computation: Part II. SIAM Journal of Numerical Analysis, 4, 1–9.

Hussain, S. A. I., Mandal, U. K., & Mondal, S. P. (2018). Decision maker priority index and degree of vagueness coupled decision making method: A synergistic approach. International Journal of Fuzzy Systems, 20(5), 1551–1566.

Kar, R., & Shaw, A. K. (2018). Some arithmetic operations on trapezoidal fuzzy numbers and its application in solving linear programming problem by simplex algorithm. International Journal of Bioinformatics and Biological Sciences, 6(2), 77–86.

Kar, R., & Shaw, A. K. (2019). Some arithmetic operations on triangular fuzzy numbers and its application in solving linear programming problem by dual-simplex algorithm. World Journal of Engineering Research and Technology, 5(6), 397–404.

Kaufmann, A. (1975). Introduction to theory of fuzzy subsets (Vol. 1). Academic Press.

Kaufmann, A., & Gupta, M. M. (1985). Introduction to fuzzy arithmetic. Van Nostrand Reinhold.

Lodwick, W. A., & Jamison, K. D. (1997). Interval methods and fuzzy optimization. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5, 239–249.

Mahapatra, G. S., & Roy, T. K. (2009). Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations. Proceedings of the World Academy of Science, Engineering and Technology, 587–595.

Majumder, P., Mondal, S. P., Bera, U. K., & Maiti, M. (2016). Application of generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment. Operations Research Perspectives, 3, 77–91.

Mon, D. L., & Cheng, C. H. (1994). Fuzzy system reliability analysis for components with different membership functions. Fuzzy Sets and Systems, 64, 145–157.

Mondal, S. P. (2016). Differential equation with interval valued fuzzy number and its applications. International Journal of System Assurance Engineering and Management, 7(3), 370–386.

Mondal, S. P. (2018). Interval valued intuitionistic fuzzy number and its application in differential equation. Journal of Intelligent and Fuzzy Systems, 34(1), 677–687.

Moore, R. E. (1979). Methods and applications of interval analysis. SIAM.

Salahshour, S., Ahmadian, A., Mahata, A., Mondal, S. P., & Alam, S. (2015). The behavior of logistic equation with Allee effect in fuzzy environment: Fuzzy differential equation approach. International Journal of Applied and Computational Mathematics, 4(2), 62–71.

Shaw, A. K., & Roy, T. K. (2011). Generalized trapezoidal triangular intuitionistic fuzzy number and its application on reliability evaluation. International Journal of Pure and Applied Science and Technology, 5(2), 60–76.

Shaw, A. K., & Roy, T. K. (2012). Some arithmetic operations on triangular intuitionistic fuzzy number and its application on reliability evaluation. International Journal of Fuzzy Mathematics and Systems, 2(4), 363–382.

Shaw, A. K., & Roy, T. K. (2015a). Fuzzy reliability optimization based on fuzzy geometric programming method using different operators. The Journal of Fuzzy Mathematics, 23(1), 79–88.

Shaw, A. K., & Roy, T. K. (2015b). Reliability analysis of the system with imprecise constant failure rate of the components. IAPQR Transactions, 40(1).

Zadeh, L. A. (1976). The concept of a linguistic variable and its applications to approximate reasoning. Information Sciences, 8, 199–249; 301–357; 9, 43–80.

Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.

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Published

2020-11-16

How to Cite

Kar, R., & Shaw, A. K. (2020). Analysis the Barrier of E-Learning in Mathematics Using Type-2 Fuzzy Data. Journal of Education and Learning Mathematics Research (JELMaR), 1(2), 58-73. https://doi.org/10.37303/jelmar.v1i2.73

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