Analysis The Barrier of E-learning in Mathematics Using Type-2 Fuzzy Data

  • Rahul Kar Springdale High School, India
  • Ashok kumar Shaw Regent Education and Research Foundation, Kolkata
Keywords: triangular intuitionistic type 2 fuzzy number (tit2fn), system reliability, parallel system, series system, e-learning mathematics


E-Learning is learning utilizing electronic technologies to access educational curriculum outside of a traditional classroom. In most cases, it refers to a course, program or degree delivered completely 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).


Alefeld,G.,and Herzberger,J. (1983). Introduction to Interval Computation. New York: Academic Press

Cheng.C.H. and Mon.D.L .(1993). Fuzzy System Reliability Analysis by Interval of Confidence”, Fuzzy Sets and Systems, 56 (1993), 29-35.

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

Cai. K.Y., Wen. C.Y.and Zhang. M.L. (1991). Survival Index for CCNs: a Measure of Fuzzy Reliability Computing Systems”, Reliability Engineering and System Safety, 33 (1991), 141-157.

Cai. K.Y. and Wen. C.Y. (1990). Streeting-Lighting Lamps Replacement: A Fuzzy Viewpoint”, Fuzzy Sets and System, 37 (1990), 161-172.

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 2019, 11, 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 2019, 11, 248.

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

Chen. S.M. and Jong. W.T. (1996). Analyzing Fuzzy System Reliability Using Interval Of Confidence”, International Journal of Information Management and Engineering, 2(1996),16-23.

Chen, S.H. (1985). Operations On Fuzzy Numbers With Function Principle. Tamkang Journal of Management Sciences, 6(1), (1985), pp 13 – 26.

Dubois, D., and H. Prade, H. (1978). Operations of Fuzzy Number’s, Internat. J. Systems Sci. 9(6) (1978), 613-626.

Dubois, D., and H. Prade, H. (1980). Fuzzy Sets And Systems, Theory And Applications. New York: Academic Press

Dwyer, P.S. (1951). Linear Computation. New York

Dwyer, P.S.. (1964). Matrix Inversion With The Square Root Method. Techno Matrices, 6(2)(1964).

Hansen, E.R. (1965). Interval Arithmetic in Matrix computations, Part Journal of SIAM series B, volume 2, number 2

Hansen, E.R., and Smith, R.R. (1967). Interval Arithmetic in Matrix computation Part II”, SIAM Journal of Numerical Analysis, 4 1-9.

Hansen, E.R. (1969). On The Solutions Of Linear Algebraic Equations With Interval Coefficients”, Linear Algebra Appl., 2 153-165.

Hansen, E.R. (1992). Global Optimization Using Interval Analysis. New York: Marcel Dekker, Inc.

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.

Kaufmann, A. (1975). Introduction to theory of Fuzzy Subsets Vol. I. New York: Academic Press,

Kaufmann, A., and Gupta, M.M. (1985). Introduction to Fuzzy Arithmetic. New York: Van Nostrand Reinhold

Lodwick, W.A., and Jamison, K.D. (1997). Interval Methods And Fuzzy Optimization. International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems, 5 239-249.

Mahapatra. G.S. and Roy. T.K. (2009). Reliability Evaluation using triangular intuitionistic Fuzzy Numbers Arithemmetic Operations, Proceedings of World Academy of Science, Engineering and Technology, 38587-595

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.

Moore, R.E. (1979). Methods and Applications of Interval Analysis. Philadelphia: SIAM,

Mon. D.L. and Cheng. C.H. (1994). Fuzzy System Reliability Analysis For Components With Different Membership Functions, Fuzzy Sets and Systems, 64 (1994),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 & Fuzzy Systems, 34(1), 677-687.

M. Deldago, J.L. Verdegay, M.A. Vila. (1989). A General Model for Fuzzy Linear Programming. Fuzzy Set and System. 29 (1989), 21-29.

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”, wjert, 2019, Vol. 5, Issue 6, 397-404.

Kar. R, Shaw, A.K. (2018). Some Arithmetic Operations On Trapezoidal Fuzzy Numbers And Its Application In Solving Linear Programming Problem By Simplex Algorithm”, Intl. J. Bioinformatics and Biological Sci.: (V. 6 n.2, p. 77-86)

Salahshour,S.; Ahmadian,A.; Mahata,A; Mondal,S.P.; Alam,S. The behavior of logistic equation with alley effect in fuzzy environment: fuzzy differential equation approach International “, Journal of Applied and Computational Mathematics 4 (2), 62.

Shaw, A.K. and Roy, T.K. (2015). Fuzzy Reliability Optimization based on Fuzzy Geometric Programming Method Using Different Operators, The Journal of Fuzzy Mathematics (USA) Vol.23, No.1, pp.79-88, 2015

Shaw, A.K. and Roy, T.K. (2015). Reliability Analysis of the System with Imprecise Constant Failure Rate of the Components”, IAPQR Transaction, Vol.40, No.1, 2015

Shaw,A.K, and Roy, T.K. (2011). Generalized Trapezoidal Triangular Intuitionistic Fuzzy Number And Its Application On Reliability Evaluation, Fuzzy Number With Its Arithmetic Operations And Its Application In Fuzzy System Reliability Analysis, International Journal Of Pure Applied Science And Technology , 5(2) (2011), 60-76.

Shaw,A.K, and Roy, T.K. (2012). Some Arithmetic Operations On Triangular Intuitionistic Fuzzy Number And Its Application On Reliability Evaluation, International Journal of Fuzzy Mathematics and System (IJFMS), Vol.2, No. 4(2012), pp.363-382

S.C. Fang, C.F Hu, S.-Y. Wu, H.-F. Wang. (1999). Linear Programming with Fuzzy Coefficients in Constraint, Computers and Mathematics with Applications, 37 (1999), 63-76.

Zadeh, L.A. (1976). The Concept Of A Linguistic Variable And Its Applications To Approximate Reasoning – Parts I, II And III”, Inform. Sci. 8(1975) 199-249; 81975 301-357; 9(1976) 43-80.

Zadeh, L.A. (1978). Fuzzy Sets As A Basis For A Theory Of Possibility, Fuzzy Sets And Systems, No.1, pp.3-28, 1978.

How to Cite
Kar, R., & Shaw, A. (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.