Original Article

Some Arithmetic Operations on Trapezoidal Fuzzy Numbers and its Application in Solving Linear Programming Problem by Simplex Algorithm

Year: 2018 | Month: December | Volume 6 | Issue 2

References (29)

1.Alefeld, G. & Herzberger, J. 1983. Introduction to Interval Computation, Academic Press, New York.

View at Google Scholar

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

View at Google Scholar

3.Cai, K.Y., Wen, C.Y. & Zhang, M.L. 1991. Fuzzy reliability modeling of gracefully degradable computing systems, Reliability Engineering and System Safety, 33: 141-157.

View at Google Scholar

4.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.

View at Google Scholar

5.Cai, K.Y. and Wen, C.Y. 1990. Streeting-lighting lamps replacement: a fuzzy viewpoint, Fuzzy Sets and System, 37: 161-172.

View at Google Scholar

6.Chen, S.M. and Jong, W.T. 1996. Analyzing fuzzy system reliability using interval of confidence, International Journal of Information Management and Engineering, 2: 16-23

View at Google Scholar

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

View at Google Scholar

8.Dubois, D. & H. Prade, H. 1978. Operations of Fuzzy Number’s, Int. J. Systems Sci., 9(6): 613-626.

View at Google Scholar

9.Dubois, D. & H. Prade, H. 1980. Fuzzy sets and systems, Theory and Applications, Academic Press, New York.

View at Google Scholar

10.Dwyer, P.S. 1964. Matrix Inversion with the square root method, Technometrices, 6(2).

View at Google Scholar

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

View at Google Scholar

12.Hansen, E.R. & Smith, R.R. 1967. Interval Arithmetic in Matrix computation Part II, SIAM Journal of Numerical Analysis, 4: 1-9.

View at Google Scholar

13.Hansen, E.R. 1969. On the solutions of linear algebraic equations with interval coefficients, Linear Algebra Appl., 2: 153-165.

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

18.Moore, R.E. 1979. Methods and Applications of Interval Analysis, SIAM, Philadelphia.

View at Google Scholar

19.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, 38: 587-595

View at Google Scholar

20.Mon. D.L. and Cheng. C.H. 1994. Fuzzy system reliability analysis for components with different membership functions, Fuzzy Sets and Systems, 64: 145-157.

View at Google Scholar

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

View at Google Scholar

22.Shaw, A.K. & Roy, T.K. 2015. Fuzzy Reliability Optimization based on Fuzzy Geometric Programming Method using different operators, The Journal of Fuzzy Mathematics (USA) 23(1): 79-88.

View at Google Scholar

23.Shaw, A.K. and Roy, T.K. 2015. Reliability Analysis of the System with Imprecise Constant Failure Rate of the Components, IAPQR Transaction, 40(1).

View at Google Scholar

24.Shaw, A.K. & 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): 60-76.

View at Google Scholar

25.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 System (IJFMS), 2(4): 363-382.

View at Google Scholar

26.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.

View at Google Scholar

27.Zadeh, L.A. 1975. The concept of a Linguistic variable and its applications to approximate reasoning – parts I, II and III”, Inform. Sci., 8: 199-249; 81975 301-357; 9(1976) 43-80.

View at Google Scholar

28.Zadeh, L.A. 1965. Fuzzy sets, Information and Control, 8: 339- 353.

View at Google Scholar

29.Zadeh, L.A. 1978. Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1: 3-28, 1978.

View at Google Scholar

@International Journal of Bioinformatics and Biological Sciences(IJBBS)| Printed by New Delhi Publishers 2554756 - Visitors since March 19, 2020