Original Article

Some Arithmetic Operations on Triangular Intuitionistic Fuzzy Number and its Application in Solving Linear Programming Problem by Simplex Algorithm

Year: 2019 | Month: June and December | Volume 7 | Issue 1 and 2

References (38)

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

View at Google Scholar

2.Cheng, C.H. and 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. and 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. and 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., and H. Prade, H., 1978. Operations of Fuzzy Number’s, Internat. J. Systems Sci., 9(6): 613-626.

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

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

View at Google Scholar

18.Kar Rahul, Shaw, A.K. Trapezoidal Intuitionistic Fuzzy Number with some arithmetic operations and its application on reliability evaluation(communicated paper).

View at Google Scholar

19.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.

View at Google Scholar

20.Luc. Jaulin, Michel Kieffer, Olivier Didrit and Eric Walter, 2001. Applied Interval Analysis, (Springer – Verlag, London.

View at Google Scholar

21.Mizumoto, M., and Tanaka, K., 1976. Some Properties of Fuzzy Set of Type 2, Inform. and Control, 31: 321-340.

View at Google Scholar

22.Mizumoto, M., and Tanaka, K., 1977. The four Operations of Arithmetic on Fuzzy Number’s, Systems Comput. Controls 7(5): 73-81.

View at Google Scholar

23.Moore, R.E. 1966. Interval Analysis, (Printice Hall, Inc. Englewood & Cliffs, N.J.).

View at Google Scholar

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

View at Google Scholar

25.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

26.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

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

View at Google Scholar

28.Nahmias, S. 1977. Fuzzy variables, Fuzzy sets and systems 1(2): 97-110.

View at Google Scholar

29.Neumaier, A. 1990. Interval Methods for systems of Equations, (Cambridge University Press, Cambridge).

View at Google Scholar

30.Nguyen, H.T. 1978. A Note on extension principle for fuzzy sets, J. Math. Anal. Appl., 64: 369-380.

View at Google Scholar

31.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), 23(1): 79-88.

View at Google Scholar

32.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

33.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): 60-76.

View at Google Scholar

34.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), 2(4): 363-382.

View at Google Scholar

35.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: 63-76.

View at Google Scholar

36.Zadeh, L.A., 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.

View at Google Scholar

37.Zadeh, L.A. 1965. Fuzzy sets, Information and Control, No.8, pp. 339-353.

View at Google Scholar

38.Zadeh, L.A. 1978. Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, No. 1, pp. 3-28.

View at Google Scholar

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