Modified new operations for triangular intuitionistic fuzzy numbers

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DOI:

https://doi.org/10.26637/mjm203/017

Abstract

Intuitionistic fuzzy sets (IFS) are a generalization of the concept of fuzzy set. In standard intuitionistic fuzzy arithmetic operations, we have some grievances in subtraction and division operations. In this paper, modified new operations for subtraction and division on triangular intuitionistic fuzzy numbers (TIFNS) are defined. Finally an illustrative example for solving Intuitionistic fuzzy multi-objective linear programming problem (IFMOLPP) using these modified operators is provided.

Keywords:

Intuitionistic fuzzy arithmetic, Triangular intuitionistic fuzzy number (TIFN), ntuitionistic fuzzy multi-objective linear programming problem (IFMOLPP)

Mathematics Subject Classification:

65K05, 90C90, 90C70, 90C29
  • R. Irene Hepzibah Department of Mathematics, AVC College of Engineering, Mayiladuthurai, Tamil Nadu, India.
  • R.Vidhya Department of Mathematics, AS-SALAM College of Engineering and Technology, Aduthurai, Tamil Nadu, India.
  • Pages: 301-307
  • Date Published: 01-07-2014
  • Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)

Atanassov.K.T., More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33(1986), 37-46. DOI: https://doi.org/10.1016/0165-0114(89)90215-7

Atanassov.K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96. DOI: https://doi.org/10.1016/S0165-0114(86)80034-3

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

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

Compas.L and Verdegay.J.L ., Linear Programming Problems and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32(1989), 1- 11. DOI: https://doi.org/10.1016/0165-0114(89)90084-5

Dubois,D.,and Prade,H., perations of Fuzzy Number’s, Internat.J. Systems Sci., 9(6)(1978), 613-626. DOI: https://doi.org/10.1080/00207727808941724

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

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

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

Kaufmann,A.,andGupta,M.M., Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, New York, 1985.

Liu H.W. Synthetic decision based on intuitionistic fuzzy relations, Journal of Shandong University of Technology, 33(5)(2003), 579-581.

G.S.Mahapatra and T.K.Roy, Reliability Evaluation using Triangular Intuitionistic Fuzzy numbers Arithmetic operations., World Academy of science, Engineering and Technology 50(2009), 574-581.

Mizumoto,M.,andTanaka,K.,The four Operations of Arithmetic on Fuzzy Numbers., Systems Comput. Controls 7(5) (1977)73-81.

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

Moore,R.E., Methods andApplications of Interval Analysis., SIAM, Philadelphia, 1979. DOI: https://doi.org/10.1137/1.9781611970906

A.Nagoorgani and K.Ponnalagu , Solving Linear Programming Problem in an Intuitionistic Environment., Proceedings of the Heber international conference on Applications of Mathematics and Statistics, HI-CAMS 5-7(2012).

A.Nagoorgani and S.N.Mohamed Assarudeen, A new operation on Triangular fuzzy number for solving linear programming problem, Applied Mathematical Sciences,6(11)(2012), 525- 532.

Nahmias, S., Fuzzy variables, Fuzzy sets and systems’, 1(2) (1977)97-110. DOI: https://doi.org/10.1016/0165-0114(78)90011-8

Neumaier, A., Interval Methods for Systems of Equations., Cambridge University Press, Cambridge, (1990). DOI: https://doi.org/10.1017/CBO9780511526473

Nguyen,H.T., A Note on extension principle for fuzzysets, J. Math. Anal. Appl., 64(1978), 369-380. DOI: https://doi.org/10.1016/0022-247X(78)90045-8

Rardin, R.L.,Optimization in Operations Research, Pearson Education, New Delhi, 2003.

Xu Z.S., Intuitionistic preference relations and their application in group decision making, Information Sciences, (177)(2007), 2363-2379. DOI: https://doi.org/10.1016/j.ins.2006.12.019

Zadeh,L.A., The concept of a Linguistic variable and its applications to approximate Reasoning-parts I, II and III”., Information Sciences, 8(1975), 199-249; 8, 1975301-357; 9(1976) 43-80. DOI: https://doi.org/10.1016/0020-0255(75)90017-1

Zadeh, L.A., Fuzzy sets, Information and Control, 8(1965), 339-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X

Zadeh,L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1(1978), 3-28. DOI: https://doi.org/10.1016/0165-0114(78)90029-5

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Published

01-07-2014

How to Cite

R. Irene Hepzibah, and R.Vidhya. “Modified New Operations for Triangular Intuitionistic Fuzzy Numbers”. Malaya Journal of Matematik, vol. 2, no. 03, July 2014, pp. 301-7, doi:10.26637/mjm203/017.

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Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)

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