| Title of paper:
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Intuitionistic fuzzy linear optimization
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| Author(s):
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| Rangasamy Parvathi
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| Department of Mathematics, Vellalar College for Women, Erode–638 012, Tamilnadu, India
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| paarvathis@rediffmail.com
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| C. Malathi
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| Department of Mathematics, Gobi Arts and Science College, Gobi–638 456, Tamilnadu, India
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| Published in:
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"Notes on IFS", Volume 18 (2012) Number 1, pages 48—56
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| Download:
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 PDF (171 Kb, Info)
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| Abstract:
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A new concept to the optimization problem in an intuitionistic fuzzy environment is introduced. A general model, of linear programming problems in which both the right hand side constants and the technological coefficients are intuitionistic fuzzy numbers, has been presented. An attempt has been made to find a general linear non-membership function and intuitionistic fuzzy index together with the membership function of the objective function and constraints in the solution of the given Intuitionistic Fuzzy Linear Programming Problem (IFLPP). Stepwise algorithm is given for solving an IFLPP and it is checked with a numerical example using intuitionistic fuzzy decisive set method.
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| Keywords:
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Intuitionistic fuzzy set, Intuitionistic fuzzy linear programming problem, Intuitionistic fuzzy optimization, Membership and non-membership functions, Intuitionistic index, Intuitionistic fuzzy decisive set method
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| AMS Classification:
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03E72.
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| References:
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- Angelov, P. Optimization in an intuitionistic fuzzy environment, Fuzzy Sets and Systems, Vol. 86, 1997, 299–306.
- Atanassov, K. T. Intuitionistic Fuzzy Sets: Theory and Applications, Springer Physica-Verlag, Heidelberg, New York, 1999.
- Atanassov, K., V. Kreinovich, Intuitionistic fuzzy interpretation of interval data, Notes on Intuitionistic Fuzzy Sets, Vol. 5, 1999, No. 1, 1–8.
- Bellman, R. E., L. A. Zadeh, Decision-making in a fuzzy environment, Management Science, Vol. 17, 1970, 141–164.
- Burillo, P., H. Bustince, V.Mohedano, Some definitions of intuitionistic fuzzy number, Proceedings of the 1st Workshop on Fuzzy Based Expert Systems, D. Lakov, Ed., Sofia, Bulgaria, September 1994, 53–55.
- Ganesan, K., P. Veeramani, Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers, Ann. Oper. Res., Vol. 143, 2006, 305–315.
- Gasimov, R. N., K. Yenilmez, Solving Fuzzy Linear Programming Problems with Linear Membership Functions, Turk. J. Math., Vol. 26, 2002, 375–396.
- Klir, G. J., B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall, New Jersey, 1995.
- Yang, L., H. Ji-xue, Y. Hong-yan, L. Ying-jie, Normal Technique for Ascertaining Nonmembership Functions of Intuitionistic Fuzzy Sets, Chinese Control and Decision Conference, 2008, 2604–2608.
- Mahapatra, B. S., G. S. Mahapatra, Intuitionistic Fuzzy Fault Tree Analysis using Intuitionistic Fuzzy Numbers, International Mathematical Forum, Vol. 5, 2010, No. 21, 1015–1024.
- Parvathi, R., C. Malathi, Intuitionistic Fuzzy Linear Programming Problems, World Applied Sciences Journal, Vol. 1, 2012, No. 1, 1–5.
- Sakawa, M., H. Yana, Interactive decision making for multi-objective linear fractional programming problems with fuzzy parameters, Cybernetics Systems Vol. 16, 1985, 377–397.
- Shaocheng, T. Interval number and Fuzzy number linear programmings, Fuzzy Sets and Systems Vol. 66, 1994, 301–306.
- Tanaka, H., T. Okuda and K. Asai, On Fuzzy Mathematical Programming, Journal of Cybernetics, Vol. 3, 1984, No. 4, 37–46.
- Zimmermann, H. J. Fuzzy Set Theory and its Applications, Kluwer Academic Publishers, London, 1991.
- Zimmermann, H. J. Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, Vol. 1, 1978, 45–55.
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