CFP last date

by
Surapati Pramanik,
Indrani Maiti,
Tarni Mandal

International Journal of Computer Applications |

Foundation of Computer Science (FCS), NY, USA |

Volume 180 - Number 45 |

Year of Publication: 2018 |

Authors: Surapati Pramanik, Indrani Maiti, Tarni Mandal |

10.5120/ijca2018917154 |

Surapati Pramanik, Indrani Maiti, Tarni Mandal . A Taylor Series based Fuzzy Mathematical Approach for Multi Objective Linear Fractional Programming Problem with Fuzzy Parameters. International Journal of Computer Applications. 180, 45 ( May 2018), 22-29. DOI=10.5120/ijca2018917154

@article{
10.5120/ijca2018917154,

author = {
Surapati Pramanik,
Indrani Maiti,
Tarni Mandal
},

title = { A Taylor Series based Fuzzy Mathematical Approach for Multi Objective Linear Fractional Programming Problem with Fuzzy Parameters },

journal = {
International Journal of Computer Applications
},

issue_date = { May 2018 },

volume = { 180 },

number = { 45 },

month = { May },

year = { 2018 },

issn = { 0975-8887 },

pages = {
22-29
},

numpages = {9},

url = {
https://ijcaonline.org/archives/volume180/number45/29447-2018917154/
},

doi = { 10.5120/ijca2018917154 },

publisher = {Foundation of Computer Science (FCS), NY, USA},

address = {New York, USA}

}

%0 Journal Article

%1 2024-02-07T01:03:40.981001+05:30

%A Surapati Pramanik

%A Indrani Maiti

%A Tarni Mandal

%T A Taylor Series based Fuzzy Mathematical Approach for Multi Objective Linear Fractional Programming Problem with Fuzzy Parameters

%J International Journal of Computer Applications

%@ 0975-8887

%V 180

%N 45

%P 22-29

%D 2018

%I Foundation of Computer Science (FCS), NY, USA

This article presents an approach to acquire the solution of multi-objective linear fractional programming problems where the parameters are assumed to be triangular fuzzy numbers. This is done through a fuzzy mathematical programming perspective based on an approximation method using Taylor series. The problem is first formulated into an equivalent deterministic form using the concept of α-cuts. The associated membership function of each objective function is formulated using the individual optimal solution and is then converted into a linear function by applying the first order Taylor series. The multi-objective linear fractional programming problem then gets reduced to a linear programming problem by applying fuzzy mathematical programming. To illustrate the computational simplicity and applicability of the proposed approach, a numerical example is solved and the results are compared with existing methods.

- Isbell, J. R., and Marlow, W. H. 1956. Attrition games. Naval Research Logistics Quarterly 3 (1-2), 71-94.
- Charnes, A., and Cooper, W. W. 1962. Programming with linear fractional functionals. Naval Research Logistics Quarterly 9 (3-4), 181-186.
- Dinklebach, W. 1967. On nonlinear fractional programming. Management Science 13 (7), 492-498.
- Schaible, S. 1976. Fractional programming. I, duality. Management Science 22 (8), 858-867.
- Gilmore, P. C., and Gomory, R. E. 1963. A linear programming approach to the cutting stock problem-Part II. Operations Research 11 (6), 863-888.
- Swarup, K. 1965. Linear fractional functional programming. Operations Research 13 (6), 1029-1036.
- Kornbluth, J. S. H., and Steur, R. E. 1981. Multiple objective linear fractional programming. Management Science 27 (9), 1024-1039.
- Nykowski, I., and Zolkiewski, Z. 1985. A compromise procedure for the multiple objective linear fractional programming problem. European Journal of Operational Research 19 (1), 91-97.
- Dey, P. P., and Pramanik, S. 2011. Goal programming approach to linear fractional bilevel programming problem based on Taylor series approximation. International Journal of Pure and Applied Sciences and Technology 6(2), 115-123.
- Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8(3), 338–353.
- Luhandjula, M. K. 1984. Fuzzy approaches for multiple objective linear fractional optimization. Fuzzy Sets and Systems 13 (1), 11-23.
- Zadeh, L. A. 1975a. The concept of a linguistic variable and its application to approximate reasoning, Part III. Information Sciences 9 (1), 43-80.
- Zadeh, L. A. 1975b. The concept of a linguistic variable and its application to approximate reasoning, Part II. Information Sciences 8 (4), 301-352.
- Zadeh, L. A. 1975c. The concept of a linguistic variable and its application to approximate reasoning, Part I. Information Sciences 8 (3), 199-244.
- Pal, B. B., Moitra, B. N., and Maulik, U. 2003. A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets and Systems 139 (2), 395-405.
- Sakawa, M., and Yano, H. 1988. An interactive fuzzy satisficing method for multiobjective linear fractional programming problems. Fuzzy Sets and Systems 28 (2), 129-144.
- Dutta, D., Tiwari, R. N., and Rao, J. R. 1992. Multiple objective linear fractional programming - a fuzzy set theoretic approach. Fuzzy Sets and Systems 52 (1), 39-45.
- Chakraborty, M., and Gupta, S. 2002. Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets and Systems 125 (3), 335-342.
- Guzel, N., and Sivri, M. 2005. Taylor series solution to multi-objective linear fractional programming problem. Trakya University Journal Sciences 6 (2), 80-87.
- Toksari, D. M. 2008. Taylor series approach to fuzzy multiobjective linear fractional programming. Information Sciences 178 (4), 1189-1204.
- Pramanik, S., and Roy, T. K. 2005. A fuzzy goal programming approach for multi-objective capacitated transportation problem. Tamsui Oxford Journal of Management Sciences 21(1), 75-88.
- Pramanik, S., and Roy, T. K. 2007. Fuzzy goal programming approach to multilevel programming problems. European Journal of Operational Research 176 (2) 1151-1166.
- Pramanik, S., & Roy, T. K. 2006. A fuzzy goal programming technique for solving multi-objective transportation problem. Tamsui Oxford Journal of Management Sciences 22 (1), 67-89.
- Pramanik, S., & Roy, T. K. 2008. Multiobjective transportation model with fuzzy parameters: a priority based fuzzy goal programming. Journal of Transportation Systems Engineering and Information Technology 8 (3), 40-48.
- Pramanik, S. 2012. Bilevel programming problem with fuzzy parameter: a fuzzy goal programming approach. Journal of Applied Quantitative Methods 7(1), 09-24.
- Pramanik, S. 2015. Multilevel programming problems with fuzzy parameters: a fuzzy goal programming approach. International Journal of Computer Applications 122 (21), 34-41.
- Pramanik, S., and Dey, P.P. 2011. Bi-level multi-objective programming problem with fuzzy parameters. International Journal of Computer Applications 30 (10) 13-20.
- Pramanik, S., Dey, P. P., and Giri. B. C. 2011. Decentralized bilevel multiobjective programming problem with fuzzy parameters based on fuzzy goal programming. Bulletin of Calcutta Mathematical Society 103 (5), 381-390.
- Pramanik, S., and Dey, P. P. 2011. Multi-objective linear fractional programming problem based on fuzzy goal programming. International Journal of Mathematical Archive 2 (10), 1875-1881.
- Pramanik, S., and Dey, P.P. 2011. A priority based fuzzy goal programming to multi-objective linear fractional programming problem. International Journal of Computer Applications 30 (10), 1-6.
- Pramanik, S., and Dey, P.P. 2011. Bi-level linear fractional programming problem based on fuzzy goal programming approach. International Journal of Computer Applications 25 (11), 34-40.
- Dey, P. P., Pramanik, S., and Giri, B.C.2013. Fuzzy goal programming algorithm for solving bi-level multi-objective linear fractional programming problems, International Journal of Mathematical Archive 4(8), 154-161.
- Pramanik, S., Dey, P. P., and Roy, T. K. 2012. Fuzzy goal programming approach to linear fractional bilevel decentralized programming problem based on Taylor series approximation. The Journal of Fuzzy Mathematics 20 (1), 231- 238.
- Dey, P.P., Pramanik, S., and Giri, B. C. 2014. Multilevel fractional programming problem based on fuzzy goal programming. International Journal of Innovative research in Technology & Science 2(4), 17-26.
- Dey, P. P., Pramanik, S., &Giri, B. C. 2014. TOPSIS approach to linear fractional bi-level MODM problem based on fuzzy goal programming, Journal of Industrial and Engineering International 10(4), 173-184.
- Banerjee, D., & Pramanik, S. 2012. Goal programming approach to chance constrained multi-objective linear fractional programming problem based on Taylor’s series approximation. International Journal of Computers & Technology 2(2), 77-80.
- Pramanik, S., and Dey, P.P. 2011. Multi-objective linear plus linear fractional programming problem based on Taylor series approximation. International Journal of Computer Applications 32 (8), 61-68.
- Pramanik, S., Banerjee, D., and Giri, B.C. 2015. Multi-level multi-objective linear plus linear fractional programming problem based on FGP approach. International Journal of Innovative Science Engineering and Technology 2 (6), 153-160.
- Banerjee, D., & Pramanik, S. 2012. Chance constrained multi-objective linear plus linear fractional programming problem based on Taylor’s series approximation. International Journal of Engineering Research and Development 1(3) 55-62.
- Pramanik, S., Banerjee, D., & Giri, B.C. 2012. Chance constrained linear plus linear fractional bi-level programming problem. International Journal of Computer Applications 56(16), 34-39.
- Pramanik, S., and Dey, P.P. 2011. Multi-objective quadratic programming problem based on fuzzy goal programming. International Journal of Pure and Applied Sciences and Technology 6(1), 45-53.
- Pramanik, S., and Dey, P.P. 2011. Multi-objective quadratic programming problem: a priority based fuzzy goal programming. International Journal of Computer Applications 26 (10), 30-35.
- Pramanik, S., and Dey, P.P. 2011. Quadratic bi-level programming problem based on fuzzy goal programming approach. International Journal of Software Engineering & Application 2(4), 41-59.
- Pramanik, S., Dey, P. P., and Giri, B.C. 2011. Fuzzy goal programming approach to quadratic bi-level multi-objective programming problem. International Journal of Computer Applications 29 (6), 09-14.
- Pramanik, S., & Banerjee, D. 2012. Chance constrained quadratic bi-level programming problem. International Journal of Modern Engineering Research 2(4), 2417-2424.
- Yano, H., and Sakawa, M. 1989. Interactive fuzzy decision making for generalized multiobjective linear fractional programming problems with fuzzy parameters. Fuzzy Sets and Systems 32 (3), 245-261.
- Sakawa, M., Yano, H., and Takahashi, J. 1992. Pareto optimality for multionjective linear fractional programming problems with fuzzy parameters. Information Sciences 63 (1-2), 33-53.
- Payan, A., and Noora, A. A. 2014. A linear modeling to solve multi-objective linear fractional programming problem with fuzzy parameters. International Journal Mathematical Modelling and Numerical Optimisation 5 (3), 210-228.
- Pop, B., and Stancu-Minasian, I. M. 2008. A method of solving fully fuzzified linear fractional programming problems. Journal of Applied Mathematics and Computing 27 (1-2), 227-242.
- Ganesan, K., and Veeramani, P. 2006. Fuzzy linear programs with trapezoidal fuzzy numbers. Annals of Operations Research 143, 305-315.
- Safaei, N. 2014. A new method for solving fully fuzzy linear fractional programming with triangular fuzzy numbers. Applied Mathematics and Computational Intelligence 3 (1), 273-281.
- Zimmermann, H. J. 1991. Fuzzy sets theory and its applications. Kluwer Academic, Boston.
- Sakawa, M. 1993. Fuzzy sets and interactive multi-objective optimization. Plenum Press, New York.
- Kauffmann, A., and Gupta, M. M. 1991 Introduction to fuzzy Arithmetic: Theory and Applications. Van Nostrand Reinhold, New York.
- Mehra, A., Chandra, S., and Bector, C. R. 2007. Acceptable optimality in linear fractional programming with fuzzy coefficients. Fuzzy Optimization Decision Making 6 (1), 5-16.
- Lee, E. S., and Li, R. J. 1993. Fuzzy multiple objective programming with Pareto optimum. Fuzzy Sets and Systems 53 (3), 275-288.

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