Document Type : Research Paper


Operations Research Department, Institute of Statistical Studies and Research, Cairo University, Giza, Egypt.


In this paper, a Multi-Criteria De Novo Linear Programming (F- MDNLP) problem has been developed under consideration of the ambiguity of parameters. These fuzzy parameters are characterized by fuzzy numbers. A fuzzy goal programming approach is applied for the corresponding multi-criteria De Novo linear programming (MDNLP) problem by defining suitable membership functions and aspiration levels. The advantage of the approach is that the decision maker's role is only the specification of the level and hence evaluate the  efficient solution for limitation of his/ her incomplete knowledge about the problem domain. A numerical example is given for illustration.


Main Subjects

[1]          Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science17(4), B-141.
[2]          Charnes, A., & Cooper, W. W. (1968). Management models and the industrial applications of linear programming. John& Wiley, New York.
[3]          Chen, Y. W., & Hsieh, H. E. (2006). Fuzzy multi-stage De-Novo programming problem. Applied mathematics and computation181(2), 1139-1147.
[4]          Chen, J. K., & Tzeng, G. H. (2009). Perspective strategic alliances and resource allocation in supply chain systems through the De Novo programming approach. International journal of sustainable strategic management1(3), 320-339.
[5]           Chen, Y. L., Chen, L. H., & Huang, C. Y. (2009). Fuzzy Goal Programming Approach to Solve the Equipment-Purchasing Problem of an FMC. International journal of industrial engineering: theory, applications and practice16(4).
[6]           Dubois, D. J. (1980). Fuzzy sets and systems: Theory and applications (Vol. 144). Academic press.
[7]          Dubois, D., & Prade, H. (1980). Systems of linear fuzzy constraints. Fuzzy sets and systems3(1), 37-48.
[8]          Fiala, P. (2011). Multi-objective De Novo Linear Programming. Acta universitatis palackianae olomucensis. Facultas rerum naturalium. Mathematica50(2), 29-36.
[9]           Garg, H. (2018). Analysis of an industrial system under uncertain environment by using different types of fuzzy numbers. International journal of system assurance engineering and management9(2), 525-538.
[10]       Gasimov, R. R., & Yenilmez, K. (2002). Solving fuzzy linear programming problems with linear membership function. Turkish journal of mathematics26(4), 375-396.
[11]      Hamadameen, O. A. (2018). A noval technique for solving multi-objective linear programming problems. Aro- the scientific journal of Koya University, 5(2): 1-8.
[12]      Huang, J. J., Tzeng, G. H., & Ong, C. S. (2006). Choosing best alliance partners and allocating optimal alliance resources using the fuzzy multi-objective dummy programming model. Journal of the operational research society57(10), 1216-1223.
[13]      Ignizio, J. P. (1982). On the (re) discovery of fuzzy goal programming. Decision sciences13(2), 331-336.
[14]      Ijiri, Y. (1965). Management goals and accounting for control (Vol. 3). North Holland Pub. Co.
[15]      Kaufmann, A., & Gupta, M. M. (1988). Fuzzy mathematical models in engineering and management science. Elsevier Science Inc.
[16]      Kiruthiga, M., & Loganathan, C. (2015). Fuzzy multi- objective linear programming problem using membership function. International journal of science, engineering, and technology, applied sciences, 5(8): 1171- 1178.
[17]       Lee, S. M. (1972). Goal programming for decision analysis (pp. 252-260). Philadelphia: Auerbach Publishers.
[18]       Li, R. J., & Lee, E. S. (1990). Multi-criteria de novo programming with fuzzy parameters. Journal of mathematical analysis and application19(1), 13-20.
[19]      Li, R. J., & Lee, E. S. (1993). De Novo programming with fuzzy coefficients and multiple fuzzy goals. Journal of mathematical analysis and applications172(1), 212-220.
[20]      Mohamed, R. H. (1997). The relationship between goal programming and fuzzy programming. Fuzzy sets and systems89(2), 215-222.
[21]      Moore, R. E. (1979). Methods and applications of interval analysis (Vol. 2). Siam.
[22]      Narasimhan, R. (1981). On fuzzy goal programming—some comments. Decision sciences12(3), 532-538.
[23]      Rommelfanger, H., Hanuscheck, R., & Wolf, J. (1989). Linear programming with fuzzy objectives. Fuzzy sets and systems29(1), 31-48.
[24]       Sakawa, M., & Yano, H. (1985). Interactive decision making for multi-objective linear fractional programmingproblems with fuzzy parameters. Cybernetics and system16(4), 377-394.
[25]      Sakawa, M., & Yano, H. (1990). An interactive fuzzy satisficing method for generalized multi-objective linear programming problems with fuzzy parameters. Fuzzy sets and systems35(2), 125-142.
[26]      Sakawa, M. (2013). Fuzzy sets and interactive multi-objective optimization. Springer Science & Business Media.
[27]      Tabucanon, M. T. (1988). Multiple criteria decision making in industry (Vol. 8). Elsevier Science Ltd.
[28]       Tanaka, H., & Asai, K. (1984). Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and systems13(1), 1-10.
[29]      Tang, Y. C., & Chang, C. T. (2012). Multicriteria decision-making based on goal programming and fuzzy analytic hierarchy process: An application to capital budgeting problem. Knowledge-based systems26, 288-293.
[30]      Umarusman, N., & Ahmet, T. (2013). Building optimum production settings using de novo programming with global criterion method. International journal of computer applications82(18).
[31]      Veeramani, C., Duraisamy, C., & Nagoorgani, A. (2011). Solving fuzzy multi-objective linear programming problems with linear membership functions. Australian journal of basic and applied sciences5(8), 1163-1171.
[32]      Zadeh, A. L. (1965). Fuzzy sets. Information and control, 8(3), 338- 353.
[33]      Zeleny, M. (1976). Multi-objective design of high-productivity systems. Joint automatic control conference (No. 13, pp. 297-300). IEEE.
[34]      Zeleny, M. (1986). Optimal system design with multiple criteria: De Novo programming approach. Engineering costs and production economics10(1), 89-94.
[35]      Engineering Costs and Production Economics, (10): 89- 94.
[36]      Zelený, M. (1990). Optimizing given systems vs. designing optimal systems: The De Novo programming approach. International journal of general systems17(4), 295-307.
[37]      Zhang, Y. M., Huang, G. H., & Zhang, X. D. (2009). Inexact de Novo programming for water resources systems planning. European journal of operational research199(2), 531-541.
[38]      Zhao, R., Govind, R., & Fan, G. (1992). The complete decision set of the generalized symmetrical fuzzy linear programming problem. Fuzzy sets and systems51(1), 53-65.
[39]       Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems1(1), 45-55.
Zimmermann, J. H. (1985). Fuzzy Sets Theory and its Application. Kluwer Academic Publisher