International Journal of Computer
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Volume 6 | Issue 6 | Year 2016 | Article Id. IJCOT-V37P306 | DOI : https://doi.org/10.14445/22492593/IJCOT-V37P306

Intuitionistic Fuzzy Optimization of Truss Design: A Comparative Study

Biswajit Singh, Mridula Sarkar, Tapan Kumar Roy

Citation :

Biswajit Singh, Mridula Sarkar, Tapan Kumar Roy, "Intuitionistic Fuzzy Optimization of Truss Design: A Comparative Study," International Journal of Computer & Organization Trends (IJCOT), vol. 6, no. 6, pp. 25-33, 2016. Crossref, https://doi.org/10.14445/22492593/IJCOT-V37P306

Abstract

In this paper, we have developed an intuitionistic fuzzy optimization (IFO) approach considering non-linear membership and non-membership function for optimizing the design of plane truss structure with single objectives subject to a specified set of constraints. In this optimum design formulation, the objective functions are the weight of the truss; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is presented here in to demonstrate the efficiency of the Intuitionistic fuzzy optimization approach with non-linear membership function. We made a comparative study of linear and non-linear membership and non-membership function to see its impact on intuitionistic fuzzy optimization and to get to the depth of such optimization process. The test problem consists of a two-bar planar truss subjected to a single load condition. This single-objective structural optimization model is solved by intuitionistic fuzzy optimization approach with non-linear membership and non-membership function. Numerical example is given to illustrate our approach. The result shows that the IFO approach is very efficient in finding the best discovered optimal solutions.

Keywords

Intuitionistic fuzzy optimization, Non-linear membership function, Non-linear non-membership function, Structural design.

References

[1] Angelov, P.P. Intuitionistic fuzzy optimization. Notes on Intutionistic Fuzzy Sets ,vol.1 ,No.2,pp. 123–129, 1995.
[2] Angelov, P.P. Optimization in intuitionistic fuzzy environment. Fuzzy Sets and Systems ,vol.86,pp. 299–306, 1997.
[3] Attanassov, K. and Das, P., “Interval valued intuitionistic fuzzy sets” Fuzzy set and systems,vol.31,pp.343-349,1989.
[4] C. J. Shih and C. J. Chang, Mixed-discrete nonlinear fuzzy optimization for multi-objective engineering design. AIAA-94-1598-CP, pp. 2240-2246, 1994.
[5] Dey,S. and Roy,T.K., “Optimized solution of two bar truss design using intuitionistic fuzzy optimization technique” , International Journal of Information Engineering and Electronic Business,vol.3, 45-51,2014.
[6] Huang,H.Z., Wang.P, Zuo., M. J., Wu,W. ,Liu.C., “A fuzzy set based solution method for multi-objective optimal design problem of mechanical and structural systems using functional-link net, Neural Comput & Applic ,vol. 15,pp-239–244,2006.
[7] Jana, B., Roy, T.K., Multi-objective intuitionistic fuzzy linear programming and its application in transportation model. Notes on Intuitionistic Fuzzy Sets, vol.13,No.1, pp.34–51, 2007.
[8] K. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, vol.20,pp.87-96, 1986.
[9] K. Atanassov, “Idea for intuitionistic fuzzy sets equation, in equation and optimization,” Notes on Intuitionistic Fuzzy Sets, vol.1, pp.17-24, 1995.
[10] K. Atanassov, “Two theorems for Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol.110,pp.267-269, 2000.
[11] L. A. Zadeh, Fuzzy set, Information and Control, vol.8, no.3, pp.338-353, 1965.
[12] Pramanik, P., Roy, T.K. An intuitionistic fuzzy goal programming approach to vector optimization problem. Notes on Intutionistic Fuzzy Sets ,vol.11,No1,pp. 1–14,2004.
[13] Rao, S.S., “ Description and optimum Design of Fuzzy Mathematical Systems”, Journal of Mechanisms, Transmissions, and Automation in Design, Vol.109,pp.126-132,1987.
[14] R.E. Bellman and L.A. Zadeh, Decision-making in a fuzzy environment, Management Science, vol.17,No.4, B141-B164, 1970.
[15] Dey,S. and Roy,T.K., “Multi-objective structural optimization using fuzzy and intuitionistic fuzzy otimization technique, ” I.J. Intelligent systems and applications ,vol.05,pp.57-65,2015.
[16] Wang,G.Y.,Wang, W.Q., “ Fuzzy optimum design of structure.” Engineering Optimization,vol. 8,pp.291-300,1985.
[17] Xu, C. “Fuzzy optimization of structures by the two-phase method”,Computer and Structure, vol.31,No.4,pp.575–580,1989.
[18] Yeh, Y.C, and Hsu, D.S. “Structural optimization with fuzzy parameters”.Computer and Structure, vol.37,no.6 917–24, 1990.
[19] Y.Luo and C.Yu, “ An fuzzy optimization method for multi criteria decision making problem based on the inclution degrees of intuitionistic fuzzy set,” Journal of Information and Computing Science,vol.3,no.2,pp.146-152,2008.
[20] Zimmermann, H.J., fuzzy linear programming with several objective function” Fuzzy sets and systems,vol.1,pp.45-55,1978.