International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 7, No. 5, 8 Apr. 2015
Cover page and Table of Contents: PDF (size: 360KB)
Multi-objective Structural Optimization Using Fuzzy and Intuitionistic Fuzzy Optimization Technique
Full Text (PDF, 360KB), PP.57-65
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Author(s)
Samir Deya
1,*
Tapan Kumar Roy
2
Index Terms
Multi-Objective Optimization, Fuzzy Optimization, Intuitionistic Fuzzy Optimization, Membership Function, Non Membership Function, Structural Optimization
Abstract
In this paper, we develop an intuitionistic fuzzy optimization (IFO) approach for optimizing the design of plane truss structure with multiple objectives subject to a specified set of constraints. In this optimum design formulation, the objective functions are the weight of the truss and the deflection of loaded joint; 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. The test problem includes a three-bar planar truss subjected to a single load condition. This multi-objective structural optimization model is solved by fuzzy optimization approach as well as intuitionistic fuzzy optimization approach. 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.
Cite This Paper
Samir Dey, Tapan Kumar Roy, "Multi-objective Structural Optimization Using Fuzzy and Intuitionistic Fuzzy Optimization Technique", International Journal of Intelligent Systems and Applications(IJISA), vol.7, no.5, pp.57-65, 2015. DOI:10.5815/ijisa.2015.05.08
Reference
[1]Wang,G.Y.,Wang, W.Q., “ Fuzzy optimum design of structure.” Engineering Optimization, 8,291-300,1985.
[2]L. A. Zadeh, Fuzzy set, Information and Control, vol.8, no.3, pp.338-353, 1965.
[3]R.E. Bellman and L.A. Zadeh, Decision-making in a fuzzy environment, Management Science, 17(4), B141-B164, 1970.
[4]Zimmermann, H.J., fuzzy linear programming with several objective function” Fuzzy sets and systems,1,45-55,1978.
[5]Dey.Samir.and Roy,Tapan.Kumar., “Structural Optimization Model with Imprecise Resources” , International Journal of Engineering Sciences & Emerging Technologies,6(3), 287-297,2013.
[6]Xu, C. “Fuzzy optimization of structures by the two-phase method”,Computer and Structure, 31(4),575–580,1989.
[7]Yeh, Y.C, and Hsu, D.S. “Structural optimization with fuzzy parameters”.Computer and Structure, 37(6), 917–24, 1990.
[8]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.
[9]Shih,C. J. and Lee, H. W. “Level-cut Approaches of First and Second Kind for Unique Solution Design in Fuzzy Engineering Optimization Problems”, Tamkang Journal of Science and Engineering, Vol. 7, No 3, pp. 189-198 ,2004.
[10]Shih,C.J., Chi,C.C. and Hsiao,J.H. “Alternative -level-cuts methods for optimum structural design with fuzzy resources”, Computers and Structures, 81,2579–2587,2003.
[11]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.
[12]K. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, 20,87-96, 1986.
[13]Angelov, P.P. Intuitionistic fuzzy optimization. Notes on Intutionistic Fuzzy Sets 1 (2), 123–129, 1995.
[14]K. Atanassov, “Idea for intuitionistic fuzzy sets equation, in equation and optimization,” Notes on Intuitionistic Fuzzy Sets, 1, 17-24, 1995.
[15]Angelov, P.P. Optimization in intuitionistic fuzzy environment. Fuzzy Sets and Systems 86, 299–306, 1997.
[16]K. Atanassov, “Two theorems for Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 110,267-269, 2000.
[17]Pramanik, P., Roy, T.K. An intuitionistic fuzzy goal programming approach to vector optimization problem. Notes on Intutionistic Fuzzy Sets 11 (1), 1–14,2004
[18]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 (2006) 15: 239–244.
[19]Jana, B., Roy, T.K., Multi-objective intuitionistic fuzzy linear programming and its application in transportation model. Notes on Intuitionistic Fuzzy Sets, 13 (1), 34–51, 2007.
[20]Dey.Samir. and Roy,Tapan.Kumar., “Optimized solution of two bar truss design using intuitionistic fuzzy optimization technique” , International Journal of Information Engineering and Electronic Business,2014(3), 45-51,2014.
[21]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, 3(2),146-152,2008.
[22]Christensen, P. W., and Klarbring, A., “An Introduction to Structural Optimization” Springer science, 2009.