Optimized Solution of Two Bar Truss Design Using Intuitionistic Fuzzy Optimization Technique

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Author(s)

Samir Deya 1,* Tapan Kumar Roy 2

1. Department of Mathematics, Asansol Engineering College, Vivekananda Sarani, Asansol-713305, West Bengal, India

2. Department of Mathematics, Indian Institute of Engineering Science and Technology, (Formally Bengal Engineering and Science University), Shibpur, P.O.-Botanic Garden, Howrah-711103, West Bengal, India

* Corresponding author.

DOI: https://doi.org/10.5815/ijieeb.2014.04.07

Received: 16 May 2014 / Revised: 10 Jun. 2014 / Accepted: 1 Jul. 2014 / Published: 8 Aug. 2014

Index Terms

Truss Design Optimization, Fuzzy Sets, Intuitionistic Fuzzy Sets, Intuitionistic Fuzzy Optimization

Abstract

The main goal of the structural optimization is to minimize the weight of structure or the vertical deflection of loaded joint while satisfying all design requirements imposed by design codes. In general fuzzy sets are used to analyze the fuzzy structural optimization. In this paper, a planer truss structural model in intuitionistic fuzzy environment has been developed. This paper proposes an intuitionistic fuzzy optimization approach to solve a non-linear programming problem in the context of a structural application. This approximation approach is used to solve structural optimization model with weight as objective function. This intuitionistic fuzzy optimization (IFO) approach is illustrated on two-bar truss structural design problem. The result of the intuitionistic fuzzy optimization obtained is compared with the other results of optimization algorithms from the literary sources. It is shown that the proposed intuitionistic fuzzy optimization approach is more efficient than the analogous fuzzy technique for structural design.

Cite This Paper

Samir Dey, Tapan Kumar Roy, "Optimized Solution of Two Bar Truss Design Using Intuitionistic Fuzzy Optimization Technique", International Journal of Information Engineering and Electronic Business(IJIEEB), vol.6, no.4, pp.45-51, 2014. DOI:10.5815/ijieeb.2014.04.07

Reference

[1]Zadeh, L.A. , “Fuzzy Sets”, Information and Control, Vol.8, pp.338-353, 1965.

[2]Bellman, R.E. and Zadeh, L.A. , “Decision-making in fuzzy environment”, Management Science, 17, B141-B164, 1970.

[3]K. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy sets and Systems, 20,87-96, 1986.

[4]Werner,B., “Interactive fuzzy programming systems. Fuzzy sets systems, 23,133-178,1987.

[5]Xu, C. “Fuzzy optimization of structures by the two-phase method”,Computer and Structure, 31(4),575–580,1989.

[6]Yeh, Y.C, and Hsu, D.S. “Structural optimization with fuzzy parameters”.Computer and Structure, 37(6), 917–24, 1990.

[7]Angelov, P.P. Intuitionistic fuzzy optimization. Notes on Intutionistic Fuzzy Sets 1 (2), 123–129, 1995.

[8]K. Atanassov, “Idea for intuitionistic fuzzy sets equation, in equation and optimization,” Notes on Intuitionistic Fuzzy Sets, 1, 17-24, 1995.

[9]Angelov, P.P. Optimization in intuitionistic fuzzy environment. Fuzzy Sets and Systems 86, 299–306, 1997.

[10]K. Atanassov, “Two theorems for Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, 110,267-269, 2000.

[11]Nicholas Ali, Kumaran Behdinan, Zouheir Fawaz, “Applicability and Viability of a GA based Finite Element Analysis Architecture for Structural Design Optimization,” Computers and Structures, 81, 2259-2271,2003.

[12]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.

[13]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

[14]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, 7( 3),189-198 ,2004.

[15]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.

[16]X. Wang, “Fuzzy Number Intuitionistic Fuzzy Arithmetic Aggregation Operators,” International Journal of Fuzzy Systems, 10( 2), pp. 104-111, 2008.

[17]Wei, G.W., Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting. Knowledge-Based Systems 21 (8), 833–836, 2008

[18]Dey.Samir. and Roy,Tapan.Kumar., “Structural Optimization Model with Imprecise Resources” , International Journal of Engineering Sciences & Emerging Technologies,6(3), 287-297,2013

[19]Dhar, Mamoni and Baruah, H .K. "Theory of Fuzzy Sets: An Overview", IJIEEB, 5(3), 22-33, 2013. DOI: 10.5815/ijieeb.2013.03.03

[20]Nasseri, S.H.,Alizadeh, Z. “ Optimized solution of a two bar truss nonlinear problem using fuzzy geometric programming .Journal of Nonlinear Analysis and Application, 2014,1-9,2014.