Intuitionistic Fuzzy Optimization of Truss Design: A Comparative Study

  IJCOT-book-cover
 
International Journal of Computer & Organization Trends  (IJCOT)          
 
© 2016 by IJCOT Journal
Volume - 6 Issue - 6
Year of Publication : 2016
Authors :  Biswajit Singh, Mridula Sarkar, Tapan Kumar Roy
DOI : 10.14445/22492593/IJCOT-V37P306

Citation

Biswajit Singh, Mridula Sarkar, Tapan Kumar Roy"Intuitionistic Fuzzy Optimization of Truss Design: A Comparative Study", International Journal of Computer & organization Trends (IJCOT), V6(6):25-33 Nov - Dec 2016, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

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.

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.

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