#### Derivation and Comparative Study on Centroid Ranking Value of TrIFN and Apply on Fuzzy Geometric Programming

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##### Author(s)

1. Dr.B.C.Roy Polytechnic, Department of Computer Science, Durgapur, 713206, India

* Corresponding author.

Received: 27 Apr. 2015 / Revised: 6 Sep. 2015 / Accepted: 18 Nov. 2015 / Published: 8 Mar. 2016

##### Index Terms

Centroid ranking method, geometric programming, fuzzy number, generalized intuitionistic fuzzy number, Trapezoidal Intuitionistic Fuzzy Number, membership and non membership value

##### Abstract

Ranking fuzzy numbers has become an important process in decision making. Many ranking methods have been proposed thus far and one of the commonly used is centroid of trapezoid. Here we try to derive detail mathematical derivation of centroids of a Trapezoidal Intuitionistic Fuzzy Number along x and y axis. After that we derive the ranking value from two centroid along x and y axis. At the end of the article ranking value on fuzzy geometric programming is used. Here we are dealing with three strong decision making concepts. Intuitionistic trapezoidal fuzzy system is much more decision oriented approach than normal fuzzy number in real life uncertain environment, where we can apply membership and non membership concept for analyzing any real life situation. Ranking value, based on centroid of any Trapezoidal Intuitionistic Fuzzy Number helps for conclusion derivation in quantitative way. We here choose most powerful non linear optimization tool, geometrical programming technique, for generating any decision, using Trapezoidal Intuitionistic Fuzzy Number with centroid ranking approach.

##### Cite This Paper

Soham Bandyopadhyay, "Derivation and Comparative Study on Centroid Ranking Value of TrIFN and Apply on Fuzzy Geometric Programming", International Journal of Information Technology and Computer Science(IJITCS), Vol.8, No.3, pp.67-74, 2016. DOI:10.5815/ijitcs.2016.03.08

##### Reference

[1]L. A. Zadeh, Fuzzy sets, “Information and Control”, Vol. 8, pp.338- 356, 1965.

[2]K. Atanassov, “Intuitionistic fuzzy sets, Fuzzy Sets and Systems”, Vol. 20, pp.87-96, 1986.

[3]Delgado, M., J. L. Verdegay and M. A. Vila. 1988. “A Procedure for Ranking Fuzzy Numbers Using Fuzzy Relations”, Fuzzy Sets and Systems. 26(1): 49–62.

[4]S.S.Rao, “Engineering Optimization: Theory and Practice, Fourth Edition”, Chapter-8 Geometric Programming.

[5]Chen, L. H. and H. W. Lu. 2001. “An Approximate Approach for Ranking Fuzzy Numbers Based on Left and Right Dominance. Computers and Mathematics with Applications. 41(12): 1589–1602.

[6]K. Atanassov, “More on intuitionistic fuzzy sets, Fuzzy Sets and Systems”, Vol.33, pp.37- 46, 1989.

[7]Bing-Yuan Cao, Xiang-Jun Xie,” Fuzzy Engineering and Operations Research”.

[8]Buckley J., “Joint solution to fuzzy programming problems”, Fuzzy Sets and Systems. 1995; 72:215-220.

[9]Jain, R. 1976. “Decision-making in the Presence of Fuzzy Variables” .IEEE Transactions on Systems, Man. and Cybernatics. 6(10): 698–703.

[10]S. P. Boyd, S.-J. Kim, D. D. Patil, and M. A. Horowitz, “Digital circuit optimization via Geometric programming,” Operations Research, vol-53, no. 6, pp. 899–932, 2005.

[11]Chia-Hui Huang,” Engineering Design by Geometric Programming”, Mathematical Problems in Engineering Volume 2013 (2013), Article ID 568098, 8 Pages.

[12]Pranab Biswas, Surapati Pramanik,” Application of Fuzzy Ranking Method to Determine the Replacement Time for Fuzzy Replacement Problem”, International Journal of Computer Applications (0975 – 8887) Volume 25– No.11, July 2011.

[13]R. Jain,” Decision-making in the presence of fuzzy variable”, IEEE Transactions on Systems, Man, and Cybernetics, 6:698-703, 1976.

[14]R. Jain,” A procedure for multi-aspect decision making using fuzzy sets”, International Journal of Systems Science, 8:1-7, 1977.

[15]S. Bass and H. Kwakernaak.,”Rating and ranking of multiple-aspect alternatives using fuzzy sets”, Automatica, 13:47-58, 1977.