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2016 Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints
A. Srinivasan, G. Geetharamani
J. Appl. Math. 2016: 1-11 (2016). DOI: 10.1155/2016/8496812

Abstract

Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

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A. Srinivasan. G. Geetharamani. "Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints." J. Appl. Math. 2016 1 - 11, 2016. https://doi.org/10.1155/2016/8496812

Information

Received: 16 August 2015; Accepted: 3 November 2015; Published: 2016
First available in Project Euclid: 10 February 2016

zbMATH: 07037297
MathSciNet: MR3448886
Digital Object Identifier: 10.1155/2016/8496812

Rights: Copyright © 2016 Hindawi

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