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Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints

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  • A. Srinivasan
  • G. Geetharamani

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.

Suggested Citation

  • A. Srinivasan & G. Geetharamani, 2016. "Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints," Journal of Applied Mathematics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnljam:v:2016:y:2016:i:1:n:8496812
    DOI: 10.1155/2016/8496812
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    References listed on IDEAS

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    1. Yi-hua Zhong & Yan-lin Jia & Dandan Chen & Yan Yang, 2013. "Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, June.
    2. Yi-hua Zhong & Yan-lin Jia & Dandan Chen & Yan Yang, 2013. "Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Jindong Qin & Xinwang Liu, 2014. "Frank Aggregation Operators for Triangular Interval Type‐2 Fuzzy Set and Its Application in Multiple Attribute Group Decision Making," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. Jindong Qin & Xinwang Liu, 2014. "Frank Aggregation Operators for Triangular Interval Type-2 Fuzzy Set and Its Application in Multiple Attribute Group Decision Making," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-24, September.
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