Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints
Autor: | G. Geetharamani, Arumugam Srinivasan |
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Rok vydání: | 2016 |
Předmět: |
Mathematical optimization
Fuzzy classification Article Subject Mathematics::General Mathematics lcsh:Mathematics 020209 energy Applied Mathematics Fuzzy set 02 engineering and technology Interval (mathematics) lcsh:QA1-939 Type-2 fuzzy sets and systems Defuzzification Fuzzy mathematics 0202 electrical engineering electronic engineering information engineering Applied mathematics Fuzzy number Fuzzy set operations 020201 artificial intelligence & image processing Mathematics |
Zdroj: | Journal of Applied Mathematics, Vol 2016 (2016) J. Appl. Math. |
ISSN: | 1687-0042 1110-757X |
Popis: | 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. |
Databáze: | OpenAIRE |
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