When seeking a solution to a linear programming problem with fuzzy coefficients in the objective function, some technique must be applied to transform to crisp values, or to translate these fuzzy elements to real values. What techniques do you suggest?
Aas I understand at present there is maybe one than more techniques to do that
There are many ways. In the attached paper, asymmetric trapezoidal membership function, defuzzified procedures is conducted based on the lower bound and upper bound of the optimal values.
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There is a huge literature on "robust" optimisation and "stochastic" optimisation. In that literature, you will find several different ways of handling uncertainties in the coefficients.
To convert the fuzzified value into a crisp value, defuzzification has to be done. There are many defuzzification methods/techniques are available in the literature. Some of those methods are signed distance, graded mean integration, regular weighted point, centroid, ranking, etc.
Dear Nancy
Once after defuzzification, you got crisp values; what stops you to use them in LP?
I am just exploring different methods for this phase, but as you said, once the defuzzification is done I will find the solution. I particularly want to explore alpha-cuts based methods. Thank you very much for your valuable answers.
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