Abstract :
The economic efficiency (EE) measure in non-convex technologies requires the data of
input/output vectors and prices to be known deterministically. But as regards the data
of the production process in many real-world applications, rather than dealing with crisp
real numbers and crisp intervals, one has to deal with ”approximate” numbers or intervals
of the type that can be described as ”numbers that are close to a given real number.” For
the aforementioned reason, development of the economic efficiency models in such a way
that they can deal with imprecise data, has become an issue of great interest. To this
end, the notion of bounded data and fuzziness has been introduced. This paper develops
a procedure to compute the economic efficiency measures with non-convex technologies in
the presence of uncertain data. In this study, uncertain EE formulas are transformed into
a family of crisp EE formulas and LP models, based on comparison intervals and ?cuts.
To obtain the bounds of the membership functions of efficiencies, we propose a family of
parametric two-level programs. This pair of parametric programming problems gives the
lower and upper bounds of ? cuts corresponding to the membership function of EE.
Then, we prove that the lower bound is computed by some closed form expressions, but to
obtain the upper bound we solve a LP model. Since the efficiency measures are expressed
by membership functions rather than by crisp values, more information is provided for
the management. Moreover, two examples are provided for illustrating the proposed approaches.
