Fuzzy Optimization Using Direct Crisp and Fuzzy Interval Comparison

Abstract

In real optimization tasks, always there are two main groups of criteria: requirements of outcomes increasing or expenses decreasing and demands of uncertainty reduction, in other words, risk minimization. Therefore, it seems advisable to formulate optimization problem under conditions of uncertainty as, at least, two-objective on the basis of local criteria of benefits increasing or expenses reduction and risk minimization. Generally, risk may be treated as the uncertainty of result obtained. In a situation considered, the degree of risk (uncertainty) may be defined in natural way as width of final interval of target function at the point of obtained optimum. To solve the problem briefly described above, the technique of two-objective crisp and fuzzy interval comparison has been developed on the base of probability approach to interval comparison taking into account the relation of compared intervals widths. To illustrate the efficiency of method proposed, the simple example of minimization in the case of interval double-extreme discontinuous cost function of real argument is presented.