Credibility constrained programming, initially introduced by Liu and
Iwamura (1998), is useful in the presence of other weak sources of information;
computing with possibilities is much simpler than with
probabilities (Zhang et al., 2012). Analogous to chance constrained programming
with stochastic parameters, it is assumed that the constraints
will hold with at least possibility α in a fuzzy environment, and the
chance is represented by the possibility that the constraints are satisfied. Generally, the credibility constrained programming is proposed
based upon credibility measure. The most-used credibility measure
was proposed by Liu and Liu (2002) which can only simulate fuzzy relationships
between a fuzzy variable and a deterministic parameter.
Thus, the derived credibility programming methods can be grouped
into two types, which can solve models with credibility constraints
and/or credibility objectives. As for the fuzzy model with credibility
constraint, most credibility programming model can only handle fuzzy
parameters in one-side of the constraints