A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values

For modelling imprecise data the literature offers two different methods: either the use of probability distributions or the use of fuzzy sets. In our opinion these two concepts should be used parallel or combined, dependent on the real situation. Moreover, in many economic problems the well-known probabilistic or fuzzy solution procedures are not suitable methods because neither the stochastic variables have a simple classical distribution nor the fuzzy values are fuzzy numbers or fuzzy intervals. For example in investment problems, the coefficients may often be described by more complex distributions or more general fuzzy sets. In this case we propose to distinguish several scenarios and to describe the parameters of the different scenarios by fuzzy intervals. For solving such stochastic linear programs with fuzzy parameters we propose a new method, which retains the original objective functions dependent on the different states of nature and which is based on the integrated chance constrained program introduced by Klein Haneveld [3] and the interactive solution process FULPAL (FUzzy Linear Programming based on Aspiration Levels), see [6, 7, 8, 9, 10].