Development and Application of LINMAP, PROMETHEEIV, and FIS in Continuous Multi-Criteria Decision-Making Problems

MCDM problems can be classified into multi-attribute decision making and multi-objective decision-making. In MADM methods, the decision space is discrete and there are a limited predetermined alternative, and preferred alternative has a total performance better than other alternatives in all criteria. Until now different version of out-ranking methods are used for decision making in discrete space while evaluated and ranked some predetermined options using several constant criteria. In most of multi-criteria decision problems, set of alternatives is not discrete and considered as a continuous sets. In this paper, PROMETHEE-IV, FIS and LINMAP techniques has been used for multi-criteria decision problems with continuous alternatives. Then we have been investigate a problem of continuous multi-criteria decision making, with four criteria and alternatives in continuous space  to evaluate the performance of the proposed method. The results of numerical examples show the capability of the proposed model in finding the preferred point(s).