Standard goal programming with fuzzy hierarchies: a sequential approach

This paper proposes a pragmatic model for multi-objective decision-making processes involving clusters of objectives which have a decisional meaning for the decision maker (DM). We provide the DMs with a comfortable tool that allows them to express their preferences both by comparing criteria of the same cluster and via the comparison between the different clusters. In standard goal programming the importance of the goals is modeled by the introduction of preferential weights or/and the incorporation of pre-emptive priorities. However, in many cases the DM is not able to establish a precise preference structure. Even in the case of precise weights the solution does not match necessarily the relative weights or, in the case of precise pre-emptive priority, the result could be very restrictive. In order to overcome these drawbacks, in this paper the normalized unwanted deviations are interpreted in terms of achievement degrees of the goals and fuzzy relations are used to model the relative importance of the goals. Thus, we show how several methodologies from the fuzzy goal programming literature can be tailored for solving standard GP problems. We apply this new modeling to problems where there is a "natural" clustering between goals of the same class. We address this situation by solving two phases; in the first one each class is handled separately taking into account the hierarchy of their goals and, in the second phase, we integrate the results of the first phase and the imprecise hierarchy of the different classes. We formulate a new goal programming model called as sequential goal programming with fuzzy hierarchy model. Because many real situations involve decision making in this environment, our proposal can be a useful tool of broad application. A numerical example illustrates the methodology.