One of the tenets of multiattribute value theory is that each attribute (criterion) must be preferencial independent from each other. There are however specific cases where this assumption do not hold. In these cases, one can proceed by building a value function based on the set of attributes that are preference dependent. For instance, the visual quality of a forest depends on attributes as the size of the trees, the density of the forest stand, the diversity of species, and the diversity of distinct heights. There are preference dependencies among these attributes. How can I assess a value function for the objective "maximize the visual quality of a forest" based on these attributes?
Hi Luiz. Thank you very much for your answer. Indeed both Choquet integral as well as Clemen and Reilly's book do focus ways to tackle this problem. However both approaches just model the interdependence between two attributes. Whenever there are more than just two (n>2) attributes, the procedure is not so straightforward. I am aware of other approaches, but they alll seem to have an assessment procedure just too elaborated to be carried out in practice (however not at all impossible). My question is also practical-oriented, as I would also like to know what kind of assessment procedures practicioners usually use to assess a preference-dependent vale function, in particular for an objective as forest aesthetics. I appreciate your answer though.
Thank you very much for your help, Luiz. I really would like to see the heuristic procedure you mentioned (can you please send it to [email protected]). On the other hand, I am not yet aware of the way I should proceed using Choquet integral to compute the measures of interaction all at once as fuzzy measures. I am planning to read your papers in order to grasp it. Looking forward to receive news from you...
When I come to cases like this, what I do is to "Merge" the two criteria into only one and constuct a scale on the meaningfull impact levels. An example could be: If "Tall Trees" should get a high score if the forest is "Dense" but a low score if the forest is Sparse then, the two criteria (Tree size and Forest Density) can be merged in only one criteria with meanigfull impact levels like "1)Tall Trees - Dense Forest; 2)Tall Trees- Sparse Forest; 3)Small Trees - Dense Forest and 4) Small Trees- Sparse Forest). This is the only solution I know for No Preferential Independence.
You might want to look at the Analytic Hierarchy Process - - - a Google search will more than get you started. // jlf