Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

Abstract

The decision maker's preference information on the importance and interaction of decision criteria can be explicitly described by the probabilistic interaction indices in the framework of the capacity based multicriteria decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices of the empty set, and propose the maximum and minimum empty set interaction principles based capacity identification methods, which can be considered as the comprehensive interaction trend preference information oriented capacity identification methods. Then, by introducing the deviation variables, the goal constraints, as well as the goal objective function, we give a new and more flexible approach to representing the decision maker's explicit preference information on the kind and degree of the interaction of any given combination of decision criteria as well as on the degree of the importance of any decision criterion, and construct the nonempty set interaction indices based capacity identification method, which can be considered as the detailed explicit preference information oriented identification method. Finally, two illustrative examples are respectively given to show the feasibility and applicability of the two kinds of methods. In addition, the comparison analysis between these two kinds of methods and some existing capacity identification methods are also mentioned.

Probabilistic bipartition interaction index of multiple decision criteria associated with the nonadditivity of fuzzy measures

“…The capacity identification model usually consists of the following three parts: the first part is the boundary and monotonicity constraints on capacity, see Definition ; the second part is the explicit preference of decision maker on the decision criteria, which is commonly expressed by some constraints of importance and interaction indices; the third part is the identification principle, acting as the objective function of the model, some of which can be described in terms of interaction indices . In the following, we show that all the three parts of the capacity identification model can be uniformly represented in terms of the marginal contributions of criteria.…”

“…The decision‐maker’s preference on the importance and interactions can be given by some basic comparison relationship or by interval form, for example, the importance of criterion is less than that of criterion , the interaction of criteria is positive, the interaction of criteria is greater than that of criteria , the interaction of criteria is less than that of criteria , and the interaction of criteria belongs to the interval . As for the objective function, for simplification, we can just maximize or minimize the interaction of some subsets, see …”

Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

“…For some given alternatives, the decision makers can also provide his/her preference about them, generally a ranking order for some alternatives, or dominance among some pairs of alternatives; in some situations, even be able to give the desired overall evaluation values of the alternatives. This preference information on the alternatives actually reflects the decision maker's preference on the decision criteria too, hence can be considered as implicit preference information …”

“…With the explicit and implicit preference information, as well as the boundary and monotonicity conditions on the capacity, we usually only get a feasible region of capacities from which the complete ranking order on the decision alternatives cannot be obtained directly. To find this ranking order, some selection principle should be adopted to obtain the most desired capacity, like the maximum entropy principle, the compromise principle, the interaction index oriented principle, the Multiple Criteria Correlation Preference Information based least square and absolute deviation principles, and learning set based principles . It is quite possible that different principles lead to different ranking orders of decision alternatives even using the same feasible capacity region.…”

“…This preference information on the alternatives actually reflects the decision maker's preference on the decision criteria too, hence can be considered as implicit preference information. [17][18][19] The most common way to calculate the overall evaluations of all alternatives is to find the most representative capacity to optimally describe the initial preference information, known as capacity identification methods. 6,11,12,[18][19][20] With the explicit and implicit preference information, as well as the boundary and monotonicity conditions on the capacity, we usually only get a feasible region of capacities from which the complete ranking order on the decision alternatives cannot be obtained directly.…”