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

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

Preference information modeling by empty interaction index based on monotone measure

In this paper, we consider the monotone measure identification issue from the perspective of the Shapley importance and interaction index, and propose Shapely importance and interaction index oriented monotone measure identification methods. We investigate some properties of the probabilistic interaction indices of the empty set, analyze the meaning of the Shapely interaction index of the empty set in the context of multicriteria decision analysis, and propose the maximum and minimum empty set interaction principles based monotone easure identification methods

A choquet capacity and integral based method to identify the overall importance of engineering characteristics in quality function deployment

Deriving the overall importance of engineering characteristics from the information of the house of quality is one of the primary tasks in the quality function deployment. In this paper, we consider the information processing of house of quality as the multicriteria ordered sorting or classification problem, in which the multiple engineering characteristics are regarded as the multiple criteria, the partial evaluations of products on multiple engineering characteristics as the multiple inputs, and the customer perceptions of products in terms of ordered classes as the aggregate outputs. Given this consideration, we adopt the Choquet capacity to describe the importance degrees of engineering characteristics as well as the correlations among engineering characteristics, employ the Choquet integral to represent the grades of products on customer requirements, and construct the Choquet capacity and integral based methodology to derive the overall importance of engineering characteristics. The steps of the proposed methodology are discussed in detail and also illustrated with a digital camera design example