Intelligent Clustering Learning & Modelling Negative Dependencies In Analytic Network Process with an Application to Proposed Legalization Gambling In Hainan, China

Ma Xutong

Abstract

In many complex real-life decision making problem, interdependence among different criteria for is very common. To represent the real world scenario in a more complete and realistic way, interdependence are un-negligible when evaluating and comparing different alternatives. Analytic Network Process proposed by Professor Thomas Saaty in 1980 utilizes a network of different clusters (goal, criteria and alternatives) with interaction arcs to represent dependencies. It is recommended to use control hierarchy (with a few control criteria) to serve as clusters of criteria. However, in real world complex situations, it may be hard to classify all criteria into control criteria properly because some criteria can have influence on multiple perspectives. Therefore, there is a need for a better clustering method to cluster all criteria according to their similarity and maintain the high efficiency of ANP.

In addition, a criterion can either amplify or reduce the effect of other criteria, which means dependencies can be either positive or negative. However, in current ANP model, only positive numbers are allowed to enter the super matrix because of the constraint of a stochastic matrix.

This paper proposes two modifications of the ANP model construction process to address these two issues in current ANP model. Firstly, a standardized clustering procedure is proposed to group criteria according to their similarity. Hierarchical clustering algorithm is utilized to perform the cluster analysis. Secondly, transpose partial super matrix is proposed to represent negative dependencies in an ANP model.

A case application to China’s potential opening of the gambling industry is done to illustrate how the proposed methods work in a real life complex decision making problem. Proposed clustering procedure will make the classification of lower level criteria and pairwise comparison of lower level criteria easier. The partial matrix transpose method enables the ANP model to represent negative dependencies and from the results of modified ANP model it can be seen that alternatives’ priority vector will change after introducing negative dependencies. The proposed method is able to perform cluster analysis of lower level criteria in a standardized yet flexible way. It can also simplify the pairwise comparison process for the experts. The partial matrix transpose method makes sure both positive and negative dependencies can be included in the ANP model and give a fair representation of a complex situation.