Adaptation of a Cluster Discovery Technique to a Decision Support System

Introduction In every day decision making there are very few decisions made without a number of competing alternatives. A decision maker must choose an alternative by evaluating a number of criteria. As the number of alternatives and criteria increases, the task of selecting the best alternative becomes increasingly difficult. A typical multi-criteria multi-alternative decision making model can be represented by a matrix, such as shown in Table 1, with M number of alternatives and N criterion such that i = 1,2,3, . , m and j = 1,2,3, . , n [14]. Each element of the matrix [a.sub. ij] indicates the user's response to alternative Ai when it is evaluated in terms of criterion [C.sub. j]. To accommodate the importance of different goals or criteria a weight value, sometimes referred to as decision weight, is associated with each criterion that signifies the importance of the criterion. A numeric value is then assigned to each cell in the matrix by the decision maker that represents the level of significance a criterion may have within a particular alternative. The populated matrix is then manipulated and a rank ordering of the alternatives is obtained. The best alternative considering the inputs by the decision maker can then be selected. Depending on the number of criteria and the units upon which each is evaluated determining the best alternative becomes a complex task. In this paper, we are proposing a modification of a clustering technique that indicates the degree of closeness of a vector to a vector representing an alternative. The alternative choices employed are different disorders of the eye and the criteria are different symptoms of the eye disorders. An alternative is determined by the cluster discovery technique ART1, an unsupervised cluster discovering technique using the set of values for 10 different symptoms. ART1 is then modified and the closeness of the new set of values representing the user's symptoms to different clusters is determined. The closest matching alternative to the given symptoms is returned by the system. This allows for determination of the best matching disorder to the set of symptoms. This paper is organized as follow. First, some typical multi-criteria decision methods (MCDM) that are utilized to validate our design are discussed. We then present the clustering technique used and the modifications of its algorithm. The results of comparisons between the typical MCDM models and our design are then presented. Finally, the implementation of and the development of future related work we are currently engaged in are discussed. MCDM Methods Different MCDM methods have been proposed for the numeric manipulation of a decision matrix to arrive at the best alternative (Chen, & Hwang, 1991; Hwang, & Yoon, 1981; Zimmerman, 1996). The first stage of processing the matrix is manipulation of the criteria to obtain a value that can best represent each alternative. However, depending on the type of values being considered, the operation may not be a straightforward process. For example, a manager is trying to decide between three different venders. The criteria on which the alternatives are compared include price, delivery cost, and restocking cost for the surplus. Each criterion is evaluated based on its dollar value and the lower the values the more attractive the alternative. The criteria are said to be homogeneous and along the same dimension. They are both costs, measured in dollar terms, and the lower the cost the better the alternative. However, if the choices are between foreign and domestic vendors one of the criterion might be the delivery time. The criteria, cost value verses time, are along different dimensions. That is, of course, to assume that time can not be measured in dollar terms. Thus it is not clear the type of operations that would result in the most accurate representation for the criteria (Hamalainen & Salo, 1997). …