A novel approach for ontological representation of analytic hierarchy process

The Analytic Hierarchy Process (AHP) is one of the widely accepted and frequently used priority assessment methods. A number of studies, which employed the AHP method, have already been carried out in different domains to support their multi-criteria decision-making definitions and applications. However, few researchers have paid attentions to extract and represent the important concepts and their relationships from the AHP method itself. The aim of this study is firstly to propose a way for representing the AHP method as an AHP Ontology together with a set of reasoning rules. Then, a prototype assessment tool is developed to show the possibility of obtaining more flexibility and reusability of this ontological representation. Introduction The Analytic Hierarchy Process, which is proposed by Saaty [1] since the 1970s, is one of the widely accepted and frequently used mathematic analysis method that supports multi-criteria decision-making. A significant number of research projects employed the AHP method to support decision-making in their works and have already been benefited from it [2]. Meanwhile, keeping pace with these increasing needs, the development of decision-making tools based on the AHP method has attracted many attentions of some software companies, such as, Decision Lens, Expert Choice, and Logical Decision. However, among these research projects and implemented toolkits, little work has been done in specifying and formalizing the important concepts together with their relationships from the AHP method itself. Recently, this existing issue is noticed by some researchers, who began to apply a kind of incomplete ontological representation of the AHP method in their decision-making approaches. For example, Kornyshova and Deneckère [3] proposed a Decision Making Ontology, which aims to formalize the concepts and their relationships inside the knowledge that related to decision-making procedures and the AHP method, for supporting the decision-making during the information systems engineering. Tran, et al. [4] developed a QoS ontology to describe the information about Web Services in detail and a QoS-based algorithm that adopted the AHP method as the evaluation mechanism to assist Web Services ranking. Wasielewska, et al. [5] presented a domain ontology, which captures the concepts that are needed by an AHP algorithm, for assisting an user in specifying required resources to execute a job and then to evaluate the contract proposals based on the those resources and their comparisons. Although efforts have been made by these researches, several existing drawbacks still can be found as follows: (i) Some researches only propose a class hierarchy in an ontology to capture the concepts from the AHP method, but without specifying the relationships 1 Decision Lens: http://www.decisionlens.com/ 2 Expert Choice: http://expertchoice.com/ 3 Logical Decision: http://www.logicaldecisions.com/ between these concepts; (ii) There exist some researches, which formalized both concepts and their relationships from the AHP method. However, the evaluation mechanisms in the AHP method are always designed as part of fixed algorithms that are embedded inside priority assessment tools; (iii) The ontological representation of the AHP method is usually mixed with the information that are needed to be assessed, which lacks of flexibility and reusability. Therefore, there remain needs for an approach to address these limitations. The purpose of this paper is to propose a way to ontologically represent the AHP method, which not only specifies the concepts and their relationships that are necessary for applying the AHP method, but also realizes the priority assessment and consistency evaluation mechanisms in the AHP method through corresponding reasoning rules. In the remains of this paper, a brief introduction of the AHP method is firstly given to describe the background of our proposition. Then, the proposed ontological representation is presented to highlight our contribution. After that, a priority assessment prototype, based on the ontological representation, is used to show the possibility of obtaining more flexibility and reusability. At the end, we conclude this paper and discuss on future works. The Analytic Hierarchy Process (AHP) The priority assessment in the AHP method is based on the mathematical analysis of a set of pairwise comparisons, in which, the priority scales between each two related terms are relying on the professional judgments of domain experts [6]. Of course, these human judgments may not be always consistent. The AHP method also provides a theory of consistency evaluation to assist experts to improve their judgments and to obtain better consistency [7]. In general, the process of applying the AHP method can be divided into the following five steps: (1) Define a problem area and determine a goal (the top level) of the decision-making. (2) Select a set of evaluation criteria (the intermediate level) and a set of alternatives (the lowest level) to structure a decision hierarchy. An example of this hierarchy can be seen in Fig. 1. Fig. 1. An Example of the Decision Hierarchy (3) Generate a set of pairwise comparison matrices, in which, all compared terms in a matrix are in the same level of the decision hierarchy and all comparisons in a matrix are with respect to a related term from upper level. Let 1 term , ... , n term be the set of criteria or alternatives in a matrix and the set of comparison weights between each two terms are 11 w , ... , nn w that are with respect to a j term in the upper level. An example of this matrix can be seen in Fig. 2.