Dissolution of Dilemma by Newly Defining Criteria Matrix in Anp

Abstract In a decision-making process, one finds that there are alternatives which can be categorized into several groups, based on his or her perspectives, and/or on expected outcome, such as whether his or her choice brings about gains or losses, or that such a choice is right or wrong. Besides, there are many cases with a dilemma where it is hard to select the best choice through transitive relations. This paper presents a new method to dissolve this dilemma by using ANP (Analytic Network Process) with a newly defined criteria matrix. The case of the super-matrix of ANP is examined in an alternative matrix with a dilemma. The paper shows mathematically that the eigenvector of the super-matrix serves as a solution to this simple dilemma, describes the proposed method, and attempts to apply this method to other dilemmas. The proposed method is limited to up to three alternatives.