Omid Bozorg-Haddad - A Handbook on Multi-Attribute Decision-Making Methods

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To reach a better understanding of any decision‐making problem, one must employ information‐gathering methods, including but not limited to surveys, questionnaires, examination, and sampling, to collect as much practical information as possible. Eventually, such attempts increase the chance of choosing the most suitable alternative, that would better reflect the needs and interests of the stakeholders of the MADM problem at hand (Tzeng and Huang 2011).

From the MADM point of view, the gathered information regarding the problem in question is generally represented in a matrix form, commonly referred to as the decision‐matrix. Based on the decision‐matrix, the decision‐maker can anticipate the stakeholders' desires and preferences, which eventually lead to choosing the most suitable available option through a mathematically supported framework. The choosing process proceeds and their assumptions are what distinguishes between the MADM methods.

A MADM problem is composed of a set of alternatives, which are the feasible discrete solutions available to the decision‐maker, and a set of evaluation criteria, which are the instruments through which the stakeholders describe their objective. Subsequently, a decision‐matrix in extended form is constructed based on the four following information sets (Yu 1990):

1 (1) The set of feasible alternatives, denoted by {ai | i = 1, 2, …, m}. Notice that each alternative represents a row in the decision‐matrix (D);

2 (2) The set of predefined evaluation criteria denoted by {cj | j = 1, 2, …, n}. Each criterion represents a column in the decision‐matrix (D);