Abstract
In this paper, a novel fuzzy MADM model with some specifications that make it distinguished from the available methods. Decision matrix is defined as a full fuzzy structure. The model only uses information on the alternatives i.e. does not require pre-assigned weight values for the attributes. The weights will be achieved through a matching mechanism between the obtainable alternatives' preferences and a fuzzy preference relation of the alternatives stated by decision makers. This is applied using a mathematical programming model. Since the resulted model is non-linear and hard to solve using the classic optimization methods, Simulated Annealing is proposed to find optimum or near optimum weights. Having the weights of attributes, the alternatives' ranking is determined using the statistical measures of their fuzzy values. The model is applied on the project selection problem to study its efficiency and applicability to MADM problems.
Highlights
Multi-criteria decision making can be characterized as making preferred decisions through evaluation, prioritization or selection of alternatives in the presence of multiple, usually conflicting criteria
The attributes' weights are determined by minimizing the difference between decision makers' fuzzy preference relation and the preference of alternatives resulted from aggregating the values of decision matrix
In order to calculate the weights of attributes, the preference relation derived from the overall evaluation values of alternatives will be compared with the preference relation of alternatives stated by decision makers
Summary
Multi-criteria decision making can be characterized as making preferred decisions through evaluation, prioritization or selection of alternatives in the presence of multiple, usually conflicting criteria. MADM refers to making decisions in a discrete decision space which is characterized by the explicit description of the set of alternatives and the attributes involved in the evaluation process. This type of problems arise in many real-world situations, e.g. the project selection or prioritization problem. In many real world decision problems various kinds of uncertainty and vagueness exist which make the models more complex In such situations, only for a small part of involved attributes, we can give exact assessments. The most important and well-known approach proposed to handle the uncertainty in various systems is fuzzy set theory first introduced by Zadeh.2 It has been increasingly applied in processing imprecise and uncertain information.
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