Multi-attribute Decision Making: Theories, Methods, And Their Applications

It has become more and more difficult to see the world around us in a unidimensional way (i.e., only in a single criterion). We always compare, rank, and order the objects with respect to"multiple criteria of choice".The problem of multiple criteria decision making can be broadly classified into two categories: Multiple Attribute Decision Making (MADM), and Multiple Objective Decision Making (MODM). In actual practice this classification is well fitted to the two facets of problem solving---MADM is for selection (evaluation), MODM is for design. This is a widely accepted classification. Research on MADM problems dated from 1957 when Churchman et. al. first treated a MADM problem (selecting business investment policy) by using simple additive weighting method. It has only 30 years history, and is 61 years late contrasting with research on MODM problems (started in 1896). Its theory method and applications must be enhanced. Although it is younger, it has become more and more valuable in practical applications. This urges us to study it further.This paper use a lots of space to review relevant problems in MCDM and MADM (one branch of MCDM) in detail. Then, important contents of MADM-----theory on attributes and solutions, improvement on existing methods and presenting of new methods, sensitivity analysis on methods and its applications are studied thoroughly.(1) The research results on attributes consist of: Firstly, other new methods for normalizing the existing attributes (profit, cost, fixation, and interval attributes) are given. Then, two new kinds of attributes (called"deviation"and"deviating interval") are defined, and methods for normalizing them are presented. Especially, the relationships between these six kinds of attributes are obtained and proved: from both the definitions of the attributes and the methods for normalizing the attributes, we conclude that the deviating interval attribute is a generalization for the deviating one, the deviating attribute is a generalization for the profit one; the interval attribute is a generalization for the fixation one, the fixation attribute is a generalization for the cost one. The usage and characteristics of all the methods for normalizing the six kinds of attributes are given.(2) The research results on solutions consist of: Based on (1), the concepts of solutions (including optimal solution, non-inferior solution and weak non-inferior solution, etc.) only suitable for MADM problems with only profit and cost attributes are generalized in order to apply to MADM problems with the six kinds of attributes. The relationships between these generalized solutions are proved to be same with the original ones.(3) Research on methods: Based on (1) and (2), twelve methods given by abroad and internal scholars (for example, Dominance, Conjunctive Method, Simple Additive Weighting Method, TOPSIS, and Two kinds of Two-base point methods) are generalized and improved. Especially, a new closeness to the ideal solution is introduced, and a new corresponding method is...