Fuzzy Multiple Attribute Decision Making Methods

Abstract

A MADM problem is given as:

$$\text{D=}\begin{matrix} {{\text{A}}_{1}}\\ {{\text{A}}_{2}}\\ \vdots\\ {{\text{A}}_{\text{m}}}\\ \end{matrix}\text{ }\left[\begin{matrix} {{\text{X}}_{1}}\text{ }{{\text{X}}_{2}}\text{ }\cdots \text{ }{{\text{X}}_{\text{n}}}\\ {{\text{X}}_{11}}\text{ }{{\text{X}}_{12}}\text{ }\cdots \text{ }{{\text{X}}_{1\text{n}}}\\ {{\text{X}}_{21}}\text{ }{{\text{X}}_{22}}\text{ }\cdots \text{ }{{\text{X}}_{\text{2n}}}\\ \vdots \text{ }\\ {{\text{X}}_{\text{m1}}}\text{ }{{\text{X}}_{\text{m2}}}\text{ }\cdots \text{ }{{\text{X}}_{\text{mn}}}\\ \end{matrix}\right]$$

$${\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{w}} = ({{w}_{1}},{{w}_{2}}, \ldots ,{{w}_{n}})$$

where A_i, i = 1, ..., m, are possible courses of action (candidates, alternatives); X_j, j = 1,...,n, are attributes with which alternative performances are measured; x_ij is the performance score (or rating) of alternative A_i with respect to attribute X_j; w_j, j = 1,...,n are the relative importance of attributes.