Normalization method for quantitative and qualitative attributes in multiple attribute decision-making problems

Abstract

In decision-making problems, attributes can be classified as quantitative or qualitative according to their nature. For quantitative attributes, it is often necessary to normalize their values for further treatment since they are usually expressed with different measurements and scales. On the other hand, linguistic terms used by decision-makers to express their preference on qualitative attributes need to be transformed into numerical values according to linguistic-number dependencies. However, existing methods devoted to normalizing quantitative attributes and expressing the linguistic terms with numerical values have some important limitations. As a first contribution, we discuss the main deficiency in the functions commonly used to normalize quantitative attributes. Our second contribution is devoted to introducing a new property that counteracts the detected limitations, preparing the ground to present a standardization format for quantitative attributes. Our last contribution consists of a new format to transform the linguistic terms into numerical values that consider the significance of each linguistic term for the experts. Towards the end, these contributions are synthesized into a new procedure to generate a normalized consensus matrix when solving decision-making problems.