Transformation of criteria with a-priori chosen optimal values

Aim of multiple criteria decision-aid (MCDA) methods is to find the best alternative among the ones that are available or to rank alternatives in the order of preference. There are the following core pillars of the methods: the set of criteria and matrix with values of criteria that characterise the evaluated alternatives (decision matrix); and vector of weights that reflect relative importance of criteria. Usually, two types of criteria are used by researchers. Maximising criteria (e.g. profits) reflect a better situation whenever the larger value has been attained. While in case a criterion is minimising (e.g. costs), the better situation is reflected when its value is smaller. Such situations, when the best value of a criterion has a certain value, which differs from the maximal or the minimal, are usually not considered. This paper aims to fill this gap. Such criteria will be named as criteria with a-priori chosen optimal values. The aim of the paper is to propose appropriate types of transformation for criteria with a-priori chosen optimal values. Such transformations appear to be general and can be used with all three types of criteria.