Decision Making Support and Expert Systems Utility Function Design on the Base of the Paired Comparison Matrix

In the multi-attribute utility theory the utility functions are usually constructed by dots. It concerns both the lottery’s method and the value increasing method. In the both cases the utility function is constructed in the absolute scale [0,1] that causes inconveniences for experts. The comparative assessments look more preferable for decision-makers. The paired comparison matrix (PCM) looks as a natural model representing the preference structure of decision-maker (DM). We use scale points of attributes as a PCM comparative entities. We use also increasing/decreasing entity priority as a criterion. Function of priorities is transformed to utility function on the base of a normalizing function. Such a function allows using the matrix power as parameter affecting the form of utility function. The PCM provides the extended possibilities to DMs to form comparative assessments both the qualitative ones (as better-worse) and the quantitative ones reflecting winnings and losses of DMs. In the paper we consider methods for utility function construction having different forms of its presentation. Among them there are utility functions based on attributes measured in nominal scales.