Integrated evidential reasoning approach in the presence of cardinal and ordinal preferences and its applications in software selection

• We propose an integrated evidential reasoning (IER) approach considering cardinal and ordinal assessments.
• We design three optimization models to generate integrated value functions of alternatives.
• Coexistence of cardinal and ordinal assessments of alternatives on specific attribute is considered in the IER approach.
• Complete and incomplete cardinal and ordinal assessments are considered in the IER approach.
• Precise and imprecise attribute weights are considered in the IER approach.

A combination of cardinal and ordinal preferences in multiple-attribute decision making (MADM) demonstrates more reliability and flexibility compared with sole cardinal or ordinal preferences derived from a decision maker. This situation occurs particularly when the knowledge and experience of the decision maker, as well as the data regarding specific alternatives on certain attributes, are insufficient or incomplete. This paper proposes an integrated evidential reasoning (IER) approach to analyze uncertain MADM problems in the presence of cardinal and ordinal preferences. The decision maker provides complete or incomplete cardinal and ordinal preferences of each alternative on each attribute. Ordinal preferences are expressed as unknown distributed assessment vectors and integrated with cardinal preferences to form aggregated preferences of alternatives. Three optimization models considering cardinal and ordinal preferences are constructed to determine the minimum and maximum minimal satisfaction of alternatives, simultaneous maximum minimal satisfaction of alternatives, and simultaneous minimum minimal satisfaction of alternatives. The minimax regret rule, the maximax rule, and the maximin rule are employed respectively in the three models to generate three kinds of value functions of alternatives, which are aggregated to find solutions. The attribute weights in the three models can be precise or imprecise (i.e., characterized by six types of constraints). The IER approach is used to select the optimum software for product lifecycle management of a famous Chinese automobile manufacturing enterprise.