Decision-Making Based on Multi-Attribute Value Theory Under Preference Uncertainty

This paper advances the multi-attribute value theory to take into account the uncertainty of the decisionmaker’s preferences with respect to the value of assessments and importance of attributes. It considers the basic steps of the original method of multi-attribute value theory against the modified one. The modified method can use the decisionmaker’s responses as fuzzy triangular numbers to construct single-attribute value functions and to find the scaling coefficients. The paper presents an approach to finding fuzzy scaling coefficients by comparing paired matches and generating a system of linear equations with fuzzy coefficients. It is proposed to solve the system of equations by representing it as a set of systems of interval equations derived by splitting fuzzy sets by α levels. Multi-attribute fuzzy assessment of alternatives is carried out by solving linear programming problems based on systems of equations pertaining to individual α levels. The paper provides an example of using the modified method for multi-attribute comparison of alternatives. Keywords—decision-making, value theory, fuzzy number, interval