Qualified decision-making using the fuzzy relation inequalities

This paper takes up the decision-making problem, in which the decision-maker imposes certain qualifications on alternatives. In most cases, the given qualifications are based on human's subjectivity and thus requirements are not sharply defined. For the problem, the paper proposes a fuzzy translation between vague requirements and criteria for evaluated alternatives. The fuzzy translation is formulated by fuzzy relation inequality, and the criteria on alternatives are obtained from the requirements, using the fuzzy backward reasoning. The resulting criteria are regarded as the weights of the evaluation items. The final aggregated score for each alternative is calculated by using fuzzy measure and fuzzy integrals. The paper also presents an effective way of solving the fuzzy relation inequality.