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Purpose     Different from manufacturing resources allocation problems, the prices and amounts of limited public service resources could not be changed with the consumers’ requirements and social fairness is the most important objective for improving allocation efficiency. To measure social fairness reasonably, the purpose of this paper is fourfold: first, divide social fairness into longitudinal comparative fairness and crosswise comparative fairness, therefore providing their calculation formula and describing the comprehensive fair degree by using the interval numbers. Second, the comparison regulations of interval numbers are given and the corresponding features are also described. Third, an extension of VIKOR method is put forward for evaluating social fairness of different allocation alternatives with interval numbers. Finally, a numerical example illustrates the proposed method and clarifies the main results developed in the paper.     Design/methodology/approach     In this paper, the author depicts the social fair degree as an interval number, and thus proposes the comparison method between any two interval numbers. Based on the basis procedure of the VIKOR method, the paper proposes an extension of the fuzzy VIKOR method with the interval numbers to rank and select the compromise allocation alternatives. Finally, a numerical example illustrates the practicability of the proposed method.     Findings     The comparison of interval numbers is very important when the author evaluates the decision alternatives. Through analyzing the present comparison methods, the paper proposes the simple method of comparing the interval numbers, which can obtain the same results with the above two methods. The fuzzy VIKOR method, a popular multi-criteria decision-making method, focusses on ranking and selecting from a set of alternatives in a fuzzy environment. For the fuzzy value, the paper also proposes the extension of the VIKOR method to perform an evaluation and get the compromise alternatives.     Originality/value     According to the huge customers’ requirement, how to improve their social fair degree has become the focus in public service resources allocation, where the social fair degree may be a comprehensive concept which includes the fair degree compared with all the other allocation alternatives and the fair degree compared with the other small group under the same allocation alternative. In the paper, the author defines the above two types of fair degree and then depicts the comprehensive fair degree as their integration, which will be interval numbers.

Limited public resources allocation model based on social fairness using an extended VIKOR method