Interval-Valued Intuitionistic Fuzzy Synthetic Measure (I-VIFSM) Based on Hellwig’s Approach in the Analysis of Survey Data

Several complex phenomena are measured with the use of tools in the form of a questionnaire where the values of criteria are assessed by the respondents using ordinal scales. Therefore, a special method of construction of synthetic measure is needed which takes into account the fact that such measurement scale allows only to determine the relationship between the states of objects: diversity, equality, minority, and majority. The main goal of this study is to propose a synthetic measure based on Hellwig’s approach and the interval-valued intuitionistic fuzzy set theory which allows to measure complex social phenomena under uncertainty, including data from questionnaire surveys. First, the method of converting ordinal data from questionnaires to interval-valued intuitionistic fuzzy sets (I-VIFS) is proposed. Next, the method of constructing a synthetic measure for I-VIFS is presented. Finally, through this synthetic measure, the optimism coefficient is defined, which allows to set the limits of the intervals for I-VIFS parameters. The usefulness of the proposed approach is showed using the results of a questionnaire survey of the subjective quality of life of inhabitants of selected communes in Poland. Results indicate that the synthetic measure is suitable and effective to evaluate complex phenomena based on ordinal data from questionnaire surveys under the conditions of measurement uncertainty. Moreover, the use of the concept of the optimism coefficient increases the flexibility of its application.