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Interval-Valued Intuitionistic Fuzzy Synthetic Measure (I-VIFSM) Based on Hellwig’s Approach in the Analysis of Survey Data
Mathematics ( IF 2.3 ) Pub Date : 2021-01-20 , DOI: 10.3390/math9030201
Ewa Roszkowska , Bartłomiej Jefmański

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.

中文翻译:

基于Hellwig方法的区间值直觉模糊综合测度(I-VIFSM)

使用问卷形式的工具对几种复杂的现象进行了测量,其中标准的值由受访者使用顺序量表进行评估。因此,需要一种特殊的构建综合度量的方法,该方法考虑到这样一个事实,即这种度量尺度只能确定对象状态之间的关系:多样性,平等,少数和多数。这项研究的主要目的是提出一种基于Hellwig方法和区间值直觉模糊集理论的综合测量方法,该方法可以测量不确定性下的复杂社会现象,包括来自问卷调查的数据。首先,提出了将问卷中的有序数据转换为区间值直觉模糊集(I-VIFS)的方法。下一个,介绍了构建I-VIFS综合指标的方法。最后,通过这种综合措施,定义了乐观系数,该乐观系数允许设置I-VIFS参数的时间间隔限制。通过对波兰部分社区居民的主观生活质量进行问卷调查的结果,表明了该方法的有效性。结果表明,在测量不确定性的条件下,基于问卷调查的有序数据,该综合措施适用于并有效地评估复杂现象。此外,乐观系数概念的使用增加了其应用的灵活性。它允许设置I-VIFS参数的间隔限制。通过对波兰部分公社居民的主观生活质量进行问卷调查的结果,表明了该方法的有效性。结果表明,在测量不确定性的条件下,基于问卷调查的有序数据,该综合措施适用于并有效地评估复杂现象。此外,乐观系数概念的使用增加了其应用的灵活性。它允许设置I-VIFS参数的间隔限制。通过对波兰部分社区居民的主观生活质量进行问卷调查的结果,表明了该方法的有效性。结果表明,在测量不确定性的条件下,基于问卷调查的有序数据,该综合措施适合并有效地评估复杂现象。此外,乐观系数概念的使用增加了其应用的灵活性。结果表明,在测量不确定性的条件下,基于问卷调查的有序数据,该综合措施适用于并有效地评估复杂现象。此外,乐观系数概念的使用增加了其应用的灵活性。结果表明,在测量不确定性的条件下,基于问卷调查的有序数据,该综合措施适用于并有效地评估复杂现象。此外,乐观系数概念的使用增加了其应用的灵活性。
更新日期:2021-01-20
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