Descriptive statistics based on precise data from a fuzzy community

Document Type : Research Paper

Authors

1 Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran

2 Faculty of Engineering Sciences, University of Tehran

Abstract

In many applied problems, the goal is to examine a fuzzy community (such as the community of young people or the community of the underprivileged in a city) based on a sample from that community. The common approach of classical statistics in dealing with these issues is to formulate the desired fuzzy community through a subset of the statistical community (for example, in classical statistics, individuals aged between 18 and 30 are considered as the community of young people). Criticizing this approach, this article proposes a new and more equitable method for investigating such practical problems. In this method, first, the desired fuzzy community is defined through a membership function. Then, the membership degrees of individual sample data in the fuzzy community are considered when examining the community. For example, in calculating the average height of young people in a community, it is fairer for younger individuals to have a greater impact compared to others. In this article, the main concepts of classical descriptive statistics, including mean, variance, standard deviation, covariance, and correlation coefficient, are extended for such problems. In this extension, the degree of membership of each data point in the desired fuzzy community determines its influence in statistical calculations. Several numerical examples are also provided to better illustrate the presented content.

Keywords

References

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Mathematics and Society
Volume 3, Issue 4 - Serial Number 4
December 2018
Pages 49-59

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History

  • Receive Date: 07 September 2017
  • Revise Date: 04 September 2019
  • Accept Date: 08 September 2019
  • Publish Date: 20 February 2019

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