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Research and application for grey relational analysis in multigranularity based on normality grey number.

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This study introduces normality grey numbers to enhance grey theory for analyzing large, multi-granular datasets. This new method enables effective knowledge acquisition from big data without prior experience.

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Area of Science:

  • Data Science
  • Uncertainty Quantification
  • Statistical Modeling

Background:

  • Classic grey theory is limited for large datasets and multi-granularity analysis.
  • Existing methods do not sufficiently consider data distribution, particularly normal distributions.
  • Need for advanced methods to handle big data and complex information structures.

Purpose of the Study:

  • To propose a novel approach for grey theory applicable to big data and multi-granularity samples.
  • To address limitations of classic grey theory in data distribution and sample size.
  • To develop an automated clustering method for knowledge acquisition.

Main Methods:

  • Introduction of the normality grey number, leveraging the universality of normal distribution.
  • Development of a definition and calculation method for relational degree between normality grey numbers.
  • Formulation of a grey relational analytical method for multi-granularity analysis and automatic clustering.

Main Results:

  • The proposed normality grey number effectively handles data distribution.
  • The grey relational analysis in multi-granularity enables automatic clustering without prior knowledge.
  • Experimental results validate the method's effectiveness for big data and multi-granularity samples.

Conclusions:

  • The normality grey number and associated analytical method significantly advance grey theory.
  • This approach provides an effective knowledge acquisition tool for big data and complex datasets.
  • The method offers automated, experience-free clustering in specified granularities.