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

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.