A Short Primer on the Correlation Coefficient of Vague Sets

  • Authors:

  • John Robinson P.;Henry Amirtharaj E.C.

  • Affiliations:

  • Bishop Heber College, India;Bishop Heber College, India

  • Venue:
  • International Journal of Fuzzy System Applications
  • Year:
  • 2011

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Abstract

Intuitionistic fuzzy sets and vague sets are generalizations of the concept of fuzzy sets. Various researchers have studied the vagueness of data through vague sets, and it was later demonstrated that vague sets are indeed intuitionistic fuzzy sets. Since its entry in the literature, vague set theory has received increased attention. Many real life problems involve information in the form of vague values, due to the increasing complexity of the socio-economic environment and the vagueness of the inherent subjective nature of human thinking. Instead of using point-based membership as in fuzzy sets, interval-based membership is used in a vague set. This paper presents a detailed comparison between vague sets and intuitionistic fuzzy sets, from various perspectives of algebraic properties, graphical representations, and practical applications. Methods of calculating the correlation coefficient of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are already found in the literature. This paper defines the correlation coefficient of vague sets through simple examples.