A Boolean Vector Method for Granule Calculation in Granular Computing

Yuqing Hu; Haoxuan Sun; Haoyuan Deng; Yuhan Zhang; Bin Bai

doi:10.54097/at0dm708

Authors

Yuqing Hu
Haoxuan Sun
Haoyuan Deng
Yuhan Zhang
Bin Bai

DOI:

https://doi.org/10.54097/at0dm708

Keywords:

Granular Computing, Isomorphic Mapping, Boolean Characteristic Vector, Hadamard Product

Abstract

Granule calculation is one of the core issues in granular computing theory. This study proposes a method for the Boolean vector representation and calculation of granules. An isomorphism is defined on the universe of discourse, and a Boolean characteristic vector uniquely corresponding to a set is constructed, which transforms set operations including intersection, union, difference, and complement into vector addition, subtraction, and the Hadamard product. Based on this, the Boolean characteristic vector of a granule in granular computing is defined, and the computational methods for granule composition, decomposition, inheritance, similarity, and difference are reconstructed, and Boolean vector operations on granules provide a new approach to granular computation.

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