Interval-valued Fuzzy Matrices with Interval-valued Fuzzy Rows and Columns

Peer review under responsibility of Fuzzy Information and Engineering Branch of the Operations Research Society of China.

Abstract

Fuzzy matrix (FM) is a very important topic of fuzzy algebra. In FM, the elements belong to the unit interval $[0,1]$. When the elements of FM are the subintervals of the unit interval $[0,1]$, then the FM is known as interval-valued fuzzy matrix (IVFM). In IVFM, the membership values of rows and columns are crisp, i.e., rows and columns are certain. But, in many real life situations they are also uncertain. So to model these types of uncertain problems, a new type of interval-valued fuzzy matrices (IVFMs) are called interval-valued fuzzy matrices with interval-valued fuzzy rows and columns (IVFMFRCs). For these matrices, null, identity, equality, etc. are defined along with some binary operators. Complement and density of IVFMFRC are defined and several important properties are investigated. An application of IVFMFRC in image representation is also given.

Keywords:

• Fuzzy matrix
• Interval-valued fuzzy matrix
• Fuzzy rows and columns
• Complement of fuzzy matrices
• Density of fuzzy matrices

Notes

Peer review under responsibility of Fuzzy Information and Engineering Branch of the Operations Research Society of China.