Level Operators over Intuitionistic Fuzzy Index Matrices

• Main Authors: Krassimir Atanassov, Peter Vassilev, Olympia Roeva
• Format: Article
• Language: English
• Published: MDPI AG 2021-02-01
• Series: Mathematics
• Subjects: index matrix; intuitionistic fuzzy pair; level operation
• Online Access: https://www.mdpi.com/2227-7390/9/4/366

The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied.