Open AccessGeneralized orthopair fuzzy matrices
Author(s) -
I. Silambarasan
Publication year - 2021
Publication title -
open journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2616-4906
pISSN - 2523-0212
DOI - 10.30538/oms2021.0165
Subject(s) - mathematics , exponentiation , fuzzy logic , algebraic number , algebra over a field , algebraic properties , fuzzy sphere , scalar multiplication , algebraic extension , algebraic operation , matrix multiplication , matrix (chemical analysis) , discrete mathematics , pure mathematics , computer science , elliptic curve , mathematical analysis , artificial intelligence , physics , differential algebraic equation , ordinary differential equation , quantum mechanics , quantum , noncommutative geometry , differential equation , materials science , composite material
A q-rung orthopair fuzzy matrix (q-ROFM), an extension of the Pythagorean fuzzy matrix (PFM) and intuitionistic fuzzy matrix (IFM), is very helpful in representing vague information that occurs in real-world circumstances. In this paper we define some algebraic operations, such as max-min, min-max, complement, algebraic sum, algebraic product, scalar multiplication \((nA)\), and exponentiation \((A^n)\). We also investigate the algebraic properties of these operations. Furthermore, we define two operators, namely the necessity and possibility to convert q-ROFMs into an ordinary fuzzy matrix, and discuss some of their basic algebraic properties. Finally, we define a new operation(@) on q-ROFMs and discuss distributive laws in the case where the operations of \(\oplus_{q}, \otimes_{q}, \wedge_{q}\) and \(\vee_{q}\) are combined each other.