Spherical fuzzy matrices

Abstract

In this paper, we introduce spherical fuzzy matrices (SFMs) which is an advanced tool of the fuzzy matrices, intuitionistic fuzzy matrices and picture fuzzy matrices. We investigate the basic properties of SFMs and compare the idea SFMs with picture fuzzy matrices. Then some algebraic operations, such as max-min, min-max, complement, algebraic sum, algebraic product are defined and investigated their algebraic properties. Further, scalar multiplication (nA) and exponentiation (An) operations of a SFM A using algebraic operations are constructed, and their desirable properties are studied. Finally, we define a new operation(@) on spherical fuzzy matrices and discuss distributive laws in the case where the operations of ?s, ?s, ?s and ?s are combined each other.