Some Equalities Connected with Fuzzy Soft Matrices

E cannot always use the classical methods to solve complicated problems in economics, engineering, social sciences, medical sciences etc. because different types of uncertainties are present in these theories. These days so many theories are available to deal with such type of uncertainties, such as, theory of fuzzy sets [1], theory of intuitionistic fuzzy sets [2], [3], theory of vague sets [4], theory of rough sets [5]. Every theory has its own problems because of the inadequacy of the parameterization tool of the theories. In 1999, Molodtsov [6] initiated the concept of fuzzy set to deal with uncertainties which is free from the above difficulties and later in 2001 Maji et al. [7] gave a hybrid model known as fuzzy soft set which is a combination of soft set and fuzzy set. They introduce the concept of union, intersection, complement etc. of Fuzzy Soft Sets and discussed their properties. These results were further revised and improved by Ahmad and Kharal [8]. Manash Jyoti Borah et al. [9] introduced the notions of symmetric, transitive, reflexive, equivalence fuzzy soft relations and discussed some related properties. The theory of matrix is commonly used in the broad areas of science and engineering. However classical matrix theory sometimes fails to solve the problems involving uncertainties, occurring in an imprecise environment. In [10], Yong Yang and Chenli Ji, using a matrix representation [10], [11] of Fuzzy Soft Set, discussed its properties and applied the same in certain decision making problems. In [12] the notion of Fuzzy Soft Matrices has been extended. In this paper, by defining some more set-operations on FSMmxn analogous to [13], [14] defined for intuitionistic fuzzy sets, an attempt has been made to derive some new results based on these operations on FSMmxn.