This paper is concerned with introducing and studying the first new
approximation operators using mixed degree system and second new
approximation operators using mixed degree system which are the core
concept in this paper. In addition, the approximations of graphs using the
operators first lower and first upper are accurate then the approximations
obtained by using the operators second lower and second upper sincefirst
accuracy less then second accuracy. For this reason, we study in detail the
properties of second lower and second upper in this paper. Furthermore, we
summarize the results for the properties of approximation operators second
lower and second upper when the graph G is arbitrary, serial 1, serial 2,
reflexive, symmetric, tra
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