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The detailed formula for the score value of each binary relations included in network structure, Sk (k = 1, 2,..., the number of binary relations) is shown in Supplementary File 1.
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There are many circumstances in which binary relations are defined between pairs of objects: in sociology there are social relations between people; in business there are trading relations between firms; in design there are functional dependencies between components.
The existing research of multi-source information system, pessimistic or optimistic multi-granulation fusion functions, provided by multi-granulation rough set (MGRS) theory, which apply disjunctive and conjunctive operators of multiple binary relations to aggregate multiple granular structures induced by different binary relations, are too relax or too restrictive to solve the practical problems.
In this paper, some coincidence point results in complete metric spaces endowed with transitive binary relations are first highlighted.
Highlighted binary relations were so-called AD hallmark pathways: amyloid plagues (amyloid β accumulation) and NFT accumulation (hyperphosphorylated tau accumulation).
Bunescu and Mooney [ 37] claim that binary relations are characterized by the tokens that occur in one of these contexts: Fore-Between (FB), Between (B) or Between-After (BA).
The binary relation is transitive and T is -nondecreasing; 3.
Rule R4 expresses the further property that this binary relation is a congruence.
A binary relation is called a preorder if it is transitive and reflexive.
The binary relation is transitive on (g(X)) if and only if is g-transitive. .
The binary relation is transitive on (g(X)) and T is -nondecreasing; 3.
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