A basic result in Ramsey theory states that any tournament contains a “large” transitive subgraph. Since transitive tournaments contain only transitive subgraphs, it is natural to ask which subgraphs must appear in any large tournament that is “far” from being transitive. One result of this type was obtained by Fox and Sudakov who characterized the tournaments that appear in any tournament that...

This article defines ranked soft sets and establishes their fundamental theory. new model of uncertain knowledge is a non-numerical yet powerful improvement sets. The relies on qualitative the basic parameterized description posed by We define relations between some existing models (N-soft sets, fuzzy probabilistic sets) that enhance set spirit with help additional quantities. Primary contribut...