Soft ordered semigroups

Abstract

Key words Soft set, soft ordered semigroup, soft ordered subsemigroup, idealistic soft ordered semigroup. MSC (2000) 03G25, 06D72, 06F05Molodtsov introduced 1999 the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to ordered semigroups. The notions of (trivial, whole) soft ordered semigroup, soft ordered subsemigroup, soft left (right) ideal, and left (right) idealistic soft ordered semigroup are introduced, and various related properties are investigated.

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