| Abstrakt: |
Rough set theory (RST) is a formal theory derived from logical properties of information systems. Rough set theory extends traditional set theory by defining a subset of a universe through the use of a pair of sets referred to as the lower and upper approximations. It is a mathematical approach for dealing with ambiguities and imprecisions in a variety of situation. Since its introduction by Zdislaw Pawlak in the late eighties of the previous century, it has evolved into pure and applied directions from mathematical, logical, and computational perspectives. The area of rough set theory in computational mathematics is rapidly developing. As far as vagueness and imprecision are concerned, rough set theory is basically a mathematical approach. An equivalence relation is a key concept in rough set models. Approximations at the lower and upper levels are constructed based on equivalence classes. There is wide application of algebraic systems in sequential machines, formal languages, arithmetic codes, and error-correction algorithms. The study of any set will be effective if an algebraic structure is developed for it. In the context of semigroups research, rough set theory can be used to analyse and understand the properties and relationships within semigroups. Semigroups and related algebraic structures and their properties can be explored more deeply when rough set theory is applied. The aim of this paper is to extend the concept of rough semigroup ideals. It has already been shown that some properties of rough (left, right) ideals in semigroups can be obtained by extending the notion of a left (right) ideal in a semigroup. As a result of considering h-ideals in semigroups, rough upper hideals (left & right) have been introduced here along with their properties. Also, the results related to rough semi-lattices and rough quotient semigroups are given. These concepts are explained with suitable examples. [ABSTRACT FROM AUTHOR] |
