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A Kind of Dynamic Rough Sets

Dong Ya Li, Bao Qing Hu

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Abstract

Pawlak's rough set theory is the static rough set theory which is to research and deal with static knowledge. This paper proposes the dynamic rough set theory which is to research and deal with dynamic knowledge, and gives the mathematical expression of dynamic rough sets by defining some concepts such as the elementary transfer coefficients, the D-rough sets and the D-approximate sets, etc, based on dynamic knowledge. And in this paper we also study the transfer characteristic of D-rough sets and give some theorems such as the D-rough set degradation theorem, the D-rough set transform theorem and the transfer equilibrium theorem etc. Finally illustrative examples are further discussed. D-rough set is a common form of Pawlak's rough set, as Pawlak's rough set can be considered as a special case of D-rough set.

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What this paper is about

Pawlak's rough set theory is the static rough set theory which is to research and deal with static knowledge. This paper proposes the dynamic rough set theory which is to research and deal with dynamic knowledge, and gives the mathematical expression of dynamic rough sets by defining some concepts such as the elementary transfer coefficients, the D-rough sets and the D-approximate sets, etc, based on dynamic knowledge. And in this paper we also study the transfer characteristic of D-rough sets and give some theorems such as the D-rough set degradation theorem, the D-rough set transform theorem and the transfer equilibrium theorem etc. Finally illustrative examples are further discussed. D-rough set is a common form of Pawlak's rough set, as Pawlak's rough set can be considered as a special case of D-rough set.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Pawlak's rough set theory is the static rough set theory which is to research and deal with static knowledge. This paper proposes the dynamic rough set theory which is to research and deal with dynamic knowledge, and gives the mathematical expression of dynamic rough sets by defining some concepts such as the elementary transfer coefficients, the D-rough sets and the D-approximate sets, etc, based on dynamic knowledge. And in this paper we also study the transfer characteristic of D-rough sets and give some theorems such as the D-rough set degradation theorem, the D-rough set transform theorem and the transfer equilibrium theorem etc. Finally illustrative examples are further discussed. D-rough set is a common form of Pawlak's rough set, as Pawlak's rough set can be considered as a special case of D-rough set.

Key concepts: Rough set, Dominance-based rough set approach, Set (abstract data type), Set theory, Mathematics, Computer science, Discrete mathematics, Data mining

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