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On $δ\mathbb{P}$-approximation Spaces

Huda Mohsin, Faik Mayah

Abstract

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of $δ\mathbb{P}$-upper and $δ\mathbb{P}$-lower approximations, that are based on the notion of $δ\mathbb{P}$-open sets, we additionally examine a few of their fundamental characteristics.

On $δ\mathbb{P}$-approximation Spaces

Abstract

In order to deal with imprecision, ambiguity, and uncertainty in data analysis, Pawlak introduced rough set theory in 1982. This paper aims to expand the scope of basic set theory developed by presenting the notions of -upper and -lower approximations, that are based on the notion of -open sets, we additionally examine a few of their fundamental characteristics.
Paper Structure (5 sections, 13 theorems, 6 equations, 1 figure, 1 table)

This paper contains 5 sections, 13 theorems, 6 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Fundamental concepts $\delta\mathbb{P}$-open sets and topology
  3. Rough set
  4. A novel approach to rough categorization using the $\delta\mathbb{P}$-open set
  5. Conclusions

Key Result

Lemma 5

17 The following hold for a subset $S$ of a topological space $(\mathbb{X},\tau)$.

Figures (1)

  • Figure 1: Showing the 24 areas given in Definition \ref{['def_01']}.

Theorems & Definitions (55)

  • Definition 1
  • Remark 2
  • Definition 3
  • Definition 4
  • Lemma 5
  • Remark 6
  • Definition 7
  • Proposition 8
  • proof
  • Definition 9
  • ...and 45 more