Representations of Vague Approximation Operators

2011 ◽  
Vol 282-283 ◽  
pp. 287-290
Author(s):  
Hai Dong Zhang ◽  
Yan Ping He
Keyword(s):  
Artificial Intelligence ◽  
Mathematical Model ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Relation ◽  
Partial Knowledge ◽  
Data Bases ◽  
Approximation Operators ◽  
Rough Approximation

As a suitable mathematical model to handle partial knowledge in data bases, rough set theory is emerging as a powerful theory and has been found its successive applications in the fields of artificial intelligence such as pattern recognition, machine learning, etc. In the paper, a vague relation is first defined, which is the extension of fuzzy relation. Then a new pair of lower and upper generalized rough approximation operators based on the vague relation is first proposed by us. Finally, the representations of vague rough approximation operators are presented.

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6175-6183
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Properties ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

On Characterization of Relation Based Rough Set Algebras

2010 ◽  
pp. 69-91
Author(s):  
Wei-Zhi Wu ◽  
Wen-Xiu Zhang
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Axiomatic Approach ◽  
Topological Spaces ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Topological Spaces

Rough set theory is one of the most advanced areas popularizing GrC. The basic notions in rough set theory are the lower and upper approximation operators. A rough set algebra is a set algebra with two additional lower and upper approximation operators. In this chapter, we analyze relation based rough set algebras in both crisp and fuzzy environments. We first review the constructive definitions of generalized crisp rough approximation operators, rough fuzzy approximation operators, and fuzzy rough approximation operators. We then present the essential properties of the corresponding lower and upper approximation operators. We also characterize the approximation operators by using the axiomatic approach. Finally, the connection between fuzzy rough set algebras and fuzzy topological spaces is established.

Measures of uncertainty for a fuzzy probabilistic approximation space

2021 ◽  
pp. 1-24
Author(s):  
Lijun Chen ◽  
Damei Luo ◽  
Pei Wang ◽  
Zhaowen Li ◽  
Ningxin Xie
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Relation ◽  
Point Of View ◽  
Approximation Space ◽  
Fuzzy Approximation ◽  
Entropy Measurement ◽  
Fuzzy Relation Matrix ◽  
Relation Matrix

 An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space. In this way, it combines three types of uncertainty (i.e., fuzziness, probability and roughness). This article is devoted to measuring the uncertainty for an FPA-space. A fuzzy relation matrix is first proposed by introducing the probability into a given fuzzy relation matrix, and on this basis, it is expanded to an FA-space. Then, granularity measurement for an FPA-space is investigated. Next, information entropy measurement and rough entropy measurement for an FPA-space are proposed. Moreover, information amount in an FPA-space is considered. Finally, a numerical example is given to verify the feasibility of the proposed measures, and the effectiveness analysis is carried out from the point of view of statistics. Since three types of important theories (i.e., fuzzy set theory, probability theory and rough set theory) are clustered in an FPA-space, the obtained results may be useful for dealing with practice problems with a sort of uncertainty.

scholarly journals IDENTIFYING KEY FACTORS FOR ADOPTING ARTIFICIAL INTELLIGENCE-ENABLED AUDITING TECHNIQUES BY JOINT UTILIZATION OF FUZZY-ROUGH SET THEORY AND MRDM TECHNIQUE

2020 ◽  
Vol 0 (0) ◽  
pp. 1-34
Author(s):  
Kuang-Hua Hu ◽  
Fu-Hsiang Chen ◽  
Ming-Fu Hsu ◽  
Gwo-Hshiung Tzeng
Keyword(s):  
Artificial Intelligence ◽  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Audit Quality ◽  
Rough Set Theory ◽  
Decision Makers ◽  
Fuzzy Rough Set ◽  
Rule Based ◽  
Cpa Firms

In today’s big-data era, enterprises are able to generate complex and non-structured information that could cause considerable challenges for CPA firms in data analysis and to issue improper audited reports within the required period. Artificial intelligence (AI)-enabled auditing technology not only facilitates accurate and comprehensive auditing for CPA firms, but is also a major breakthrough in auditing’s new environment. Applications of an AI-enabled auditing technique in external auditing can add to auditing efficiency, increase financial reporting accountability, ensure audit quality, and assist decision-makers in making reliable decisions. Strategies related to the adoption of an AI-enabled auditing technique by CPA firms cover the classical multiple criteria decision-making (MCDM) task (i.e., several perspectives/criteria must be considered). To address this critical task, the present study proposes a fusion multiple rule-based decision making (MRDM) model that integrates rule-based technique (i.e., the fuzzy rough set theory (FRST) with ant colony optimization (ACO)) into MCDM techniques that can assist decision makers in selecting the best methods necessary to achieve the aspired goals of audit success. We also consider potential implications for articulating suitable strategies that can improve the adoption of AI-enabled auditing techniques and that target continuous improvement and sustainable development.

scholarly journals Soft Rough Approximation Operators and Related Results

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Zhaowen Li ◽  
Bin Qin ◽  
Zhangyong Cai
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Generalized Rough Set ◽  
Special Case

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

Similarity measure for multi-granularity rough approximations of vague sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1609-1621
Author(s):  
Jie Yang ◽  
Wei Zhou ◽  
Shuai Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Target Concept ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Vague Sets ◽  
Rough Approximation ◽  
Vague Concept

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

Use of Rough Set Theory and Neural Networks Methods in Supply Chain Management

2020 ◽  
Vol 22 (1) ◽  
pp. 44-49
Author(s):  
Artem Lopatin ◽  
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Supply Chain ◽  
Supply Chain Management ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Science Field ◽  
Chain Management ◽  
Practical Implications

Introduction The decision to align a specific order with a supplier depends on a no of criteria. Generally the buyer’s decision depends on his assessment of the supplier’s ability to meet the criteria of quality, volume, terms of delivery, price and service. But to evaluate these criteria, the company needs to manage information from different sources through whole supply chain. One way to control may comprise artificial intelligence methods. The main purposes of this article are to identify the AI subsectors that are most suitable for SCM programs, and characterize other subsectors in terms of their usefulness for improving SC performance. Synthesize the existing research on the appliance of rough set theory and neural networks methods touching SCM, on their practical implications and technical merits. Summarize research trends in rough set theory and neural networks methods and identify potential utilization of SCM that haven’t yet been studied in Ukrainian science field. Justify future prospects for expanding existing AI literature and unused AI research in Ukrainian science field topics related to SCM. Results The article identifies the sub-sectors of artificial intelligence that are most suitable for supply chain management programs, and describes other sub-sectors in terms of their usefulness for improving the efficiency of supply chain management. Synthesize the existing literature on the appliance of rough set theory and neural networks methods in supply chains, on their practical implications and technical merits. The tendencies of researches of rough set theory and neural networks methods are generalized and potential spheres of their appliance in management of supply chains which haven’t been investigated yet are defined. Conclusions. Despite the long history of AI, the potential of AI as a means of solving complex issues and finding info in the field of SC hasn’t been fully used in the past especially in the Ukrainian scientific literature. In particular, some groups of AI technologies, such as expert systems and GAs, are increasingly used to solve management issues, including inventory management, procurement, location planning, shipment coordination between contractors, and routing / planning issues. Further study of the issue requires consideration of the use of other AI methods in supply chain management, such as fuzzy logic and agent modeling and recognition of their practical aspects.

scholarly journals The Use of Artificial Intelligence Methods to Assess the Effectiveness of Lean Maintenance Concept Implementation in Manufacturing Enterprises

2020 ◽  
Vol 10 (21) ◽  
pp. 7922
Author(s):  
Katarzyna Antosz ◽  
Lukasz Pasko ◽  
Arkadiusz Gola
Keyword(s):  
Artificial Intelligence ◽  
Decision Making ◽  
Decision Trees ◽  
Set Theory ◽  
Rough Set ◽  
Intelligent Systems ◽  
High Efficiency ◽  
Rough Set Theory ◽  
Conservation Strategy ◽  
Artificial Intelligence Methods

The increase in the performance and effectiveness of maintenance processes is a continuous aim of production enterprises. The elimination of unexpected failures, which generate excessive costs and production losses, is emphasized. The elements that influence the efficiency of maintenance are not only the choice of an appropriate conservation strategy but also the use of appropriate methods and tools to support the decision-making process in this area. The research problem, which was considered in the paper, is an insufficient means of assessing the degree of the implementation of lean maintenance. This problem results in not only the possibility of achieving high efficiency of the exploited machines, but, foremost, it influences a decision process and the formulation of maintenance policy of an enterprise. The purpose of this paper is to present the possibility of using intelligent systems to support decision-making processes in the implementation of the lean maintenance concept, which allows the increase in the operational efficiency of the company’s technical infrastructure. In particular, artificial intelligence methods were used to search for relationships between specific activities carried out under the implementation of lean maintenance and the results obtained. Decision trees and rough set theory were used for the analysis. The decision trees were made for the average value of the overall equipment effectiveness (OEE) indicator. The rough set theory was used to assess the degree of utilization of the lean maintenance strategy. Decision rules were generated based on the proposed algorithms, using RSES software, and their correctness was assessed.

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