Some results on fuzzy relations

2021 ◽  
pp. 1-17
Author(s):  
Yini Wang ◽  
Sichun Wang
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Attribute Reduction ◽  
Heterogeneous Data ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Main Research ◽  
Effectiveness Analysis ◽  
Uncertainty Measurement ◽  
Partial Dependence

Fuzzy relation is one of the main research contents of fuzzy set theory. This paper obtains some results on fuzzy relations by studying relationships between fuzzy relations and their uncertainty measurement. The concepts of equality, dependence, partial dependence and independence between fuzzy relations are first introduced. Then, uncertainty measurement for a fuzzy relation is investigated by using dependence between fuzzy relations. Moreover, the basic properties of uncertainty measurement are obtained. Next, effectiveness analysis is carried out. Finally, an application of the proposed measures in attribute reduction for heterogeneous data is given. These results will be helpful for understanding the essence of a fuzzy relation.

Generating Fuzzy Sets and Fuzzy Relations Based on Information

2021 ◽  
Vol 20 ◽  
pp. 178-185
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced

scholarly journals Implementation of Equilibrium Optimizer Algorithm for MPPT in a wind turbine with PMSG

2021 ◽  
Vol 16 ◽  
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Wind Turbine ◽  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced.

Information structures and uncertainty in an image information system

2021 ◽  
Vol 40 (1) ◽  
pp. 295-317
Author(s):  
Gangqiang Zhang ◽  
Zhaowen Li ◽  
Pengfei Zhang ◽  
Ningxin Xie
Keyword(s):  
Information System ◽  
Kernel Method ◽  
Attribute Reduction ◽  
Gaussian Kernel ◽  
Information Structures ◽  
Image Information ◽  
Effectiveness Analysis ◽  
Uncertainty Measurement ◽  
Properties Of Information ◽  
Information Values

An information system as a database that stands for relationships between objects and attributes is an important mathematical model. An image information system is an information system where each of its information values is an image and its information structures embody internal features of this type of information system. Uncertainty measurement is an effective tool for evaluation. This paper explores measures of uncertainty for an information system by using the proposed information structures. The distance between two objects in an image information system is first given. After that, the fuzzy Tcos-equivalence relation, induced by this system by using Gaussian kernel method, is obtained, where Gaussian kernel is based on this distance. Next, information structures of this system are described by set vectors, dependence between information structures is studied and properties of information structures are given by using inclusion degree, and application for information structures and uncertainty measures of an image information system are investigated by the information structures. Moreover, effectiveness analysis is done to show the feasibility of the proposed measures from the angle of statistics. Finally, an application of the proposed measurement for attribute reduction is given. These results will be helpful for understanding the essence of uncertainty in an image information system.

A SIMILARITY-BASED GENERALIZATION OF FUZZY ORDERINGS PRESERVING THE CLASSICAL AXIOMS

2000 ◽  
Vol 08 (05) ◽  
pp. 593-610 ◽  
Author(s):  
ULRICH BODENHOFER
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Main Part ◽  
Equivalence Relations ◽  
Fuzzy Relations ◽  
Strong Connection ◽  
Alternative Approach ◽  
Key Concepts ◽  
Fuzzy Partitions ◽  
Fuzzy Orderings

Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of fuzzy orderings is still lagging far behind, although there are a lot of possible applications, for instance, in fuzzy preference modeling and fuzzy control. The present paper is devoted to this missing link. After a brief motivation, we will critically analyze the existing approach to fuzzy orderings. In the main part, an alternative approach to fuzzy orderings, which also takes the strong connection to gradual similarity into account, is proposed and studied in detail, including several constructions and representation results.

scholarly journals Parallel Attribute Reduction Algorithm for Complex Heterogeneous Data Using MapReduce

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Tengfei Zhang ◽  
Fumin Ma ◽  
Jie Cao ◽  
Chen Peng ◽  
Dong Yue
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Heterogeneous Data ◽  
Reduction Algorithm ◽  
Numerical Attributes ◽  
Reduction Efficiency ◽  
Speed Up

Parallel attribute reduction is one of the most important topics in current research on rough set theory. Although some parallel algorithms were well documented, most of them are still faced with some challenges for effectively dealing with the complex heterogeneous data including categorical and numerical attributes. Aiming at this problem, a novel attribute reduction algorithm based on neighborhood multigranulation rough sets was developed to process the massive heterogeneous data in the parallel way. The MapReduce-based parallelization method for attribute reduction was proposed in the framework of neighborhood multigranulation rough sets. To improve the reduction efficiency, the hashing Map/Reduce functions were designed to speed up the positive region calculation. Thereafter, a quick parallel attribute reduction algorithm using MapReduce was developed. The effectiveness and superiority of this parallel algorithm were demonstrated by theoretical analysis and comparison experiments.

Granular Computing Based Data Mining in the Views of Rough Set and Fuzzy Set

2010 ◽  
pp. 148-178 ◽  
Author(s):  
Guoyin Wang ◽  
Jun Hu ◽  
Qinghua Zhang ◽  
Xianquan Liu ◽  
Jiaqing Zhou
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Rule Sets ◽  
Incomplete Information Systems

Granular computing (GrC) is a label of theories, methodologies, techniques, and tools that make use of granules in the process of problem solving. The philosophy of granular computing has appeared in many fields, and it is likely playing a more and more important role in data mining. Rough set theory and fuzzy set theory, as two very important paradigms of granular computing, are often used to process vague information in data mining. In this chapter, based on the opinion of data is also a format for knowledge representation, a new understanding for data mining, domain-oriented data-driven data mining (3DM), is introduced at first. Its key idea is that data mining is a process of knowledge transformation. Then, the relationship of 3DM and GrC, especially from the view of rough set and fuzzy set, is discussed. Finally, some examples are used to illustrate how to solve real problems in data mining using granular computing. Combining rough set theory and fuzzy set theory, a flexible way for processing incomplete information systems is introduced firstly. Then, the uncertainty measure of covering based rough set is studied by converting a covering into a partition using an equivalence domain relation. Thirdly, a high efficient attribute reduction algorithm is developed by translating set operation of granules into logical operation of bit strings with bitmap technology. Finally, two rule generation algorithms are introduced, and experiment results show that the rule sets generated by these two algorithms are simpler than other similar algorithms.

scholarly journals Three-way weighted combination-entropies based on three-layer granular structures

2017 ◽  
Vol 2 (2) ◽  
pp. 329-340 ◽  
Author(s):  
Wang Jun ◽  
Tang Lingyu ◽  
Zhang Xianyong ◽  
Luo Yuyan
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Uncertain Information ◽  
Uncertainty Measurement ◽  
The Hierarchical Structure ◽  
Information Theoretic Measures ◽  
New Perspective ◽  
Weighted Combination

AbstractRough set theory is an important theory for the uncertain information processing. The information theoretic measures have been introduced into rough set theory and provided a new effective method in uncertainty measurement and attribute reduction. However, most of them did not consider the hierarchical structure of a decision table (D-Table). Thus, this paper concretely constructs three-way weighted combination-entropies based on the D-Table’s three-layer granular structures and Bayes’ theorem from a new perspective, and reveals the granulation monotonicity and systematic relationships of three-way weighted combination-entropies. The relevant conclusion provides a more complete and updated interpretation of granular computing for the uncertainty measurement, and it also establishes a more effective basis for the quantitative application in attribute reduction.

scholarly journals Functional Partial Fuzzy Relations

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2191
Author(s):  
Martina Daňková
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Membership Functions ◽  
Fuzzy Relations ◽  
Partial Functions ◽  
Special Operations ◽  
Suitable Combination ◽  
Basic Characteristics ◽  
Definition Of ◽  
Meaningful Definition

We study fuzzy relations that satisfy the functionality property and that their membership functions can be partial functions. Such fuzzy relations are called partial fuzzy relations, and the variable-domain fuzzy set theory is a framework that provides powerful tools for handling these objects. There, the special operations based on connectives and quantifiers of a partial fuzzy logic are in use. The undefined degrees of membership are carried via those special operations. Furthermore, we show that a suitable combination of these operations leads to a meaningful definition of the functionality property, and we investigate its basic characteristics.

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