An Approach of Fuzzy Relation Equation and Fuzzy-Rough Set for Multi-label Emotion Intensity Analysis

2016 ◽  
pp. 65-80 ◽  
Author(s):  
Chu Wang ◽  
Daling Wang ◽  
Shi Feng ◽  
Yifei Zhang
Keyword(s):  
Rough Set ◽  
Fuzzy Relation ◽  
Intensity Analysis ◽  
Fuzzy Rough Set ◽  
Fuzzy Relation Equation ◽  
Emotion Intensity

scholarly journals Picture Fuzzy Rough Set and Rough Picture Fuzzy Set on Two Different Universes and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Dliouah Ahmed ◽  
Binxiang Dai
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Fuzzy Relation ◽  
Type I ◽  
Type Ii ◽  
Fuzzy Rough Set ◽  
Fuzzy Approximation ◽  
Picture Fuzzy Set ◽  
Decision Making Problem ◽  
Picture Fuzzy Sets

The major concern of this article is to propose the notion of picture fuzzy rough sets (PFRSs) over two different universes which depend on δ , ζ , ϑ -cut of picture fuzzy relation ℛ on two different universes (i.e., by combining picture fuzzy sets (PFSs) with rough sets (RSs)). Then, we discuss several interesting properties and related results on the PFRSs. Furthermore, we define some notions related to PFRSs such as (Type-I/Type-II) graded PFRSs, the degree α and β with respect to ℛ δ , ζ , ϑ on PFRSs, and (Type-I/Type-II) generalized PFRSs based on the degree α and β with respect to ℛ δ , ζ , ϑ and investigate the basic properties of above notions. Finally, an approach based on the rough picture fuzzy approximation operators on two different universes in decision-making problem is introduced, and we give an example to show the validity of this approach.

Rough Approximations on Hesitant Fuzzy Sets

2016 ◽  
pp. 265-279
Author(s):  
D. Deepak ◽  
Sunil Jacob John
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Fuzzy Relation ◽  
Equivalence Relations ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
Dual Nature ◽  
Fuzzy Environment ◽  
Lower And Upper Approximations

Introduction of hesitant fuzzy rough sets would facilitate the use of rough set based techniques to hesitant fuzzy environment. Hesitant fuzzy rough sets deal with the lower and upper approximations in a hesitant fuzzy domain. For this purpose concepts of hesitant fuzzy relations are discussed first to create a theoretical framework to study hesitant fuzzy rough sets. The concepts of equivalence relations are discussed. Hesitant fuzzy rough sets and the properties of the approximations are discussed. The dual nature of the lower and upper approximations is proved. This chapter introduces the model of a hesitant fuzzy rough set which approximates a hesitant fuzzy set using a hesitant fuzzy relation.

Bipolar fuzzy rough set model on two different universes and its application

2012 ◽  
Vol 35 ◽  
pp. 94-101 ◽  
Author(s):  
Hai-Long Yang ◽  
Sheng-Gang Li ◽  
Shouyang Wang ◽  
Jue Wang
Keyword(s):  
Rough Set ◽  
Fuzzy Rough Set

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

Unsupervised fuzzy-rough set-based dimensionality reduction

2013 ◽  
Vol 229 ◽  
pp. 106-121 ◽  
Author(s):  
Neil Mac Parthaláin ◽  
Richard Jensen
Keyword(s):  
Dimensionality Reduction ◽  
Rough Set ◽  
Fuzzy Rough Set
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