scholarly journals L-Fuzzy Rough Approximation Operators Based on Co-Implication and Their (Single) Axiomatic Characterizations

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 134
Author(s):  
Qiu Jin ◽  
Lingqiang Li
Keyword(s):  
Residuated Lattice ◽  
Fuzzy Relation ◽  
Approximation Operator ◽  
Dual Operator ◽  
Fuzzy Relations ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Single Axiom

For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual operator of the Qiao–Hu L-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the L-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean L-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively.

scholarly journals Soft Covering Based Rough Sets and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Şaziye Yüksel ◽  
Zehra Güzel Ergül ◽  
Naime Tozlu
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Prostate Cancer Risk ◽  
Approximation Operator ◽  
Soft Sets ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Model Combining ◽  
Rough Approximation ◽  
Generalized Rough Set

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.

scholarly journals The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qiao-Ling Song ◽  
Hu Zhao ◽  
Juan-Juan Zhang ◽  
A. A. Ramadan ◽  
Hong-Ying Zhang ◽  
...  
Keyword(s):  
Complete Lattice ◽  
Lattice Isomorphism ◽  
Double Negative ◽  
Lattice Structures ◽  
Fuzzy Relations ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Neighborhood System ◽  
Generalized Neighborhood System

Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism.

On Simplified Axiomatic Characterizations of (υ σ)-Fuzzy Rough Approximation Operators

2017 ◽  
Vol 25 (03) ◽  
pp. 457-476 ◽  
Author(s):  
Hongying Zhang ◽  
Haijuan Song
Keyword(s):  
Rough Sets ◽  
Axiomatic Approach ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Constructive Approach ◽  
Axiomatic Characterizations ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Potential Applications ◽  
Two Universes

The axiomatic approach is more appropriate than constructive approach for studying the algebraic structure of rough sets. In this paper, the more simple axiomatic characterizations of (υ σ)-fuzzy rough approximation operators are explored where υ is a residuated implicator and σis its dual implicator. Firstly, we review the existing independent axiomatic sets to characterize various types of υ-lower and σ-upper fuzzy rough approximation operators. Secondly, we present one-axiom characterizations of (υ σ)-fuzzy rough approximation operators constructed by a serial fuzzy relation on two universes. Furthermore, we show that (υ σ)-fuzzy rough approximation operators, corresponding to reexive, symmetric and T-transitive fuzzy relations, can be presented by only two axioms respectively. We conclude the paper by introducing some potential applications and future works.

Algorithms and Algorithm Analysis of Logical Difference Operation of Variable Precision Lower Approximation Operator and Grade Upper Approximation Operator

2011 ◽  
Vol 204-210 ◽  
pp. 2015-2018
Author(s):  
Xian Yong Zhang ◽  
Zhi Wen Mo ◽  
Fang Xiong
Keyword(s):  
Time Complexity ◽  
Space Complexity ◽  
Algorithm Analysis ◽  
Approximation Operator ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Variable Precision ◽  
Approximation Operators ◽  
Difference Operation

This paper aims to construct new operation of approximation operators, and explore its calculation. First it proposes logical difference operation of variable precision lower approximation operator and grade upper approximation operator. Then regular algorithm and structural algorithm are proposed and analyzed, and furthermore, a conclusion is drawn that structural algorithm has advantages in time complexity and space complexity. Finally a practical example is given to illustrate the new operation and its algorithms.

Interval-valued pythagorean fuzzy rough approximation operators and its application

2020 ◽  
Vol 39 (3) ◽  
pp. 3067-3084
Author(s):  
Hai-Long Yang ◽  
Jia-Jia Zhou
Keyword(s):  
Fuzzy Relations ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Rough Set ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Proposed Model ◽  
Rough Approximation ◽  
Different Types ◽  
Interval Valued

By combining interval-valued Pythagorean fuzzy sets with rough sets, the interval-valued Pythagorean fuzzy rough set model is first constructed in this paper. The connections between special interval-valued Pythagorean fuzzy relations and interval-valued Pythagorean fuzzy approximation operators are established subsequently. Then, we study the axiomatic characterizations of interval-valued Pythagorean fuzzy lower and upper approximation operators. Different axiom sets of interval-valued Pythagorean fuzzy set-theoretic operators ensure the existence of different types of interval-valued Pythagorean fuzzy relations producing the same operators. Finally, we give an example to illustrate the practical application of the newly proposed model.

L-fuzzy rough approximation operators via three new types of L-fuzzy relations

2019 ◽  
Vol 23 (22) ◽  
pp. 11433-11446 ◽  
Author(s):  
Bin Pang ◽  
Ju-Sheng Mi ◽  
Wei Yao
Keyword(s):  
Fuzzy Relations ◽  
Approximation Operators ◽  
Rough Approximation

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.

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