scholarly journals New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Mostafa K. El-Bably ◽  
Muhammad I. Ali ◽  
El-Sayed A. Abo-Tabl
Keyword(s):  
Heart Failure ◽  
Rough Sets ◽  
Building Blocks ◽  
Vital Role ◽  
Medical Applications ◽  
Soft Sets ◽  
Accuracy Measure ◽  
Decision Making Problem ◽  
Lower And Upper Approximations ◽  
The Universe

There are many approaches to deal with vagueness and ambiguity including soft sets and rough sets. Feng et al. initiated the concept of possible hybridization of soft sets and rough sets. They introduced the concept of soft rough sets, in which parameterized subsets of a universe set serve as the building blocks for lower and upper approximations of a subset. Topological notions play a vital role in rough sets and soft rough sets. So, the basic objectives of the current work are as follows: first, we find answers to some very important questions, such as how to determine the probability that a subset of the universe is definable. Some more similar questions are answered in rough sets and their extensions. Secondly, we enhance soft rough sets from topological perspective and introduce topological soft rough sets. We explore some of their properties to improve existing techniques. A comparison has been made with some existing studies to show that accuracy measure of proposed technique shows an improvement. Proposed technique has been employed in decision-making problem for diagnosing heart failure. For this two algorithms have been given.

scholarly journals Soft Classes and Soft Rough Classes with Applications in Decision Making

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Faruk Karaaslan
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Novel Method ◽  
Lower And Upper Approximations

Rough set was defined by Pawlak in 1982. Concept of soft set was proposed as a mathematical tool to cope with uncertainty and vagueness by Molodtsov in 1999. Soft sets were combined with rough sets by Feng et al. in 2011. Feng et al. investigated relationships between a subset of initial universe of soft set and a soft set. Feng et al. defined the upper and lower approximations of a subset of initial universe over a soft set. In this study, we firstly define concept of soft class and soft class operations such as union, intersection, and complement. Then we give some properties of soft class operations. Based on definition and operations of soft classes, we define lower and upper approximations of a soft set. Subsequently, we introduce concept of soft rough class and investigate some properties of soft rough classes. Moreover, we give a novel decision making method based on soft class and present an example related to novel method.

A Lattice Structure on Minimal Soft Rough Sets and Its Applications

2020 ◽  
Vol 16 (02) ◽  
pp. 255-269
Author(s):  
B. Praba ◽  
G. Gomathi ◽  
M. Aparajitha
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Culture System ◽  
Lattice Structure ◽  
Vital Role ◽  
Inclusion Relation ◽  
Soft Sets ◽  
Medical Diagnoses ◽  
Soft Rough Set ◽  
Made In

Rough sets defined in terms of soft sets play a vital role in decision making problems. Covering-based soft rough sets and modified soft rough sets are some of the recently developing concepts. In this paper, for a given soft sets [Formula: see text] on a universe [Formula: see text] we define a novel rough set called as minimal soft rough sets using minimal soft description of the objects. The relation between modified soft rough set and minimal soft rough set is analyzed. The set of all minimal soft rough sets is proved to be a Poset with the inclusion relation having a GLB and LUB and hence is a lattice. An attempt is made in applying this concepts in medical diagnoses and also in analyzing the organizational culture system.

Modified rough bipolar soft sets

2020 ◽  
Vol 39 (3) ◽  
pp. 4259-4283
Author(s):  
Muhammad Shabir ◽  
Rizwan Gul
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Group Decision ◽  
Soft Set ◽  
New Technique ◽  
Approximation Space ◽  
Soft Sets ◽  
Accuracy Measure ◽  
Soft Rough Set ◽  
A New Technique

Bipolar soft sets and rough sets are two different techniques to cope with uncertainty. A possible fusion of rough sets and bipolar soft sets is proposed by Karaaslan and Çağman. They introduced the notion of bipolar soft rough set. In this article, a new technique is being introduced to study roughness through bipolar soft sets. In this new technique of finding approximations of a set, flavour of both theories of bipolar soft set and rough set is retained. We call this new hybrid model modified rough bipolar soft set MRBS-set. Moreover, accuracy measure and roughness measure of modified rough bipolar soft sets are defined in MRBS-approximation space and its application in multi-criteria group decision making is presented.

scholarly journals Bi-covering rough sets

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2361-2369
Author(s):  
Mohamed Abo-Elhamayel
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Inclusion Relation ◽  
Different Types ◽  
Paper Construct ◽  
Lower And Upper Approximations ◽  
The Universe

Rough set theory is a useful tool for knowledge discovery and data mining. Covering-based rough sets are important generalizations of the classical rough sets. Recently, the concept of the neighborhood has been applied to define different types of covering rough sets. In this paper, based on the notion of bi-neighborhood, four types of bi-neighborhoods related bi-covering rough sets were defined with their properties being discussed. We first show some basic properties of the introduced bi-neighborhoods. We then explore the relationships between the considered bi-covering rough sets and investigate the properties of them. Also, we show that new notions may be viewed as a generalization of the previous studies covering rough sets. Finally, figures are presented to show that the collection of all lower and upper approximations (bi-neighborhoods of all elements in the universe) introduced in this paper construct a lattice in terms of the inclusion relation ?.

Topological Properties of Multigranular Rough sets on Fuzzy Approximation Spaces

2019 ◽  
Vol 6 (2) ◽  
pp. 1-18
Author(s):  
B.K. Tripathy ◽  
Suvendu Kumar Parida ◽  
Sudam Charan Parida
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Topological Properties ◽  
Approximation Spaces ◽  
Fuzzy Approximation ◽  
Accuracy Measure ◽  
Multiple Granularity ◽  
The Universe ◽  
Single Relation ◽  
Proximity Relation

One of the extensions of the basic rough set model introduced by Pawlak in 1982 is the notion of rough sets on fuzzy approximation spaces. It is based upon a fuzzy proximity relation defined over a Universe. As is well known, an equivalence relation provides a granularization of the universe on which it is defined. However, a single relation defines only single granularization and as such to handle multiple granularity over a universe simultaneously, two notions of multigranulations have been introduced. These are the optimistic and pessimistic multigranulation. The notion of multigranulation over fuzzy approximation spaces were introduced recently in 2018. Topological properties of rough sets are an important characteristic, which along with accuracy measure forms the two facets of rough set application as mentioned by Pawlak. In this article, the authors introduce the concept of topological property of multigranular rough sets on fuzzy approximation spaces and study its properties.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

Synthesis and Biological Potentials of Quinoline Analogues: A Review of Literature

2019 ◽  
Vol 16 (7) ◽  
pp. 653-688 ◽  
Author(s):  
Leena Kumari ◽  
Salahuddin ◽  
Avijit Mazumder ◽  
Daman Pandey ◽  
Mohammad Shahar Yar ◽  
...  
Keyword(s):  
Biological Activity ◽  
Heterocyclic Compounds ◽  
Building Blocks ◽  
Vital Role ◽  
Review Of Literature ◽  
Drug Discovery Process ◽  
Active Compounds ◽  
Lead Compounds ◽  
Synthetic Approaches ◽  
Derivatives Of

Heterocyclic compounds are well known for their different biological activity. The heterocyclic analogs are the building blocks for synthesis of the pharmaceutical active compounds in the organic chemistry. These derivatives show various type of biological activity like anticancer, antiinflammatory, anti-microbial, anti-convulsant, anti-malarial, anti-hypertensive, etc. From the last decade research showed that the quinoline analogs plays a vital role in the development of newer medicinal active compounds for treating various type of disease. Quinoline reported for their antiviral, anticancer, anti-microbial and anti-inflammatory activity. This review will summarize the various synthetic approaches for synthesis of quinoline derivatives and to check their biological activity. Derivatives of quinoline moiety plays very important role in the development of various types of newer drugs and it can be used as lead compounds for future investigation in the field of drug discovery process.

scholarly journals Acid-Catalysed Liquid-to-Solid Transitioning of Arylazoisoxazole Photoswitches

2021 ◽  
Author(s):  
Luuk Kortekaas ◽  
Julian Simke ◽  
Niklas Arndt ◽  
Marcus Böckmann ◽  
Nikos Doltsinis ◽  
...  
Keyword(s):  
Building Blocks ◽  
Vital Role ◽  
Responsive Materials ◽  
Molecular Building Blocks ◽  
Physical Changes

Molecular photoswitches play a vital role in the development of responsive materials. These molecular building blocks are particularly attractive when multiple stimuli can be combined to bring about physical changes,...

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