Rough Sets and Vague Sets

2007 ◽  
pp. 122-132 ◽  
Author(s):  
Zbigniew Bonikowski ◽  
Urszula Wybraniec-Skardowska
Keyword(s):  
Rough Sets ◽  
Vague Sets

Intuitionistic Fuzzy Soft Ideals

2020 ◽  
pp. 91-104
Author(s):  
Shuker Khalil
Keyword(s):  
Social Science ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Real Life ◽  
Soft Sets ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Sets Theory

The basic notions of soft sets theory are introduced by Molodtsov to deal with uncertainties when solving problems in practice as in engineering, social science, environment, and economics. This notion is convenient and easy to apply as it is free from the difficulties that appear when using other mathematical tools as theory of theory of fuzzy sets, rough sets, and theory of vague sets. The soft set theory has recently gaining significance for finding rational and logical solutions to various real-life problems, which involve uncertainty, impreciseness, and vagueness. The concepts of intuitionistic fuzzy soft left almost semigroups and the intuitionistic fuzzy soft ideal are introduced in this chapter, and some of their basic properties are studied.

Some Information Measures for Fuzzy Rough Sets

2021 ◽  
Vol 10 (2) ◽  
pp. 82-102
Author(s):  
Omdutt Sharma ◽  
Pratiksha Tiwari ◽  
Priti Gupta
Keyword(s):  
Information Theory ◽  
Rough Sets ◽  
Real Life ◽  
Conditional Entropy ◽  
Scientific Data ◽  
Entropy Measure ◽  
Vague Sets ◽  
Medical Diagnoses ◽  
Information Measures ◽  
Decision Making Problem

Information theory is a tool to measure uncertainty; these days, it is used to solve various challenging problems that involve hybridization of information theory with the fuzzy set, rough sets, vague sets, etc. In order to solve challenging problems in scientific data analysis and visualization recently, various authors are working on hybrid measures of information theory. In this paper, using the relation between information measures, some measures are proposed for the fuzzy rough set. Firstly, an entropy measure is derived using the fuzzy rough similarity measure, and then corresponding to this entropy measure, some other measures like mutual information measure, joint entropy measure, and conditional entropy measure are also proposed. Some properties of these measures are also studied. Later, the proposed measure is compared with some existing measures to prove its efficiency. Further, the proposed measures are applied to pattern recognition, medical diagnoses, and a real-life decision-making problem for incorporating software in the curriculum at the Department of Statistics.

Generalized Set Theories Applied in Uncertain Information Processing

2014 ◽  
Vol 644-650 ◽  
pp. 2419-2423
Author(s):  
Qing Bo Yang ◽  
Jian Long Zhou
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Uncertain Information ◽  
Vague Sets ◽  
Intuitionistic Fuzzy

Uncertain factors in information bring us serious challenges. In order to apply information effectively, many researchers are committed to the research on uncertain information processing. Generalized set theories are widely used in the research. Several kinds of theories such as Fuzzy sets, Intuitionistic fuzzy sets, Vague sets, Rough sets and Extension sets are introduced in this paper. And a comparation and analysis of them is given in the following.

BUSINESS FAILURE PREDICTION USING ROUGH SETS: A COMPARISON WITH MULTIVARIATE ANALYSIS TECHNIQUES

1999 ◽  
Vol 04 (01) ◽  
Author(s):  
C. Zopounidis ◽  
M. Doumpos ◽  
R. Slowinski ◽  
R. Susmaga ◽  
A. I. Dimitras
Keyword(s):  
Multivariate Analysis ◽  
Rough Sets ◽  
Failure Prediction ◽  
Business Failure ◽  
Analysis Techniques

Approximation Sets of Rough Sets

2012 ◽  
Vol 23 (7) ◽  
pp. 1745-1759 ◽  
Author(s):  
Qing-Hua ZHANG ◽  
Guo-Yin WANG ◽  
Yu XIAO
Keyword(s):  
Rough Sets
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