Soft Rough Set based span for unsupervised keyword extraction

2021 ◽  
pp. 1-8
Author(s):  
Niladri Chatterjee ◽  
Aayush Singha Roy ◽  
Nidhika Yadav
Keyword(s):  
Greedy Algorithm ◽  
Rough Set ◽  
Rough Sets ◽  
Text Summarization ◽  
The Other ◽  
Keyword Extraction ◽  
Effective Solution ◽  
Input Text ◽  
Soft Rough Set ◽  
The Universe

The present work proposes an application of Soft Rough Set and its span for unsupervised keyword extraction. In recent times Soft Rough Sets are being applied in various domains, though none of its applications are in the area of keyword extraction. On the other hand, the concept of Rough Set based span has been developed for improved efficiency in the domain of extractive text summarization. In this work we amalgamate these two techniques, called Soft Rough Set based Span (SRS), to provide an effective solution for keyword extraction from texts. The universe for Soft Rough Set is taken to be a collection of words from the input texts. SRS provides an ideal platform for identifying the set of keywords from the input text which cannot always be defined clearly and unambiguously. The proposed technique uses greedy algorithm for computing spanning sets. The experimental results suggest that extraction of keywords using the proposed scheme gives consistent results across different domains. Also, it has been found to be more efficient in comparison with several existing unsupervised techniques.

scholarly journals Distinguishing Vagueness from Ambiguity in Rough Set Approximations

2018 ◽  
Vol 26 (Suppl. 2) ◽  
pp. 89-125 ◽  
Author(s):  
Salvatore Greco ◽  
Benedetto Matarazzo ◽  
Roman Słowiński
Keyword(s):  
Fuzzy Sets ◽  
Rough Set ◽  
Rough Sets ◽  
The Other ◽  
New Approach ◽  
Variable Precision ◽  
Rough Approximation ◽  
Imperfect Knowledge ◽  
Disjoint Sets ◽  
The Universe

In this paper we present a new approach to rough set approximations that permits to distinguish between two kinds of “imperfect” knowledge in a joint framework: on one hand, vagueness, due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity, due to granularity of knowledge originating from the coarseness typical of rough sets. The basic idea of our approach is that each concept is represented by an orthopair, that is, a pair of disjoint sets in the universe of knowledge. The first set in the pair contains all the objects that are considered as surely belonging to the concept, while the second set contains all the objects that surely do not belong to the concept. In this context, following some previous research conducted by us on the algebra of rough sets, we propose to define as rough approximation of the orthopair representing the considered concept another orthopair composed of lower approximations of the two sets in the first orthopair. We shall apply this idea to the classical rough set approach based on indiscernibility, as well as to the dominance-based rough set approach. We discuss also a variable precision rough approximation, and a fuzzy rough approximation of the orthopairs. Some didactic examples illustrate the proposed methodology.

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.

scholarly journals Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation

2014 ◽  
Vol 1 (2) ◽  
pp. 49-61 ◽  
Author(s):  
Mary A. Geetha ◽  
D. P. Acharjya ◽  
N. Ch. S. N. Iyengar
Keyword(s):  
Information System ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Granular Computing ◽  
Real Life ◽  
Equivalence Relations ◽  
Life Problems ◽  
Algebraic Properties ◽  
The Universe

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.

scholarly journals AN OVERVIEW OF ROUGH SET SEMANTICS FOR MODAL AND QUANTIFIER LOGICS

2000 ◽  
Vol 08 (01) ◽  
pp. 93-118 ◽  
Author(s):  
CHURN-JUNG LIAU
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Possible Worlds ◽  
Rough Set Theory ◽  
Modal Logics ◽  
The Other ◽  
Approximation Space ◽  
The Universe

In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some well-known results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.

scholarly journals Rough Set Approximation as Formal Concept

2006 ◽  
Vol 10 (5) ◽  
pp. 606-611 ◽  
Author(s):  
Nozomi Ytow ◽  
◽  
David R. Morse ◽  
David McL. Roberts ◽  
◽  
...  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
The Other ◽  
Formal Concept ◽  
Object Based ◽  
Formal Concepts ◽  
Set Approximation

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

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.

Rough Set on Two Universal Sets Based on Multigranulation

2014 ◽  
pp. 159-179 ◽  
Author(s):  
D. P. Acharjya ◽  
Mary A. Geetha
Keyword(s):  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Real Life ◽  
Equivalence Relations ◽  
Topological Characterization ◽  
Life Problems ◽  
Multigranulation Rough Set ◽  
Algebraic Properties ◽  
The Universe

The fundamental concept of crisp set has been extended in many directions in the recent past. The notion of rough set by Pawlak is noteworthy among them. The rough set philosophy is based on the concept that there is some information associated with each object of the universe. There is a need to classify objects of the universe based on the indiscernibility relation among them. In the view of granular computing, rough set model is researched by single granulation. It has been extended to multigranular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. However, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multigranulation rough set on single universal set to multigranulation rough set on two universal sets. This chapter defines multigranulation rough set for two universal sets U and V. In addition, the algebraic properties, measures of uncertainty and topological characterization that are interesting in the theory of multigranular rough sets are studied. This helps in describing and solving real life problems more accurately.

Novel multi-criteria decision-making methods with soft rough q-rung orthopair fuzzy sets and q-rung orthopair fuzzy soft rough sets

2021 ◽  
pp. 1-19
Author(s):  
Muhammad Riaz ◽  
Nawazish Ali ◽  
Bijan Davvaz ◽  
Muhammad Aslam
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Smart Phone ◽  
Optimal Decision ◽  
Multi Criteria Decision Making ◽  
Public Parks ◽  
Decision Attributes ◽  
Develop Algorithm ◽  
Soft Rough Set

The aim of this paper is to introduce the concepts of soft rough q-rung orthopair fuzzy set (SRqROFS) and q-rung orthopair fuzzy soft rough set (qROPFSRS) based on soft rough set and fuzzy soft relation, respectively. We define some fundamental operations on both SRqROFS and qROPFSRS and discuss some key properties of these models by using upper and lower approximation operators. The suggested models are superior than existing soft rough sets, intuitionistic fuzzy soft rough sets and Pythagorean fuzzy soft rough sets. These models are more efficient to deal with vagueness in multi-criteria decision-making (MCDM) problems. We develop Algorithm i (i = 1, 2, 3, 4, 5) for the construction of SRqROFS, construction of qROFSRS, selection of a smart phone, ranking of beautiful public parks, and ranking of government challenges, respectively. The notions of upper reduct and lower reduct based on the upper approximations and lower approximations by variation of the decision attributes are also proposed. The applications of the proposed MCDM methods are demonstrated by respective numerical examples. The idea of core is used to find a unanimous optimal decision which is obtained by taking the intersection of all lower reducts and upper reducts.

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