scholarly journals Semantics of Fuzzy Sets in Rough Set Theory

2004 ◽  
pp. 297-318 ◽  
Author(s):  
Yiyu Yao
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory

On Multi-Fuzzy Rough Sets, Relations, and Topology

2019 ◽  
Vol 8 (1) ◽  
pp. 101-119
Author(s):  
Gayathri Varma ◽  
Sunil Jacob John
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Topological Spaces ◽  
Fuzzy Topology ◽  
Primitive Concept ◽  
Closed Sets ◽  
Fuzzy Topological Spaces

This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy sets. It is proved that the set of all lower approximation of multi-fuzzy sets under a reflexive and transitive multi-fuzzy relation forms a multi-fuzzy topology.

Decision Making by Using Intuitionistic Fuzzy Rough Set

2017 ◽  
pp. 268-286
Author(s):  
T. K. Das
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Sets ◽  
Fuzzy Rough Set ◽  
Intuitionistic Fuzzy ◽  
Intelligent Technique

This chapter begins with a brief introduction of the theory of rough set. Rough set is an intelligent technique for handling uncertainty aspect in the data. This theory has been hybridized by combining with many other mathematical theories. In recent years, much decision making on rough set theory has been extended by embedding the ideas of fuzzy sets, intuitionistic fuzzy sets and soft sets. In this chapter, the notions of fuzzy rough set and intuitionistic fuzzy rough (IFR) sets are defined, and its properties are studied. Thereafter rough set on two universal sets has been studied. In addition, intuitionistic fuzzy rough set on two universal sets has been extensively studied. Furthermore, we would like to give an application, which shows that intuitionistic fuzzy rough set on two universal sets can be successfully applied to decision making problems.

Uncertainty and Vagueness Concepts in Decision Making

2011 ◽  
pp. 901-909
Author(s):  
Georg Peters
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
17Th Century ◽  
Basic Principles ◽  
In The Beginning

One of the main challenges in decision making is how to deal with uncertainty and vagueness. The classic uncertainty concept is probability, which goes back to the 17th century. Possible candidates for the title of father of probability are Bernoulli, Laplace, and Pascal. Some 40 years ago, Zadeh (1965) introduced the concept of fuzziness, which is sometimes interpreted as one form of probability. However, we will show that the terms fuzzy and probability are complementary. Recently, in the beginning of the ’80s, Pawlak (1982) suggested rough sets to manage uncertainties. The objective of this article is to give a basic introduction into probability, fuzzy set, and rough set theory and show their potential in dealing with uncertainty and vagueness. The article is structured as follows. In the next three sections we will discuss the basic principles of probability, fuzzy sets, and rough sets, and their relationship with each other. The article concludes with a short summary.

scholarly journals Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations

2022 ◽  
Vol 7 (2) ◽  
pp. 2891-2928
Author(s):  
Rukchart Prasertpong ◽  
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Prime Ideals ◽  
Fuzzy Relations ◽  
Binary Relations ◽  
Soft Sets ◽  
Rough Fuzzy Set

<abstract><p>In the philosophy of rough set theory, the methodologies of rough soft sets and rough fuzzy sets have been being examined to be efficient mathematical tools to deal with unpredictability. The basic of approximations in rough set theory is based on equivalence relations. In the aftermath, such theory is extended by arbitrary binary relations and fuzzy relations for more wide approximation spaces. In recent years, the notion of picture hesitant fuzzy relations by Mathew et al. can be considered as a novel extension of fuzzy relations. Then this paper proposes extended approximations into rough soft sets and rough fuzzy sets from the viewpoint of its. We give corresponding examples to illustrate the correctness of such approximations. The relationships between the set-valued picture hesitant fuzzy relations with the upper (resp., lower) rough approximations of soft sets and fuzzy sets are investigated. Especially, it is shown that every non-rough soft set and non-rough fuzzy set can be induced by set-valued picture hesitant fuzzy reflexive relations and set-valued picture hesitant fuzzy antisymmetric relations. By processing the approximations and advantages in the new existing tools, some terms and products have been applied to semigroups. Then, we provide attractive results of upper (resp., lower) rough approximations of prime idealistic soft semigroups over semigroups and fuzzy prime ideals of semigroups induced by set-valued picture hesitant fuzzy relations on semigroups.</p></abstract>

A rough set theory application in forecasting models

2020 ◽  
Vol 3 (2) ◽  
pp. 1-21 ◽  
Author(s):  
Haresh Sharma ◽  
◽  
Kriti Kumari ◽  
Samarjit Kar ◽  
◽  
...  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Forecasting Models ◽  
Theory Application
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