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>

Approximations in Rough Sets vs Granular Computing for Coverings

2012 ◽  
pp. 152-163
Author(s):  
Guilong Liu ◽  
William Zhu
Keyword(s):  
Knowledge Discovery ◽  
Binary Relation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Knowledge Discovery In Databases ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Covering Rough Set

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also focuses on the authors’ study of the condition under which the covering rough set can be generated by a binary relation and the binary relation based rough set can be generated by a covering.

Approximations in Rough Sets vs Granular Computing for Coverings

2010 ◽  
Vol 4 (2) ◽  
pp. 63-76 ◽  
Author(s):  
Guilong Liu ◽  
William Zhu
Keyword(s):  
Binary Relation ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Knowledge Discovery In Databases ◽  
Equivalence Relations ◽  
Binary Relations ◽  
Covering Rough Set

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also focuses on the authors’ study of the condition under which the covering rough set can be generated by a binary relation and the binary relation based rough set can be generated by a covering.

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.

Topological structures of a type of granule based covering rough sets

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3129-3141
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Spaces ◽  
Topological Properties ◽  
Binary Relations ◽  
Upper Approximation ◽  
Approximation Operators

Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindel?f property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

scholarly journals Using Rough Set to Construct the Enterprise Information Management System

2012 ◽  
Vol 6-7 ◽  
pp. 641-646
Author(s):  
Xing Wei
Keyword(s):  
Information Management ◽  
Set Theory ◽  
Rough Set ◽  
Management System ◽  
Rough Set Theory ◽  
Information Management System ◽  
Equivalence Relations ◽  
Knowledge Representation And Reasoning ◽  
Enterprise Information ◽  
Cpu Time

Rough set theory as a new hotspot in the field of artificial intelligence, it can effectively deal with incomplete and uncertain knowledge representation and reasoning. Rough set theory is built on the basis of the classification mechanism, it will be classified understand in a particular space on the equivalence relation, equivalence relations constitute the division of space. The paper puts forward using rough set to construct the enterprise information management system. The experiment shows the CPU Time in the attribute numbers, indicating that Jelonek is superior to rough set in building enterprise information management system.

Using Rough Set to Develop the Building Materials Management System

2013 ◽  
Vol 281 ◽  
pp. 658-663
Author(s):  
Jian Xu
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Equivalence Relation ◽  
Management System ◽  
Building Materials ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Materials Management ◽  
Cpu Time ◽  
Materials Used

Materials used in buildings are collectively referred to building materials. Building materials can be divided into structural materials, decoration materials and some special materials. Rough set theory is built on the basis of the classification mechanism, it will be classified understand in a particular space on the equivalence relation, equivalence relations constitute the division of space. The paper puts forward using rough set to develop the building materials management system. The experiment shows the CPU Time in the attribute numbers, indicating that rough set is superior to FCA in building materials management system.

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.

Sign in / Sign up

Export Citation Format

Share Document