Fundamental Properties With Respect to the Completeness of Intuitionistic Fuzzy Partially Ordered Set

Intuitionistic fuzzy set (A-IFS), originally introduced by Atanassov in 1983, is a generalization of a fuzzy set. The basic elements of an A-IFS are intuitionistic fuzzy values (IFVs), based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. To avoid relying too much upon t...

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Published inIEEE transactions on fuzzy systems Vol. 25; no. 6; pp. 1741 - 1751
Main Authors Ai, Zhenghai, Xu, Zeshui, Lei, Qian
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Calculus
Completeness
Decision making
Fuzzy sets
Indexes
Infimum
Integral equations
intuitionistic fuzzy calculus (IFC)
intuitionistic fuzzy partially ordered set
intuitionistic fuzzy set (IFS)
Programmable logic arrays
supremum
Systematics
Online AccessGet full text
ISSN1063-6706
1941-0034
DOI10.1109/TFUZZ.2016.2633369

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Abstract Intuitionistic fuzzy set (A-IFS), originally introduced by Atanassov in 1983, is a generalization of a fuzzy set. The basic elements of an A-IFS are intuitionistic fuzzy values (IFVs), based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. To avoid relying too much upon the classical calculus and make the IFC to be an independent subject, it is necessary to develop the limit theory of the IFC. In this paper, we first define the concepts of the supremum and the infimum with respect to IFVs, and investigate their properties in detail. Then, we reveal the relationships among them and four types of limits, and finally, we give a series of fundamental theorems with respect to the completeness of intuitionistic fuzzy partially ordered set.
AbstractList Intuitionistic fuzzy set (A-IFS), originally introduced by Atanassov in 1983, is a generalization of a fuzzy set. The basic elements of an A-IFS are intuitionistic fuzzy values (IFVs), based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. To avoid relying too much upon the classical calculus and make the IFC to be an independent subject, it is necessary to develop the limit theory of the IFC. In this paper, we first define the concepts of the supremum and the infimum with respect to IFVs, and investigate their properties in detail. Then, we reveal the relationships among them and four types of limits, and finally, we give a series of fundamental theorems with respect to the completeness of intuitionistic fuzzy partially ordered set.
Author Qian Lei
Zeshui Xu
Zhenghai Ai
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Snippet Intuitionistic fuzzy set (A-IFS), originally introduced by Atanassov in 1983, is a generalization of a fuzzy set. The basic elements of an A-IFS are...
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SubjectTerms Calculus
Completeness
Decision making
Fuzzy sets
Indexes
Infimum
Integral equations
intuitionistic fuzzy calculus (IFC)
intuitionistic fuzzy partially ordered set
intuitionistic fuzzy set (IFS)
Programmable logic arrays
supremum
Systematics
Title Fundamental Properties With Respect to the Completeness of Intuitionistic Fuzzy Partially Ordered Set
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Volume 25
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