scholarly journals Distance Measures between the Interval-Valued Complex Fuzzy Sets

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 549 ◽  
Author(s):  
Songsong Dai ◽  
Lvqing Bi ◽  
Bo Hu
Keyword(s):  
Unit Circle ◽  
Fuzzy Set ◽  
Complex Number ◽  
Daily Life ◽  
Distance Measures ◽  
Real Numbers ◽  
Complex Fuzzy Set ◽  
Fuzzy Distance ◽  
Euclidean Metrics ◽  
Interval Valued

Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.

scholarly journals New Distance Measures between the Interval-Valued Complex Fuzzy Sets with Applications to Decision-Making

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Haifeng Song ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Yingying Xu ◽  
Songsong Dai
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measures ◽  
Complex Numbers ◽  
Complex Fuzzy Set ◽  
Decision Making Problem ◽  
Euclidean Distances ◽  
Fuzzy Distances ◽  
New Research ◽  
Interval Valued

As a generalization of complex fuzzy set (CFS), interval-valued complex fuzzy set (IVCFS) is a new research topic in the field of CFS theory, which can handle two different information features with the uncertainty. Distance is an important tool in the field of IVCFS theory. To enhance the applicability of IVCFS, this paper presents some new interval-valued complex fuzzy distances based on traditional Hamming and Euclidean distances of complex numbers. Furthermore, we elucidate the geometric properties of these distances. Finally, these distances are used to deal with decision-making problem in the IVCFS environment.

scholarly journals Extension of competition graphs under complex fuzzy environment

2020 ◽  
Author(s):  
Muhammad Akram ◽  
Aqsa Sattar ◽  
Faruk Karaaslan ◽  
Sovan Samanta
Keyword(s):  
Unit Circle ◽  
Fuzzy Set ◽  
Economic Competition ◽  
Complex Fuzzy Set ◽  
Fuzzy Environment ◽  
Research Article ◽  
Fuzzy Graphs ◽  
Proposed Model ◽  
Present Complex ◽  
Phase Term

Abstract A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

Decision Making in Medical Diagnosis via Distance Measures on Interval Valued Fuzzy Sets

2017 ◽  
Vol 6 (4) ◽  
pp. 63-83 ◽  
Author(s):  
Palash Dutta
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Distance Measures ◽  
Medical Documentation ◽  
Interesting Area ◽  
Interval Valued

The uncertain and sometimes vague, imprecise nature of medical documentation and information make the field of medical diagnosis is the most important and interesting area for applications of fuzzy set theory (FST), intuitionistic fuzzy set (IFS) and interval valued fuzzy set (IVFS). In this present study, first resemblance between IFS and IVFS has been established along with reviewed some existing distance measures for IFSs. Later, an attempt has been made to derive distance measures for IVFSs from IFSs and establish some properties on distance measures of IVFSs. Finally, medical diagnosis has been carried out and exhibits the techniques with a case study under this setting.

Interval-Valued Intuitionistic Multiplicative Sets

2014 ◽  
Vol 22 (03) ◽  
pp. 385-406 ◽  
Author(s):  
Yuan Jiang ◽  
Zeshui Xu ◽  
Jiuping Xu
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Basic Component ◽  
Distance Measures ◽  
Weighted Distance ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
The Difference ◽  
Interval Valued

A generalization of the notion of intuitionistic multiplicative set (IMS) is given in this paper, which is called interval-valued intuitionistic multiplicative set (IVIMS). The IVIMS uses an unsymmetrical scale (Saaty's 1-9 scale) instead of the ordinary symmetrical scale in an intuitionistic fuzzy set or an interval-valued intuitionistic fuzzy set. IVIMSs can reflect our intuition more objectively in some special situations. The basic component of an IVIMS is interval-valued intuitionistic multiplicative number (IVIMN). To rank IVIMNs, the comparison laws are developed. Based on the pseudo-multiplication, we explore some interval-valued intuitionistic multiplicative operations and obtain several specific results when some specific forms are assigned. In addition, some distance measures and weighted distance measures between IVIMSs are developed to describe the difference of any two IVIMSs. By analyzing the range of the uncertain degree, a generalized interval-valued intuitionistic multiplicative set is presented, which is a generalization of the notions of IMS and IVIMS. Finally, a numerical example is given to illustrate our results.

A Class of New Interval-Valued Intuitionistic Fuzzy Distance Measures and their Applications in Discriminant Analysis

2012 ◽  
Vol 182-183 ◽  
pp. 1743-1745 ◽  
Author(s):  
Hua Zhao ◽  
Ming Fang Ni ◽  
Hai Feng Liu
Keyword(s):  
Discriminant Analysis ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Fuzzy Information ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Interval Valued

In this paper we develop a class of new distance measures for interval-valued intuitionistic fuzzy sets. Then we discuss some of the special cases of it by taking different parameters. Finally we apply them for discriminant analysis with interval-valued intuitionistic fuzzy information.

scholarly journals Complex Fuzzy Set-Valued Complex Fuzzy Measures and Their Properties

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shengquan Ma ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Complex Number ◽  
Complex Numbers ◽  
Complex Fuzzy Set ◽  
Fuzzy Measures

LetF*(K)be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance onF*(K), fuzzy complex number-valued measure onF*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous from above, autocontionuous from below, and autocontinuity of the defined fuzzy complex number-valued measures. Properties of fuzzy complex number-valued measures are studied in detail.

scholarly journals Picture Hesitant Fuzzy Clustering Based on Generalized Picture Hesitant Fuzzy Distance Measures

Knowledge ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 40-51
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Kifayat Ullah
Keyword(s):  
Fuzzy Set ◽  
Real Life ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Membership Degree ◽  
Future Directions ◽  
Clustering Problem ◽  
Fuzzy Distance ◽  
Picture Fuzzy Set ◽  
Life Issues

Certain scholars have generalized the theory of fuzzy set, but the theory of picture hesitant fuzzy set (PHFS) has received massive attention from distinguished scholars. PHFS is the combination of picture fuzzy set (PFS) and hesitant fuzzy set (HFS) to cope with awkward and complicated information in real-life issues. The well-known characteristic of PHFS is that the sum of the maximum of the membership, abstinence, and non-membership degree is limited to the unit interval. This manuscript aims to develop some generalized picture hesitant distance measures (GPHDMs) as a generalization of generalized picture distance measures (GPDMs). The properties of developed distance measures are investigated, and the generalization of developed theory is proved with the help of some remarks and examples. A clustering problem is solved using GPHDMs and the results obtained are explored. Some advantages of the proposed work are discussed, and some concluding remarks based on the summary of the proposed work and as well as future directions, are added.

scholarly journals Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 949
Author(s):  
Zhen Li ◽  
Xiaoyan Zhang
Keyword(s):  
Information Theory ◽  
Pattern Recognition ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Fuzzy Set ◽  
Equivalence Relation ◽  
Target Concept ◽  
Actual Case ◽  
Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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