Correlation of fuzzy sets

Chiang, Ding-An; Lin, Nancy

doi:10.1016/s0165-0114(97)00127-9

Cited by 202 publications

(85 citation statements)

References 6 publications

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“…Correlation coefficients are an effective tool for addressing the relationship between elements with uncertain information that have been deeply studied [21,[24][25][26][27]. Chen et al [12] introduced the informational energy, correlation and correlation coefficients of hesitant fuzzy sets.…”

Section: Correlation Coefficient Of Hesitant Fuzzy Setsmentioning

confidence: 99%

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Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making

Lü

Liang

2017

Symmetry

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Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the length of extended hesitant fuzzy elements (EHFEs) and the correlation coefficients without taking into account the length of EHFEs, as a new extension of existing correlation coefficients for hesitant fuzzy sets (HFSs) and apply them to decision making under extended hesitant fuzzy environments. A real-world example based on the energy policy problem is employed to illustrate the actual need for dealing with the difference of evaluation information provided by different experts without information loss in decision making processes.

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Section: Correlation Coefficient Of Hesitant Fuzzy Setsmentioning

confidence: 99%

“…As many real-world data may be fuzzy, the concept of correlation has been extended to fuzzy environments [21,[24][25][26] and intuitionistic fuzzy environments [27][28][29][30][31][32][33]. For instance, Gerstenkorn and Manko [27] introduced the correlation coefficients of intuitionistic fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making

Lü

Liang

2017

Symmetry

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“…In this paper, the method proposed by C. Kao and S.T. Liu is followed due to the advantages it has, compared to the earlier proposed fuzzy correlation methods [7]. This method works good especially in an environment of fuzzy numbers.…”

Section: From Fuzzy Association Analysis To Fuzzy Correlation Analysismentioning

confidence: 99%

A Strategic Study of Mining Fuzzy Association Rules Using Fuzzy Multiple Correlation Measues

John¹,

Samuel²,

Prakash

2012

Journal of Algorithms & Computational Technology

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Two different data variables may behave very similarly. Correlation is the problem of determining how much alike the two variables actually are and association rules are used just to show the relationships between data items. Mining fuzzy association rules is the job of finding the fuzzy item-sets which frequently occur together in large fuzzy data set, where the presence of one fuzzy item-set in a record does not necessarily imply the presence of the other one in the same record. In this paper a new method of discovering fuzzy association rules using fuzzy correlation rules is proposed, because the fuzzy support and confidence measures are insufficient at filtering out uninteresting fuzzy correlation rules. To tackle this weakness, a fuzzy correlation measure for fuzzy numbers, is used to augment the fuzzy support-confidence framework for fuzzy association rules. We have extended the Apriori algorithm to fuzzy multiple correlation analysis, which is the new approach presented in this paper comparing to most of the previous works. A practical study over the academic behaviour of a particular school is done and some valuable suggestions are given, based on the results obtained.

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“…Chiang and Lin [24] discussed the correlation for fuzzy data based on the conventional statistics and derived a formula for the correlation coefficient of fuzzy sets. Liu and Kao [25] researched the correlation coefficient of fuzzy numbers by using a mathematical programming approach based on the classical definition of correlation coefficients.…”

Section: Introductionmentioning

confidence: 99%

A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application

Garg

Kumar

2017

Scientia Iranica

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Set pair analysis (SPA) is an updated theory for dealing with the uncertainty, which overlaps the other theories of uncertainty such as probability, vague, fuzzy and intuitionistic fuzzy set (IFS). Considering the fact that the correlation coefficient plays an important role during the decision-making process, in this paper, after pointing out the weakness of the existing correlation coefficients between the IFSs, we propose a novel correlation coefficient and weighted correlation coefficients formulation to measure the relative strength of the different IFSs. For it, firstly corresponding to each intuitionistic fuzzy number, the connection number of the SPA theory has been formulated in the form of the degree of identity, discrepancy and contrary and then based on its, a novel correlation coefficient measures have been defined. Pairs of identity, discrepancy and contrary of the connection number have been taken as a vector representation during the formulation. Lastly, a decision-making approach based on the proposed measures has been presented which has been illustrated by two numerical examples in pattern recognition and medical diagnosis.

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Correlation of fuzzy sets

Cited by 202 publications

References 6 publications

Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making

Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making

A Strategic Study of Mining Fuzzy Association Rules Using Fuzzy Multiple Correlation Measues

A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application

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