Association measures on the set of subintervals of [0,1]

The methods of construction of non-statistical association measures on the set of subintervals of [0,1] are proposed. These measures are defined as functions satisfying the properties generalizing properties of correlation coefficient. The proposed association measures can be extended on interval valued fuzzy sets and on interval valued intuitionistic fuzzy sets.

[1]  Lukas Furst,et al.  Multivariate Data Analysis With Readings , 2016 .

[2]  Vladik Kreinovich,et al.  Interval-Valued Degrees of Belief: Applications of Interval Computations to Expert Systems and Intelligent Control , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  K. Qin,et al.  Similarity measures of interval-valued fuzzy sets , 2015, J. Intell. Fuzzy Syst..

[4]  Vladik Kreinovich,et al.  One More Geometric Interpretation of Pearson’s Correlation , 2015 .

[5]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[6]  Ildar Z. Batyrshin,et al.  On the structure of involutive, contracting and expanding negations , 2003, Fuzzy Sets Syst..

[7]  C. A. Murthy,et al.  Correlation between two fuzzy membership functions , 1985 .

[8]  S. Ovchinnikov,et al.  On strict preference relations , 1991 .

[9]  Ildar Z. Batyrshin,et al.  Association Measures on Sets with Involution and Similarity Measure , 2014, WCSC.

[10]  Ildar Z. Batyrshin,et al.  Up and Down Trend Associations in Analysis of Time Series Shape Association Patterns , 2012, MCPR.

[11]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[12]  Ildar Z. Batyrshin,et al.  Time series shape association measures and local trend association patterns , 2016, Neurocomputing.

[13]  Association Measures , 2008, Encyclopedia of GIS.

[14]  Ildar Z. Batyrshin.  Association Measures and Aggregation Functions , 2013, MICAI.

[15]  Ildar Z. Batyrshin,et al.  Association measures on [0, 1] , 2015, J. Intell. Fuzzy Syst..