# On Probabilistic Correlation Coefficients for Fuzzy Numbers

• Robert Fullér
• István Á. Harmati
• Péter Várlaki
Part of the Topics in Intelligent Engineering and Informatics book series (TIEI, volume 2)

## Abstract

In this paper we introduce alternative definitions for the measure of interactivity between fuzzy numbers by defining non-uniform probability distributions on the γ-level sets (γ-cuts) of their joint possibility distribution. These probability distributions are determined by the shape function of the joint possibility distribution if we consider this as a probability density function (with an appropriate constant multiplier), so we use only the information contained in the joint possibility distribution. We also show some detailed examples for the calculation when the joint possibility distributions are defined by well-known t-norms, such as Mamdani, Lukasiewicz and Larsen t-norms.

## Keywords

Probability Density Function Fuzzy Number Joint Probability Density Function Fuzzy Measure Membership Grade
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Robert Fullér
• 1
• István Á. Harmati
• 2
• Péter Várlaki
• 3
• 4
1. 1.Institute of Intelligent Engineering Systems, John von Neumann Faculty of InformaticsÓbuda UniversityBudapestHungary
2. 2.Department of Mathematics and Computational ScienceSzéchenyi István UniversityGyőrHungary
3. 3.Széchenyi István UniversityGyőrHungary
4. 4.Budapest University of Technology and EconomicsBudapestHungary