Fuzzy correlational analysis for dynamic consolidation of virtual machines in cloud computing environment

This theoretical research in fuzzy correlation analysis integrates data uncertainty analysis by measuring the strength of the linear relationship restricted to two fuzzy sets. As the relevant contribution to this research area, this paper presents the axiomatic definition of the n-dimensional generalized fuzzy correlation coefficient (nGCC), assigning to n input fuzzy sets an output value in the interval [-1,1]. Thus, the properties of general overlap functions and fuzzy negations are studied, discussing binary non-normed restricted dissimilarity functions, and the n-dimensional non-normed conjunctive functions. This study provides new methods for the n-dimensional generalized fuzzy correlation coefficient analysis, regarding their applications in solving multi-criteria and decision-making problems founded on fuzzy logic extensions. The n-dimensional non-normed conjunctive aggregation functions are also introduced, as range domain extensions from [0,1] to [-1.1], covering the interpretation of negative to positive variable associations. The proposal correlation analysis promotes a better evaluation and data selection even when more than one algorithm is applied to evaluate the reduction methods in the defuzzification process based on Interval-valued Fuzzy Logic. We also investigate the relevance to determine a reliable result from the fuzzy inference system based on the nGCC methodology. This correlation methodology applied to the Interval Fuzzy Load Balancing for Cloud Computing (Int-FLBCC) model contributes as a flexible approach for virtual machines dynamic consolidation enabling improvements in resource usage and power efficiency, improving the computational system's energy efficiency. So, the nGCC methodology extends the Int-FLBCC model by adding other degrees of reliability to the results obtained with diverse evaluations through n-dimensional generalized fuzzy correlation coefficient expressions, exploring average aggregations as arithmetic and exponential means and the median operator.

Automated summary

This paper presents the axiomatic definition of n-dimensional generalized fuzzy correlation coefficient and studies the properties of general overlap functions and fuzzy negations. It provides new methods for analyzing the n-dimensional generalized fuzzy correlation coefficient and explores its applications in solving multi-criteria and decision-making problems based on fuzzy logic extensions.