Extension of the correlation coefficient analysis via fuzzy aggregations applied in the dynamic consolidation of virtual machine in cloud computing

Abstract

The fuzzy set (FS) theory has been widely used in many fields of modern society since it was proposed by Zadeh in 1965. The traditional fuzzy set faces a specific limit as it fails to present a comprehensive description of all information from investigated problems. The theory of Atanassov’s Intuitionistic Fuzzy Sets (A-IFS) provide an important fuzzy extension to better explore and modelling situations where there is hesitancy, dealing with the membership and non-membership fuzzy information. Atanassov and Gargov presented the concept of the Atanassov’s interval-valued intuitionistic fuzzy set (A-IVIFS) and extended the A-IFS capability, dealing not only with the hesitance but also with imprecise information. In such approaches, the correlation analysis considers the extension of Pearce’s coefficient correlation, applied in many research areas such as clustering analysis, decision making, digital image processing and medical diagnosis. This work proposes the extension of the correlation coefficient analysis, introducing the study and application of a generalization the correlation coefficient following distinct approaches: (i) The constructive method of generalizing the n-dimensional fuzzy correlation coefficient is presented, based on ndimensional non-normed conjunctive functions, n-dimensional average operators and bivariate non-normed dissimilarity functions. (ii) The correlation coefficient extension from A-IFS to A-IVIFS is introduced, based on the n-dimensional generalized fuzzy correlation coefficient applied to the projection-functions of interval-valued intuitionistic fuzzy indexes. (iii) The study of main properties and algebraic expressions of the generalized correlation coefficient for the A-IFS and A-IVIFS are discussed, focusing on fuzzy modal connectives and, also considering dual and conjugate operators. (iv) The extension of the component named as Interval Fuzzy Load Balancing for Cloud Computing (Int-FLBCC) is conceived, by adding a degree of reliability on the correlate information results, which are obtained by evaluation through the n-dimensional generalized fuzzy correlation coefficient, which is performed over the fuzzy sets related to defuzzification step. The proposed correlation methodology is integrated Int-FLBCC model, as an additional potential analysis, collaborating to achieve a flexible approach for virtual machines dynamic consolidation, enabling to model uncertainty in resource usage and power efficiency in cloud computing.