Big data are products of human collective intelligence that are exponentially increasing in all facets of quantity, complexity, semantics, distribution, and processing costs in computer science, cognitive informatics, web-based computing, cloud computing, and computational intelligence. This paper presents fundamental big data analysis and mining technologies in the domain of social networks as a typical paradigm of big data engineering. A key principle of computational sociology known as the characteristic opinion equilibrium is revealed in social networks and electoral systems. A set of numerical and fuzzy models for collective opinion analyses is formally presented. Fuzzy data mining methodologies are rigorously described for collective opinion elicitation and benchmarking in order to enhance the conventional counting and statistical methodologies for big data analytics.