1. INTRODUCTIONTHE INTERNET IS BECOMING AN INCREASINGLY VITAL TOOL IN OUR EVERYDAY LIFE, BOTH PROFESSIONAL AND PERSONAL, AS ITS USERS ARE BECOMING MORE NUMEROUS. IT IS NOT SURPRISING THAT BUSINESS IS INCREASINGLY CONDUCTED OVER THE INTERNET. PERHAPS ONE OF THE MOST REVOLUTIONARY CONCEPTS OF RECENT YEARS IS CLOUD COMPUTING. THE CLOUD, AS IT IS OFTEN REFERRED TO, INVOLVES USING COMPUTING RESOURCES -HARDWARE AND SOFTWARE – THAT ARE DELIVERED AS A SERVICE OVER THE INTERNET (SHOWN AS A CLOUD IN MOST IT DIAGRAMS). MANY COMPANIES ARE CHOOSING AS AN ALTERNATIVE TO BUILDING THEIR OWN IT INFRASTRUCTURE TO HOST DATABASES OR SOFTWARE, HAVING A THIRD PARTY TO HOST THEM ON ITS LARGE SERVERS, SO THE COMPANY WOULD HAVE ACCESS TO ITS DATA AND SOFTWARE OVER THE INTERNET.THE USE OF CLOUD COMPUTING IS GAINING POPULARITY DUE TO ITS MOBILITY, HUGE AVAILABILITY AND LOW COST. ON THE OTHER HAND IT BRINGS MORE THREATS TO THE SECURITY OF THE COMPANY’S DATA AND INFORMATION. AT AN EQUALLY SIGNIFICANT EXTENT IN RECENT YEARS, DATA MINING TECHNIQUES HAVE EVOLVED AND BECAME MORE USED, DISCOVERING KNOWLEDGE IN DATABASES BECOMING INCREASINGLY VITAL IN VARIOUS FIELDS: BUSINESS, MEDICINE, SCIENCE AND ENGINEERING, SPATIAL DATA ETC. THE EMERGING CLOUD COMPUTING TRENDS PROVIDES FOR ITS USERS THE UNIQUE BENEFIT OF UNPRECEDENTED ACCESS TO VALUABLE DATA THAT CAN BE TURNED INTO VALUABLE INSIGHT THAT CAN HELP THEM ACHIEVE THEIR BUSINESS OBJECTIVES. [ALEX BERSON (AUTHOR), STEPHEN J.SMITH (AUTHOR), BERSON (AUTHOR), KURT THEARLING (AUTHOR), 2013, ROGER JENNINGS, 2014,MERRIAM-WEBSTER, 2012]IN Bayesian analysis, PRECISE A-PRIORI DISTRIBUTIONS ARE OFTEN NOT AVAILABLE. TO CAPTURE SUCH UNCERTAINTY, A MORE GENERAL FORM OF A-PRIORI INFORMATION CAN BE EXPRESSED BY USING SOFT MODELS. THE MATHEMATICAL BASES FOR SUCH MODELS ARE FUZZY NUMBERS AND FUZZY VALUED FUNCTIONS, ESPECIALLY THE SO-CALLED FUZZY PROBABILITY DENSITIES. BASED ON THESE GENERALIZED PROBABILITY DENSITIES, BAYES’ THEOREM CAN BE GENERALIZED. MOREOVER, THE CONCEPTS OF PREDICTIVE DISTRIBUTIONS AND STATISTICAL DECISION MODELS CAN BE ADAPTED ACCORDINGLY. THESE CONCEPTS YIELD MORE REALISTIC APPROACHES FOR CAPTURING THE UNCERTAINTY OF DATA AND A-PRIORI INFORMATION. [MARK JEFFERY, 2013].