Abstract
Probabilistic set theory is discussed from a mathematical point of view. It is constructed considering ambiguity or variety of objects and subjectivity or evolution of knowledge of observers, and it includes fuzzy set theory. The background of the idea is first explained and some inconveniences of fuzzy set theory are pointed out. A probabilistic set on a total space is defined by a pointwise measurable function from a parameter space to a characteristic space. The main result is that the family of probabilistic sets constitutes a complete pseudo Boolean algebra. Some new concepts are shown such as probabilistic mappings, moment analysis, and expected cardinal numbers. The possibility of moment analysis is an important result and it cannot be seen in other theories.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
