The Sigma-Max System Induced from Randomness and Fuzziness

• DOI: 10.48550/arxiv.2110.07722
• Publication Date: 2021-01-01
• Authors: Wei Mei; Ming Li; Yuanzeng Cheng; Limin Liu
• Keywords: Operator (biology); Axiomatic system

This paper managed to induce probability theory (sigma system) and possibility (max respectively from randomness fuzziness, through which the premature of is expected be well founded. Such an objective achieved by addressing three open key issues: a) lack clear mathematical definitions fuzziness; b) intuitive definition possibility; c) abstraction procedure axiomatic probability/possibility their definitions. Especially, last issue involves question why axiom "maxitivity" adopted for measure. By taking advantage properties well-defined we derived important conclusion that "max" only but un-strict disjunctive operator applicable across fuzzy event space, exact feature extraction assures max inference mechanism. It fair claim long-standing problem consensus foundation resolved, would facilitate wider adoption in practice promote cross prosperity two uncertainty theories possibility.