Machine Learning and Statistics aren’t very different fields. Actually, someone recently defined Machine Learning as ‘doing statistics on a Mac’. Some of the fundamental Statistical and Probability Theory needed for ML are Combinatorics, Probability Rules & Axioms, Bayes’ Theorem, Random Variables...
uncertainty/ C1160 Combinatorial mathematics C1290 Applications of systems theoryThe 'aggregative operator' introduced by Combi (1982) in his analysis of 'basic concepts for a theory of evaluation' in this journal is based on the axioms of associativity, continuity, and monotonicity. In this paper...
Even the Roman numeral system has no way of representing the concept of zero (0). That concept is critical in the Hindu-Arabic number system, however, where 0 is treated in exactly the same way as any other number. Axioms in arithmetic ...
BIG DISCLAIMER: This blog post uses one particular concept of infinity. There are different concepts of infinity in mathematics (e.g., see the “shapes and flavors” link early in this post), and for those, some of the answers are different. For example, “2^infinity = infinity” is tru...
It was natural, in a decade when the axiomatic method was still a fresh idea, to attempt to find the fundamental properties of dependence common to these notions, postulate them as axioms, and derive their common properties from the axioms in a purely abstract manner. This was done by many...
An Axiomatic Basic for Computer Programming.Explores the logical foundations of computer programming using techniques first applied in the study of geometry and have later been extended to other branches of mathematics. Elucidation of sets of axioms and rules of inference used in proofs of the ...
Liu L, Li K (2005) Fuzzy filters of BL-algebras. Inf Sci 173(1):141–154. https://doi.org/10.1016/j.ins.2004.07.009 Article MathSciNet Google Scholar McCune W, Veroff R, Fitelson B, Harris K, Feist A, Wos L (2002) Short single axioms for Boolean algebra. J Autom Reason 29...
For example, any “concrete” normal space (i.e. normality can be shown without using extra set theory axioms) is likely to be countably paracompact. Thus any space that is normal and not paracompact is likely countably paracompact (if the fact of being normal and not paracompact is ...
Geometry postulates, or axioms, are accepted statements or facts. Thus, there is no need to prove them. For example, the following statements are axioms: Human beings cannot live without oxygen. The sun sets in the west. Human beings are more intelligent than reptiles....
Dubois D., Kerre E., Mesiar R. and Prade H. (1999). Fuzzy interval analysis.Fundamentals of Fuzzy Sets(Dubois D. and Prade H., eds.), Kluwer Acad. Publ., 1999. This volume. Google Scholar Dubois D. and Koning J.L. (1991). Social choice axioms for fuzzy set aggregation,Fuzzy ...