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Fuzzy data in statistics

Milan Mareš (2007)

Kybernetika

The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data...

Generalized deductive systems in subregular varieties

Ivan Chajda (2003)

Mathematica Bohemica

An algebra 𝒜 = ( A , F ) is subregular alias regular with respect to a unary term function g if for each Θ , Φ Con 𝒜 we have Θ = Φ whenever [ g ( a ) ] Θ = [ g ( a ) ] Φ for each a A . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset C A is a class of some congruence on Θ containing g ( a ) if and only if C is this generalized deductive system. This method is efficient (needs a finite number of steps).

Generalized inflations and null extensions

Qiang Wang, Shelly L. Wismath (2004)

Discussiones Mathematicae - General Algebra and Applications

An inflation of an algebra is formed by adding a set of new elements to each element in the original or base algebra, with the stipulation that in forming products each new element behaves exactly like the element in the base algebra to which it is attached. Clarke and Monzo have defined the generalized inflation of a semigroup, in which a set of new elements is again added to each base element, but where the new elements are allowed to act like different elements of the base, depending on the context...

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