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From computing with numbers to computing with words - From manipulation of measurements to manipulation of perceptions

Lotfi Zadeh (2002)

International Journal of Applied Mathematics and Computer Science

Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired...

From two- to four-valued logic

Chris Brink (1993)

Banach Center Publications

The purpose of this note is to show that a known and natural four-valued logic co-exists with classical two-valued logic in the familiar context of truth tables. The tool required is the power construction.

From well to better, the space of ideals

Raphaël Carroy, Yann Pequignot (2014)

Fundamenta Mathematicae

On the one hand, the ideals of a well quasi-order (wqo) naturally form a compact topological space into which the wqo embeds. On the other hand, Nash-Williams' barriers are given a uniform structure by embedding them into the Cantor space. We prove that every map from a barrier into a wqo restricts on a barrier to a uniformly continuous map, and therefore extends to a continuous map from a countable closed subset of the Cantor space into the space of ideals of the wqo. We then...

Function operators spanning the arithmetical and the polynomial hierarchy

Armin Hemmerling (2010)

RAIRO - Theoretical Informatics and Applications

A modified version of the classical µ-operator as well as the first value operator and the operator of inverting unary functions, applied in combination with the composition of functions and starting from the primitive recursive functions, generate all arithmetically representable functions. Moreover, the nesting levels of these operators are closely related to the stratification of the arithmetical hierarchy. The same is shown for some further function operators known from computability and complexity theory....

Functional monadic n -valued Łukasiewicz algebras

A. V. Figallo, Claudia A. Sanza, Alicia Ziliani (2005)

Mathematica Bohemica

Some functional representation theorems for monadic n -valued Łukasiewicz algebras (qLk n -algebras, for short) are given. Bearing in mind some of the results established by G. Georgescu and C. Vraciu (Algebre Boole monadice si algebre Łukasiewicz monadice, Studii Cercet. Mat. 23 (1971), 1027–1048) and P. Halmos (Algebraic Logic, Chelsea, New York, 1962), two functional representation theorems for qLk n -algebras are obtained. Besides, rich qLk n -algebras are introduced and characterized. In addition,...

Functions Equivalent to Borel Measurable Ones

Andrzej Komisarski, Henryk Michalewski, Paweł Milewski (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.

Functions of Baire class one

Denny H. Leung, Wee-Kee Tang (2003)

Fundamenta Mathematicae

Let K be a compact metric space. A real-valued function on K is said to be of Baire class one (Baire-1) if it is the pointwise limit of a sequence of continuous functions. We study two well known ordinal indices of Baire-1 functions, the oscillation index β and the convergence index γ. It is shown that these two indices are fully compatible in the following sense: a Baire-1 function f satisfies β ( f ) ≤ ω ξ ₁ · ω ξ ₂ for some countable ordinals ξ₁ and ξ₂ if and only if there exists a sequence (fₙ) of Baire-1 functions...

Fundamentals of a mathematical theory of fuzzy sets

Jindřich Spal (1982)

Aplikace matematiky

Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.

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