BF-algebra - Wikipedia

This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages)

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.
Find sources: "BF-algebra" – news · newspapers · books · scholar · JSTOR (November 2015) (Learn how and when to remove this message)

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (November 2015) (Learn how and when to remove this message)

This article is an orphan, as no other articles link to it. Please introduce links to this page from related articles; try the Find link tool for suggestions. (January 2019)

The topic of this article may not meet Wikipedia's general notability guideline. Please help to demonstrate the notability of the topic by citing reliable secondary sources that are independent of the topic and provide significant coverage of it beyond a mere trivial mention. If notability cannot be shown, the article is likely to be merged, redirected, or deleted.
Find sources: "BF-algebra" – news · newspapers · books · scholar · JSTOR (July 2022) (Learn how and when to remove this message)

(Learn how and when to remove this message)

In mathematics, BF algebras are a class of algebraic structures arising out of a symmetric "Yin Yang" concept for Bipolar Fuzzy logic, the name was introduced by Andrzej Walendziak in 2007. The name covers discrete versions, but a canonical example arises in the BF space [-1,0]x[0,1] of pairs of (false-ness, truth-ness).

Definition

[edit]

A BF-algebra is a non-empty subset $X$ with a constant $0$ and a binary operation $*$ satisfying the following:

$x*x=0$
$x*0=x$
$0*(x*y)=y*x$

Example

[edit]

Let $Z$ be the set of integers and ' $-$ ' be the binary operation 'subtraction'. Then the algebraic structure $(Z,-)$ obeys the following properties:

$x-x=0$
$x-0=x$
$0-(x-y)=y-x$

References

[edit]

Walendziak, Andrzej (2007), "On BF-algebras", Math. Slovaca, 57 (2): 119–128, doi:10.2478/s12175-007-0003-x, MR 2357811