fntom 0.2.0

Implements a finite, negative, totally ordered monoid together with methods to compute its one-element Rees coextensions

fntom

This package contains an implementation of the algorithm that serves to find all the one-element Rees co-extensions of a given finite, negative totally ordered monoid (abbreviated by f. n. tomonoid).

Note that a commutative f. n. tomonoid represents a conjunction in the semantics of a many-valued (fuzzy) logic that has finitely many totally ordered logical values.

Installation

Install the package from PyPI utilizing the pip module:

python -m pip install fntom

Alternatively, you can download and unpack this package and install it by:

python -m pip install path

where path refers to the directory where setup.py is present.

Example

The following program defines a f. n. tomonoid with the Cayley table:

0	x	y	z	1
0	0	0	x	z
0	0	0	0	y
0	0	0	0	x
0	0	0	0	0

Subsequently, it finds all its commutative one-element Rees co-extensions and displays both the f. n. tomonoid and its co-extensions on the terminal output:

    import fntom
    counter = fntom.Counter()
    xyzTable = [['0' ,'x' ,'y' ,'z' ,'1'],
                ['0' ,'0' ,'0' ,'x' ,'z'],
                ['0' ,'0' ,'0' ,'0' ,'y'],
                ['0' ,'0' ,'0' ,'0' ,'x'],
                ['0' ,'0' ,'0' ,'0' ,'0']]
    fntom = fntom.FNTOMonoid(counter.getNew(), xyzTable = xyzTable)
    coextensions = fntom.computeCoExtensions(counter, commutative = True)
    fntom.show()
    for coext in coextensions:
        coext.show()

Documentation

For a detailed decription of the program and its purpose, see the documentation generated by pdoc3 in the directory docs/ or read the papers listed in References below.

References

For the theoretical description of the problem and for the description of the algorithm se the paper:

• M. Petrik and Th. Vetterlein. Rees coextensions of finite, negative tomonoids. Journal of Logic and Computation 27 (2017) 337-356. DOI: 10.1093/logcom/exv047, PDF.

For a more detailed description of the algorithm see the papers:

• M. Petrik and Th. Vetterlein. Algorithm to generate finite negative totally ordered monoids. In: IPMU 2016: 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Eindhoven, Netherlands, June 20-24, 2016. PDF.

• M. Petrik and Th. Vetterlein. Algorithm to generate the Archimedean, finite, negative tomonoids. In: Joint 7th International Conference on Soft Computing and Intelligent Systems and 15th International Symposium on Advanced Intelligent Systems. Kitakyushu, Japan, Dec. 3-6, 2014. DOI: 10.1109/SCIS-ISIS.2014.7044822. PDF.

For more details on one-element co-extensions of finite, negative, tomonoids see the paper:

• M. Petrik and Th. Vetterlein. Rees coextensions of finite tomonoids and free pomonoids. Semigroup Forum 99 (2019) 345-367. DOI: 10.1007/s00233-018-9972-z, PDF.