Fuzzy Logic norms

In this package, you will find some utilities to apply fuzzy logic t-norms and t-conorms to datasets.

You can find all the information about the T-norms and T-conorms in the following links: - T-norms and T-conorms - Construction of T-norms

The inputs for the script are:

• dataset-id: (dataset-id) Dataset where norms are applied
• field-id1: (string) Field ID or name of the first operand
• field-id2: (string) Field ID or name of the second operand
• norms: (list) List of norms to apply, with params if needed. See more information below.

The outputs for the script are:

• fuzzy-dataset: (dataset-id) Dataset with some new columns with the result of applying the norms (t-norms or t-conorms).

Fields used as operands must contain real values between 0 and 1. As they are logical values it doesn't make sense having values outside this range. In this case, the script will raise an error.

The script will create a new column in the dataset for each one of the norms specified in the norms list.

T-norms and T-conorms

Bellow, you can find an example of the content of the norms input:

["min-tnorm","product","lukasiewicz", "drastic-tnorm",
"nilpotent-min",["schweizer-sklar", 0.5], ["hamacher", 0,5]]

As you can see there are some norms that need a parameter, that has to be specified in this way.

These are the possibles t-norms:

• min-tnorm: Minimum t-norm. Also called the Gödel t-norm. No parameters.
• product: Product t-norm. The ordinary product of real numbers. No parameters.
• lukasiewicz: Łukasiewicz t-norm. No parameters.
• drastic-tnorm: Drastic t-norm. No parameters.
• nilpotent-min: Nilpotent minimum t-norm. No parameters.
• [schweizer-sklar p]: Schweizer–Sklar t-norms. Parameter p in the range [-∞, ∞]
• [hamacher p]: Hamacher t-norms. Parameter p in the range [0, ∞]
• [yager p]: Yager t-norms. Parameter p in the range [0, ∞]
• [aczel-alsina p]: Aczél–Alsina t-norms. Parameter p in the range [0, ∞]
• [dombi p]: Dombi t-norms. Parameter p in the range [0, ∞]
• [sugeno-weber p]: Sugeno–Weber t-norms. Parameter p in the range [-1, ∞]

These are the possible t-conorms:

• max-tconorm: Maximum t-norm. Dual to the minimum t-norm, is the smallest t-conorm. No parameters
• probabilistic: Probabilistic t-norm. It's dual to the product t-norm. No parameters.
• bounded: Bounded t-norm. It'ss dual to the Łukasiewicz t-norm. No parameters.
• drastic-tconorm: Drastic t-conorm. It's dual to the drastic t-norm. No paramters.
• nilpotent-max: Nilpotent maximum t-conorm. It's dual to the nilpotent minumum.
• einstein-sum: Einstein t-conorm. It's a dual to one of the Hamacher t-norms.

Tests

Tests are included for this whizzml script. You can find more info about the tests in the top-level readme file.