Learn R Programming
frbs (version 1.0-0)

inference: The process of fuzzy reasoning

Description

Inference refers to the process of fuzzy reasoning.

Usage

inference(MF, rule, names.varinput, type.tnorm,
    type.snorm)

Arguments

MF
a matrix of the degrees of membership functions which is a result of the fuzzifier.
rule
a matrix or list of fuzzy IF-THEN rules. See rulebase.
names.varinput
a list of names of the input variables.
type.tnorm
a value between 1 and 5 which represents the type of t-norm to be used:
  • 1means standard t-norm: min(x1, x2).
  • 2means Hamacher product: (x1 * x2)/(x1 + x2 - x1 * x2).
  • 3means Yager class (wit
type.snorm
a value between 1 and 5 which represents the type of s-norm to be used:
  • 1means standard s-norm: max(x1, x2).
  • 2means Hamacher sum: (x1 + x2 - 2x1 * x2) / 1 - x1 * x2.
  • 3means Yager class (wi

Value

  • a matrix of the degrees of the rules.

Details

There are two methods of inference for fuzzy systems based on linguistic rules: The Mamdani and Takagi Sugeno Kang model.

The Mamdani model: A fuzzy system with, e.g., two inputs x1 and x2 (antecedents) and a single output y (consequent) is described by the following fuzzy IF-THEN rule:

IF x1 is A1 and x2 is A2 THEN y is B

where A1 and A2 are the fuzzy sets representing the antecent pairs and B is the fuzzy set representing the consequent.

The Takagi Sugeno Kang model: Suppose we have two inputs x1 and x2 and output y, then the fuzzy IF-THEN rule is as follows:

IF x1 is A1 and x2 is A2 THEN y is y = f(x1, x2)

where y = f(x1, x2) is a crisp function in the consequent part which is usually a polynomial function, and A1 and A2 are the fuzzy sets representing the antecent pairs.

Futhermore, this function has the following capabilities:

  • It supports unary operators (not) and binary operators (AND and OR).
  • It provides linguistic hedge (extremely, very, somewhat, slightly).
  • there are several methods for the t-norm and s-norm.

See Also

defuzzifier, rulebase, and fuzzifier.