combination_GRFN function

Combination of Gaussian random fuzzy numbers

combination_GRFN combines two Gaussian random fuzzy numbers using the generalized product-intersection rule with soft or hard normalization.

combination_GRFN(GRFN1, GRFN2, soft = TRUE)

Arguments

• GRFN1: A Gaussian random fuzzy number, encoded as a list with components mu, sig and h.
• GRFN2: A Gaussian random fuzzy number, encoded as a list with components mu, sig and h.
• soft: If TRUE (default), the combination rule with soft normalization is used. Otherwise, hard normalization is employed.

Returns

A list with two components:

• GRFN: The combined Gaussian random fuzzy number, encoded as a list with components mu, sig and h.
• conflict: The degree of conflict (equal to 0 if soft==FALSE).

Examples

GRFN1<-list(mu=1,sig=1,h=2)
GRFN2<-list(mu=2,sig=2,h=3)
GRFN12s<-combination_GRFN(GRFN1,GRFN2) # soft normalization
GRFN12h<-combination_GRFN(GRFN1,GRFN2,soft=FALSE) # hard normalization
print(GRFN12s)
print(GRFN12h)

References

Thierry Denoeux. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models. Fuzzy Sets and Systems, Vol. 453, Pages 1-36, 2023.

See Also

Bel, Pl, pl_contour