μ A ¯ : Membership function of the fuzzy set A ¯ .

X: Referential set.

I: Valuation set.

: Set of real numbers.

I X : Set of all fuzzy sets from X to I.

A ¯ α : α-cut of a fuzzy set A ¯ .

A ¯ α + : Strong α-cut of a fuzzy set A ¯ .

: For all.

: There exist.

A ¯ C : Complement of a fuzzy set A ¯ .

A ¯ B ¯ : Intersection of two fuzzy sets A ¯ and B ¯ .

A ¯ B ¯ : Union of two fuzzy sets A ¯ and B ¯ .

X ¯ C : Classical solution.

X ¯ e : Extension Principle solution.

X ¯ I : α-cut and interval arithmetic solution.