Several diierent basic properties are used for developing a system of calculus for subdiierentials. They are a nonlocal fuzzy sum rule in 5, 25], a multidirectional mean value theorem in 7, 8], local fuzzy sum rules in 14, 15] and an extremal principle in 19, 21]. We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.

If we view fuzzy logic as a logic, i.e., as a particular case of a multivalued logic, then one of the most natural questions to ask is whether the corresponding propositional logic is decidable, i.e., does there exist an algorithm that, given two propositional formulas F and G, decides whether these two formulas always have the same truth value. It is known that the simplest fuzzy logic, in whi...

This paper presents new results concerning the effective practical computation of the membership function of the infinite sum (defined via the supHamacher-norm convolution) of triangular fuzzy numbers. Namely, we shall calculate the limit distribution of the Hγ-sum ã1 ⊕ ã2 ⊕ · · · ⊕ ãn ⊕ · · · of triangular fuzzy numbers ãi, i ∈ N, for γ = 0, 1, 2.

Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...