The Nonlinear Separation Theorem and a Representation Theorem for Bishop–Phelps Cones

2015 ◽  
pp. 419-430 ◽  
Author(s):  
Refail Kasimbeyli ◽  
Nergiz Kasimbeyli
Keyword(s):  
Representation Theorem ◽  
Separation Theorem ◽  
Nonlinear Separation

scholarly journals A note on homomorphisms of Hilbert algebras

2002 ◽  
Vol 29 (1) ◽  
pp. 55-61 ◽  
Author(s):  
Sergio Celani
Keyword(s):  
Representation Theorem ◽  
Separation Theorem ◽  
Boolean Algebras ◽  
Order Ideal ◽  
Hilbert Algebra ◽  
Ordered Sets ◽  
Hilbert Algebras ◽  
Deductive Systems ◽  
Similar Notion

We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-homomorphism as a generalization of the similar notion of Boolean algebras and we study its relation with the homomorphism and with the deductive systems.

scholarly journals Study of Two Families of Generalized Yager’s Implications for Describing the Structure of Generalized (h,e)-Implications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1490
Author(s):  
Raquel Fernandez-Peralta ◽  
Sebastia Massanet ◽  
Arnau Mir
Keyword(s):  
Representation Theorem ◽  
Internal Factors ◽  
Fuzzy Implication ◽  
The Family

In this study, we analyze the family of generalized (h,e)-implications. We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized (h,e)-implication in terms of two families of fuzzy implication functions. These two families can be interpreted as particular cases of the (f,g) and (g,f)-implications, which are two families of fuzzy implication functions that generalize the well-known f and g-generated implications proposed by Yager through a generalization of the internal factors x and 1x, respectively. The behavior and additional properties of these two families are also studied in detail.

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