Analysing Properties, Conjugate and Dual Constructions on Fuzzy s-X(N)or Connectives

The main contribution of this paper is the study of a fuzzy X(N)or class, named as fuzzy s-(N)Xor, which is explicitly defined and graphically represented by the product t-norm, probabilistic sum and standard negation. The fuzzy s-Xor (co)implications obtained by such fuzzy s-X(N)or connectives are also considered along with the corresponding conjugate functions. The relationship between a fuzzy s-Xor E and its conjugate function E^ρ is discussed in the following together with their dual constructions. Additionally, for a fuzzy s-Xor E connective both constructions, its dual connective XNor E_N and its conjugate E^ρ, satisfy analogous properties of the e-Xor class.