On some inexact relations in probabilized Boolean algebras.
This paper is devoted to characterize monotonicity, conditionality and transitivity of some rational relations defined in a probabilized Boolean Algebra.
Modus ponens on Boolean algebras revisited.
In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.
Ovchinnikov's automorphisms revisited.
In [6] an approach to the representation of synonyms and antonyms via the automorphisms of the De Morgan Algebra [0,1] was suggested. In [3], Ovchinnikov established a representation theorem for automorphisms of the function's complete and completely distributive lattice [0,1] with the pointwise extension of Min and Max operations in [0,1]. Ovchinnikov results are now inmediately generalized by using a positive t-norm T and its dual eta-dual t-conorm T*. These results are applied to study the automorphism...
On the identity of fuzzy material conditionals.
Averaging premises.
This paper deals with the sets of strict conjectures and consequences of a given collection P of premises. The set of Averaging Functions is introduced on lattices and some properties of these functions are shown. Averaging Functions allow to interpret restricted consequences as averages of premises. The subset of consequences C*(P) and the subset of conjectures Φ*(P) defined by means of the averaging function g are introduced, and their properties are studied. This sets allow to give decomposition...
Searching degrees of self-contradiction in Atanassov's fuzzy sets.
In [11] and [12] Trillas et al. introduced the study of contradiction in the framework of Fuzzy Logic because of the significance to avoid contradictory outputs in the processes of inference. Later, the study of contradiction in the framework of intuitionistic or Atanassov s fuzzy sets was initiated in [6] and [5]. The aim of this work is to go into the problem of measuring the self-contradiction in the case of intuitionistc fuzzy sets, since it is interesting to know not only if a set is contradictory,...
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