We introduce the notion of n-fold implicative filters and n-fold implicative lattice implication algebras. We give characterizations of n-fold implicative filters and nfold implicative lattice implication algebras. Finally, we construct an extension property for n-fold implicative filter. 2000 Mathematics Subject Classification. 03G10, 06B10.

In order to research the logical system whose propositional value is given in a lattice from the semantic viewpoint, Xu [7] proposed the concept of lattice implication algebras, and discussed some of their properties. Xu and Qin [8] introduced the notion of implicative filters in a lattice implication algebra, and investigated some of their properties. Turunen [5] introduced the notion of Boole...

This paper describes an algorithmic means for inducing implication networks from empirical data samples. The induced network enables efficient inferences about the values of network nodes if certain observations are made. This implication induction method is approximate in nature as probablistic network requirements are relaxed in the construction of dependence relationships based on statistica...

In a propositional calculus based on combinatory logic it is necessary to have a restriction on the deduction theorem for implication as otherwise Curry's paradox results (see [5]). In [1] and [2] we restricted the deduction theorem for implication as follows: where Δ is any sequence of obs and HX stands for "X is a proposition". Motivation for this deduction theorem was given in [2] using the ...

Yager introduced a fuzzy screening procedure to select, from a large class of alternatives, a small subset to be further investigated. In his methodology the Kleene-Dienes implication operator was employed to find the unit score of each alternative by each expert. Generalizing Yager’s principle we suggest the use of Sand R-implication operators to find the unit score.

This paper deals with some dependencies between fuzzy conjunctions and fuzzy implications. More precisely, a fuzzy implication generated from a fuzzy conjunction and a fuzzy conjunction induced by a fuzzy implication is considered. In the case of a fuzzy conjunction only border conditions and monotonicity are assumed. The results are illustrated by examples of weak fuzzy connectives.

Introduction of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that...

In this paper, three new operations have been introduced on intuitionistic fuzzy soft sets. They are based on Second Zadeh‟s implication, conjunction and disjunction operations on intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied. Index Terms — Second Zadeh‟s implication, Second Zadeh‟s conjunction, Second Zadeh‟s disjunctio...

In this paper, we propose a new method for choosing implications. Our method allows to compare two fuzzy implications. If the truth value of the antecedent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication consequent.

In this paper, the concept of v-filters on lattice implication algebras is introduced by linking the Vague set and filter theory of lattice implication algebras; The properties and equivalent characterizations of v-filters are investigated; The relations between v-filters and filters are studied.