Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...

This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple impli...

in this paper, the notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF -)F -soft lattice implication algebras) are introduced. Basic properties of (IF -)F -soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(∈,∈ ∨qk)((∈,∈ ∨ qk))-fuzzy (...

the aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in bcialgebras and to investigate some of their properties. several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of bci-algebras i...

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.

as a generalization of the triple i method, the universal triple imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. the universal triple i principle is putforward, which improves the previous triple i principle. then,unified form of universal triple i method is established based onthe (0,1)-implication or r-implication. moreover, the reversibilityproperty o...

The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...

As a generalization of the triple I method, the universal triple Imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. The universal triple I principle is putforward, which improves the previous triple I principle. Then,unified form of universal triple I method is established based onthe (0,1)-implication or R-implication. Moreover, the reversibilityproperty o...

We introduce a fuzzy implication stemming from a fuzzy lattice inclusion measure. We study “reasonable axioms” and properties of the aforementioned fuzzy implication, which (properties) are typicaly required in the literature and could be important in certain applications.