In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

in this paper, we firstly show that the $n$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $n$-dual operation. as a dual result, the $n$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

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...

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

In this paper, a set of axioms is given that characterizes those functions I : [0, 1] → [0, 1] for which a left-continuous uninorm U exists in such a way that I is the residual implication derived from U . A characterization for the particular case when U is representable is also given. Keywords— Implication function, left-continuity, residual implication, uninorm.

In this paper, we study the relationships between left (right) semi-uninorms and implications on a complete lattice. We firstly discuss the residual operations of left and right semi-uninorms and show that the right (left) residual operator of a conjunctive right (left) ∨-distributive left (right) semi-uninorm is a right ∧-distributive implication that satisfies the neutrality principle. Then, ...

In a recent preprint of F. Gouvea and N. Yui (see arxiv.org/abs/0902.1466) a detailed account is given of a patching argument due to Serre that proves that the modularity of all rigid Calabi-Yau threefolds defined over Q follows from Serre’s modularity conjecture. In this note (a letter to N. Yui) we give an alternative proof of this implication. The main difference with Serre’s argument is tha...