In this paper, we will derive some twist criteria for the periodic solution of a periodic scalar Newtonian equation using the third order approximation. As an application to the forced pendulum ẍ + ω2 sinx = p(t), we will find an explicit bound P (ω) for the L1 norm, ‖p‖1, of the periodic forcing p(t) using the frequency ω as a parameter such that the least amplitude periodic solution of the fo...

Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T -transitivity. It will be shown that preservation of T -transitivity is closely relat...

The aim of this work is to introduce an approach for interval-valued R-implications, which satisfy some analogous properties of R-implications. We show that the best interval representation of an R-implication that is obtained from a left continuous tnorm coincides with the interval-valued R-implication obtained from the best interval representation of such t-norm, whenever this is an inclusion...

Propositional fuzzy logics given by a combination of a continuous SBL t-norm with finitely many idempotents and of an involutive negation are investigated. A characterization of continuous t-norms which, in combination with different involutive negations, yield either isomorphic algebras or algebras with distinct and incomparable sets of propositional tautologies is presented.

It is an open question whether a non-trivial convex combination of triangular norms (resp. conorms) can be a triangular norm (resp. conorm). We investigate the analogous question for S-implications and R-implications.

We introduce the notion of sensible fuzzy ideals of BCK-algebras with respect to a t-conorm and investigate some of their properties. We give the conditions for a sensible fuzzy subalgebra with respect to a t-conorm to be a sensible fuzzy ideal with respect to a t-conorm. Some properties of the direct product and S-product of fuzzy ideals of BCK-algebras with respect to a t-conorm are also disc...

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of s...

In this work we have solved an open problem related to the continuity of R-implications. We have fully characterized the class of continuous R-implications obtained from any arbitrary t-norm. Using this result, we also determine the exact intersection between the continuous subsets of R-implications and (S,N)implications. Keywords— R-implication, (S,N)-implication, Łukasiewicz implication, t-norm.