The OWA operators are traditionally used in the context of decision making as the means to aggregate the satisfaction of single criteria into a overall preference index. They belong to the class of averages, entailing compensatory properties. Differently, t-norms and t-conorms entail the reinforcement property, since there is a kind of interaction between the degree of criteria satisfaction. A ...

In this article, we derive approximations and effective boundary laws for solutions uε of the Poisson equation on a domain Ωε ⊂ Rn whose boundary differs from the smooth boundary of a domain Ω ⊂ R n by rapid oscillations of size ε. First, we construct a boundary layer correction which yields an O(ε3/2) approximation in the energy norm, and an O(ε2) approximation in the L2-norm if Ω is bounded. ...

A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. These schemes are based on the Frank t-norm family and preserve transitivity in the fuzzification process.

Let dν be the metric associated with a strictly positive submeasure ν on some boolean algebra P. If dν is bounded from above by 1, Eν = 1 − dν is a (fuzzy) similarity relation on P at least w.r.t. the Lukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms. In this paper, we show that under certain assumptions on P and ν, we may associate with ν in a natural way a continuous t-nor...

A generalization of bags is proposed and fundamental operations are described. That is, a real-valued bag is proposed which is a straightforward generalization of the traditional bags, but is necessary for complementation, and s-norm and t-norm operations. We mainly describe how complementation and s-norms are related. As a result a duality theorem between s-norm and t-norm is obtained. R-bag r...

Triangular subnorms are associative commutative non-decreasing operations on the unit interval, upper bounded by the minimum. Continuous triangular subnorms are shown to be ordinal sum of Archimedean continuous t-subnorms with at most one proper t-subnorm summand. Special attention is paid to generate continuous t-subnorms. An application of continuous t-subnorms to the construction of left-con...

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...

The class of discrete uninorms U such that their underlying t-norm T and t-conorm S are smooth is studied. The different cases combining when T is the minimum or the Łukasiewicz t-norm and S is the maximum or the Łukasiewicz t-conorm, are characterized and the number of discrete uninorms with these underlying operators is given. It is also studied the general case when T and/or S are smooth, bu...

1.1. t-norms. A triangular norm (shortly t-norm) is a binary operationT : [0,1]×[0,1]→ [0,1] := I which is commutative, associative, monotone in each place, and has 1 as the unit element. Basic examples are TL : I × I → I , TL(a,b) =Max(a+ b− 1,0) (Łukasiewicz t-norm), TP(a,b) = ab, and TM(a,b) = Min{a,b}. We also mention the following families of tnorms: (i) Sugeno-Weber family (T λ )λ∈(−1,∞),...