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,∞),...

Transitivity is a very important property in order to provide coherence to a preference relation. Usually, t-norms are considered to define the transitivity of fuzzy relations. In this paper we deal with conjunctors, a wider family than t-norm, to define the transitivity. This more general definition allows to impove the results found in the literature. We characterize the behaviour with respec...

The law of importation for fuzzy implications is studied and it is solved for S, R, QL and D-implications derived from uninorms. Along this study many new solutions of this property appears different from those already known for implications derived from t-norms and t-conorms.

This paper presents a variety of cardinality concepts offered by cardinality theory of triangular norm-based fuzzy sets, including the scalar and the "fuzzy" streams.