Related papers: When is the convolution a t-norm on normal, convex…
Type-2 fuzzy set (T2 FS) were introduced by Zadeh in 1965, and the membership degrees of T2 FSs are type-1 fuzzy sets (T1 FSs). Owing to the fuzziness of membership degrees, T2 FSs can better model the uncertainty of real life, and thus,…
This paper studies t-norms on the space $\mathbf{L}$ of all normal and convex fuzzy truth values. We first prove that the only non-convolution form type-2 t-norm constructed by Wu et al. satisfies the distributivity law for meet-convolution…
In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered $t_{r}$-norm, which is not…
In this paper, a new interval type-2 fuzzy neural network able to construct non-separable fuzzy rules with adaptive shapes is introduced. To reflect the uncertainty, the shape of fuzzy sets considered to be uncertain. Therefore, a new form…
Fuzzy rule based classification systems are one of the most popular fuzzy modeling systems used in pattern classification problems. This paper investigates the effect of applying nine different T-norms in fuzzy rule based classification…
This paper proves that a binary operation ${\star}$ on ${[0, 1]}$, ensuring that the binary operation ${\curlywedge}$ is a ${t}$-norm or ${\curlyvee}$ is a ${t}$-conorm, is a ${t}$-norm, where ${\curlywedge}$ and ${\curlyvee}$ are special…
Classical machine learning classifiers tend to be overconfident can be unreliable outside of the laboratory benchmarks. Properly assessing the reliability of the output of the model per sample is instrumental for real-life scenarios where…
In the conventional Takagi-Sugeno-Kang (TSK)-type fuzzy models, constant or linear functions are usually utilized as the consequent parts of the fuzzy rules, but they cannot effectively describe the behavior within local regions defined by…
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation…
The generalized Parseval equality for the Mellin transform is employed to prove the inversion theorem in L_2 with the respective inverse operator related to the Hartley transform on the nonnegative half-axis (the half-Hartley transform).…
One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model…
In this article, working in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions, we go deeper into the study of some type of decompositions defined by t-norms and t-conorms. This allows us to…
The concept of uncertainty is posed in almost any complex system including parallel robots as an outstanding instance of dynamical robotics systems. As suggested by the name, uncertainty, is some missing information that is beyond the…
In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the…
This paper constructs a $t_{r}$-norm and a $t_{r}$-conorm on the set of all normal and convex functions from ${[0, 1]}$ to ${[0, 1]}$, which are not obtained by using the following two formulas on binary operations ${\curlywedge}$ and…
A prominent problem in knowledge representation is how to answer queries taking into account also the implicit consequences of an ontology representing domain knowledge. While this problem has been widely studied within the realm of…
We present a procedure for the construction of multi-valued t-norms and t-conorms. Our procedure makes use of a pair of single-valued t-norms and the respective dual t-conorms and produces interval-valued t-norms and t-conorms. In this…
It is known that fuzzy set theory can be viewed as taking place within a topos. There are several equivalent ways to construct this topos, one is as the topos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lower topology.…
The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds…
Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve…