In this paper, a novel justification of the disjunctive combination rule for multiple independent sources of information based on the redefined combination-mapping rule of multiple multi-valued mappings in the product space of multiple independent sources of information is being proposed. The combination rule reveals a type of logical inference in the human judgment, that is, the OR rule. It ov...

In this paper, the problem of modelling ambiguous (multi-valued) mappings from noisy experimental data and the use of these models in control strategies are considered. An inference method based on an equation image of a rulebase and minimisation of a performance index (inference error) is described so that the ideal model is the one that minimizes contradiction. Its functional interpretation i...

A modified mapping method is used to obtain variable separation solutions with two arbitrary functions of the (2+1)-dimensional modified dispersive water-wave system. Based on the variable separation solution and by selecting appropriate functions, we discuss interaction behaviours among special anti-solitons constructed by multi-valued functions. The analysis results exhibit that the interacti...

Decision-making in the control of complex systems is based on the analysis of multidimensional data. These data need to recognize them and establish functional dependences. The search for effective methods to the pattern recognition is continued. An essential step in the development of the effective methods of encoding is to create recognition systems, using sparse coding and self-learning [1]....

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

AbstractFitting the continuous valid logic of the exclusive OR (XOR) problem requires more than a minimal neural network configuration. This letter shows that the simplest logic to fit the XOR problem involves boundaries that cannot be mapped by a Multi-Layer Perceptron (MLP) with just two hidden nodes. This observation calls into question rule extraction methodologies based on pruning, since t...

Interval diagram techniques have been applied successfully to symbolic formal verification of process networks, Petri nets, and timed automata, outperforming conventional approaches and avoiding some of their drawbacks. Our approach is based on a novel, efficient form of representation for multi-valued functions called interval decision diagram (IDD) and the corresponding image computation tech...

The extension of mathematical morphology operators to multi-valued functions, and in particular to color images, is neither direct nor general. In this paper is proposed a generalisation of distance-based and lexicographical-based approaches, allowing the extension of morphological operators to color images for any color representation (e.g. RGB, LSH and L*a*b*) and for any metric distance to a...

In this paper, we present a new type of extra-gradient method for generalized variational inequalities with multi-valued mapping in an infinite-dimensional Hilbert space. For this method, the generated sequence possesses an expansion property with respect to the initial point, and the existence of the solution to the problem can be verified through the behavior of the generated sequence. Furthe...