相关论文: Bi-capacities -- Part I: definition, M\"obius tran…

Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models such…

One of the key challenges in machine learning is to find interpretable representations of learned functions. The M\"obius transform is essential for this purpose, as its coefficients correspond to unique importance scores for sets of input…

Considering a linearly ordered set, we introduce its symmetric version, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring. We show that imposing symmetry…

In this paper we introduce the concept of multiple bipolar fuzzy measures as a generalization of a bipolar fuzzy measure. We also propose a new definition of a group, which is based on the multidimensional bipolar fuzzy relations of its…

M\"obius inversion, originally a tool in number theory, was generalized to posets for use in group theory and combinatorics. It was later generalized to categories in two different ways, both of which are useful. We provide a unifying…

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define exdended…

Information related measures are useful tools for multi variable data analysis, as measures of dependence among variables, and as descriptions of order in biological and physical systems. Information related measures, like marginal…

We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. We introduce topological analogues of well known class of exact games and show that these classes form subfunctors of the…

This paper introduces the concept of a bi-scale metric for use in the cooperative phase of the self-organizing map (SOM) algorithm. Use of a bi-scale metric allows segmentation of the map into a number of regions, corresponding to…

Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation…

Fuzzy skill multimaps can describe individuals' knowledge states from the perspective of latent cognitive abilities. The significance of discriminative knowledge structure is reducing repeated testing and the workload for students, which…

The transitivity of fuzzy relations plays an important role in fuzzy set theory, artificial intelligence, clustering and decision-making. However, it is often difficult for fuzzy relations to satisfy the transitivity property in many…

Bipartite experiments are a recent object of study in causal inference, whereby treatment is applied to one set of units and outcomes of interest are measured on a different set of units. These experiments are particularly useful in…

Open bisimilarity is defined for open process terms in which free variables may appear. The insight is, in order to characterise open bisimilarity, we move to the setting of intuitionistic modal logics. The intuitionistic modal logic…

Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be…

There has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems, but the comparison at this level is too coarse. Recently, a finer behavioral measure, bisimulation, has been introduced to fuzzy…

This paper introduces a new behavioral system model with distinct external and internal signals possibly evolving on different time scales. This allows to capture abstraction processes or signal aggregation in the context of control and…

Bisimilarity as an equivalence notion of systems has been central to process theory. Due to the recent rise of interest in quantitative systems (probabilistic, weighted, hybrid, etc.), bisimilarity has been extended in various ways:…

We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…

Cooperation is an important research object in economics, sociology, and biology, and the evolution of cooperation in structured populations is a interesting research topic. We mainly focus on the evolution of cooperation with two-order and…