Related papers: Roughness and entropy measures of a soft set
Robustness of neural networks has recently attracted a great amount of interest. The many investigations in this area lack a precise common foundation of robustness concepts. Therefore, in this paper, we propose a rigorous and flexible…
In 1999, Molodtsov initiated the concept of Soft Sets Theory as a new mathematical tool and a completely different approach for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied…
In this paper, concept of possibility neutrosophic soft set and its operations are defined, and their properties are studied. An application of this theory in decision making is investigated. Also a similarity measure of two possibility…
In safety-critical deep learning applications, robustness measures the ability of neural models that handle imperceptible perturbations in input data, which may lead to potential safety hazards. Existing pre-deployment robustness assessment…
Study of soft sets was first proposed by Molodtsov in 1999 to deal with uncertainty in a non-parametric manner. The researchers did not pay attention to soft set theory at that time but now the soft set theory has been developed in many…
Conventional approaches to grasp planning require perfect knowledge of an object's pose and geometry. Uncertainties in these quantities induce uncertainties in the quality of planned grasps, which can lead to failure. Classically, grasp…
The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also…
The fidelity-based smooth min-relative entropy is a distinguishability measure that has appeared in a variety of contexts in prior work on quantum information, including resource theories like thermodynamics and coherence. Here we provide a…
The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making…
Rough set theory models uncertainty by approximating target concepts through lower and upper sets induced by indiscernibility, or more generally, by granulation relations in data tables. This perspective captures vagueness caused by limited…
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently-flat surfaces is…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
The theory of disordered elastic systems is one of the most powerful frameworks to assess the physics of multiple systems that span from ferromagnets to migrating biological cells. In this formalism, one assumes that the system can be…
This paper introduces a novel Choquet distance using fuzzy rough set based measures. The proposed distance measure combines the attribute information received from fuzzy rough set theory with the flexibility of the Choquet integral. This…
Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable…