Set operations
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Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activations Open
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for th…
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Guaranteed State Estimation for Nonlinear Discrete-Time Systems via Indirectly Implemented Polytopic Set Computation Open
This paper proposes a new set-membership technique to implement polytopic set computation for nonlinear discrete-time systems indirectly. The proposed set-membership technique is applied to solve the guaranteed state estimation problem for…
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A Development of Complex Multi-Fuzzy Hypersoft Set With Application in MCDM Based on Entropy and Similarity Measure Open
Hypersoft set (HSS) was proposed in 2018 as a generalization of the soft set (SS). In this paper, the novelty of complex multi-fuzzy hypersoft set (CMFHSS) is discussed, which can deal with uncertainties, vagueness, and unclearness of data…
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Reachability Analysis and Safety Verification for Neural Network Control Systems Open
Autonomous cyber-physical systems (CPS) rely on the correct operation of numerous components, with state-of-the-art methods relying on machine learning (ML) and artificial intelligence (AI) components in various stages of sensing and contr…
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Joinable Parallel Balanced Binary Trees Open
In this article, we show how a single function, join , can be used to implement parallel balanced binary search trees ( BSTs ) simply and efficiently. Based on join , our approach applies to multiple balanced tree data structures, and a va…
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Bipolar Hypersoft Sets Open
Hypersoft set theory is an extension of soft set theory and is a new mathematical tool for dealing with fuzzy problems; however, it still suffers from the parametric tools’ inadequacies. In order to boost decision-making accuracy even more…
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An Approach toward a Q-Neutrosophic Soft Set and Its Application in Decision Making Open
A neutrosophic set was proposed as an approach to study neutral uncertain information. It is characterized through three memberships, T , I and F, such that these independent functions stand for the truth, indeterminate, and false-membersh…
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Soft Classes and Soft Rough Classes with Applications in Decision Making Open
Rough set was defined by Pawlak in 1982. Concept of soft set was proposed as a mathematical tool to cope with uncertainty and vagueness by Molodtsov in 1999. Soft sets were combined with rough sets by Feng et al. in 2011. Feng et al. inves…
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Approximating Private Set Union/Intersection Cardinality With Logarithmic Complexity Open
The computation of private set union/intersection cardinality (PSU-CA/PSI-CA) is one of the most intensively studied problems in Privacy Preserving Data Mining (PPDM). However, existing protocols are computationally too expensive to be emp…
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A NEW SOFT SET OPERATION: COMPLEMENTARY SOFT BINARY PIECEWISE UNION (∪) OPERATION Open
Molodtsov’s soft set theory has been used in various disciplines both theoretically and practically. It is an effective mathematical tool for dealing with uncertainty. Since its debut, numerous types of soft set operations have been presen…
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A New Soft Set Operation: Complementary Soft Binary Piecewise Intersection (∩) Operation Open
The soft set theory developed by Molodtsov has been applied both theoretically and practically in many fields. It is a useful piece of mathematics for handling uncertainty. Numerous variations of soft set operations have been described and…
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Development of Hybrids of Hypersoft Set with Complex Fuzzy Set, Complex Intuitionistic Fuzzy set and Complex Neutrosophic Set Open
The complex fuzzy soft set and its generalized hybrids are such eective structures which not only minimize the impediments of all complex fuzzy-like structures for dealing uncertainties but also fulll all the parametric requirements of sof…
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Distributed Measurement with Private Set-Union Cardinality Open
This paper introduces a cryptographic protocol for efficiently aggregating a count of unique items across a set of data parties privately - that is, without exposing any information other than the count. Our protocol allows for more secure…
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COMPLEMENTAL BINARY OPERATIONS OF SETS AND THEIR APPLICATION TO GROUP THEORY Open
Set theory is considered as the foundation of all mathematics since many mathematical concepts cannot be defined precisely without using set-theoretical concepts. In this study, we define new complemental binary operations, called union co…
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A NEW SOFT SET OPERATION: COMPLEMENTARY SOFT BINARY PIECEWISE GAMMA(𝜸) OPERATION Open
Soft set theory, introduced by Molodtsov, is as an efficacious mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspect. Since its inception, different kinds of soft set o…
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Intuitionistic Type-2 Fuzzy Set and Its Properties Open
Decision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vit…
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Utilizing dependencies to obtain subsets of reachable sets Open
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
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Generalized Q-Neutrosophic Soft Expert Set for Decision under Uncertainty Open
Neutrosophic triplet structure yields a symmetric property of truth membership on the left, indeterminacy membership in the centre and false membership on the right, as do points of object, centre and image of reflection. As an extension o…
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PRISM: Private Verifiable Set Computation over Multi-Owner Outsourced Databases Open
This paper proposes Prism, a secret sharing based approach to compute private set operations (i.e., intersection and union), as well as aggregates over outsourced databases belonging to multiple owners. Prism enables data owners to pre-loa…
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Hypersoft Expert Set With Application in Decision Making for Recruitment Process Open
Many researchers have created some models based on soft set, to solve problems in decision making and medical diagnosis, but most of these models deal only with one expert. This causes a problem with the users, especially with those who us…
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Three-party quantum private computation of cardinalities of set intersection and union based on GHZ states Open
Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA) are two cryptographic primitives whereby two or more parties are able to obtain the cardinalities of the intersection and the union of their respectiv…
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Vertical Federated Learning without Revealing Intersection Membership Open
Vertical Federated Learning (vFL) allows multiple parties that own different attributes (e.g. features and labels) of the same data entity (e.g. a person) to jointly train a model. To prepare the training data, vFL needs to identify the co…
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New Approach to Set Representation and Practical Private Set-Intersection Protocols Open
Private set intersection (PSI) is a fundamental cryptographic protocol, which has many important applications, such as personal properties matching, data sharing, or data mining. PSI has been widely studied in the literature, and many PSI …
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Data-Driven Set-Based Estimation using Matrix Zonotopes with Set Containment Guarantees Open
We propose a method to perform set-based state estimation of an unknown dynamical linear system using a datadriven set propagation function. Our method comes with set containment guarantees, making it applicable to safety-critical systems.…
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A “Learned” Approach to Quicken and Compress Rank/Select Dictionaries Open
We address the well-known problem of designing, implementing and experimenting compressed data structures for supporting rank and select queries over a dictionary of integers. This problem has been studied far and wide since the end of the…
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Dense RepPoints: Representing Visual Objects with Dense Point Sets Open
We present a new object representation, called Dense RepPoints, that utilizes a large set of points to describe an object at multiple levels, including both box level and pixel level. Techniques are proposed to efficiently process these de…
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A NEW SOFT SET OPERATION: COMPLEMENTARY SOFT BINARY PIECEWISE PLUS (+) OPERATION Open
Soft set theory, introduced by Molodtsov, is as an important mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspects. Since 1999, different kinds of soft set operations …
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Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices Open
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical s…
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Distributed Set-Based Observers Using Diffusion Strategy. Open
Distributed estimation is more robust against single points of failure and requires less communication overhead compared to the centralized version. Among distributed estimation techniques, set-based estimation has gained much attention as…
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Conditional Cuckoo Filters Open
Bloom filters, cuckoo filters, and other approximate set membership sketches have a wide range of applications. Oftentimes, expensive operations can be skipped if an item is not in a data set. These filters provide an inexpensive, memory e…