The basic set operations between fuzzy sets are defined using the min and max functions; however, later on, new operators were introduced that used other functions, which, nevertheless, had similar properties to functions min and max. The resulting f...
Many real-life problems are well represented only by sets which allow repetition(s), such as the multiset. Although not limited to the following, such cases may arise in a database query, chemical structures and computer programming. The set of roots...
Hybrid sets are defined as multisets having also negative multiplicities, i.e. as functions from a crisp set to the group of all integers. In this article, we introduce a significant advancement in hybrid sets through the concept of group-valued mult...
This paper extends the classical approach of primal topology by embedding the multiset model. In multiset theory, the element multiplicity plays a fundamental structural role using the family
In this paper, we consider rings of multisets consisting of elements of a Banach algebra. We investigate the algebraic and topological structures of such rings and the properties of their homomorphisms. The rings of multisets arise as natural domains...
In the paper, we consider a ring structure on the Cartesian product of two sets of integer multisets. In this way, we introduce a ring of integer multinumbers as a quotient of the Cartesian product with respect to a natural equivalence. We examine th...
Based on the multiplicity evaluation in some real situations, this paper firstly introduces a single-valued neutrosophic multiset (SVNM) as a subclass of neutrosophic multiset (NM) to express the multiplicity information and the operational relations...
In real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information, and plenty of research has indicated that generalized fuzzy...
In this article, we show how to define a metric on the finite power multisets of positive real numbers. The metric, based on the minimal matching, consists of two parts: the matched part and the mismatched part. We also give some concrete application...
The problem of the analysis of datasets formed by the results of group expert assessment of objects by a certain set of features is considered. Such datasets may contain mismatched, including conflicting values of object evaluations by the analyzed f...
This paper proposes a new data structure, multiset-trie, that is designed for storing and efficiently processing a set of multisets. Moreover, multiset-trie can operate on a set of sets without efficiency loss. The multiset-trie structure is a search...
Based on dynamic information collected from different time intervals in some real situations, this paper firstly proposes a dynamic single valued neutrosophic multiset (DSVNM) to express dynamic information and operational relations of DSVNMs. Then,...
Neutrosophic components (NC) under addition and product form different algebraic structures over different intervals. In this paper authors for the first time define the usual product and sum operations on NC. Here four different NC are defined using...
Cut sets, decomposition theorem and representation theorem have a great influence on the realization of the transformation of fuzzy sets and classical sets, and the single-valued neutrosophic multisets (SVNMSs) as the generalization of fuzzy sets, wh...
This paper explores the concepts of
Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify...
In machine learning, when the labeled portion of data needs to be processed, a semi-supervised learning algorithm is used. A dataset with missing attribute values or labels is referred to as an incomplete information system. Addressing incomplete inf...
The performance of pattern classification is affected significantly by feature selection. However, for security applications, selecting proper features is difficult, as malicious software continuously changes its characteristics. Thus, compression-ba...
Missing data introduce uncertainty in data mining, but existing set-valued approaches ignore frequency information. We propose unsupervised attribute reduction algorithms for multiset-valued data to address this gap. First, we define a multiset-value...
In this paper, we have investigated neutrosophic soft expert multisets (NSEMs) in detail. The concept of NSEMs is introduced. Several operations have been defined for them and their important algebraic properties are studied. Finally, we define a NSE...
This paper explores the concept of multiset dimensions (Mdim) of compressed zero-divisor graphs (CZDGs) associated with rings. The authors investigate the interplay between the ring-theoretic properties of a ring
A fuzzy multiset is a generalization of a fuzzy set. This paper aims to combine the innovative notion of fuzzy multisets and hypergroups. In particular, we use fuzzy multisets to introduce the concept of fuzzy multi-hypergroups as a generalization of...
Full-duplex (FD) communication has been shown to provide an increased achievable rate, while millimeter wave (mmWave) communications benefit from a large available bandwidth that further improves the achievable rate. On the other hand, the concept of...
Although numerous reports using methods such as molecular dynamics, cellular automata, and artificial chemistry have clarified the process connecting non-life and life on protocell simulations, none of the models could simultaneously explain the emer...
In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization...
The concept of fuzzy multiset is well established in dealing with many real life problems. It is possible to find various applications of algebraic hypercompositional structures in natural, technical and social sciences, where symmetry, or the lack o...
The research of multimodal emotion recognition based on facial expressions, speech, and body gestures is crucial for oncoming intelligent human–computer interfaces. However, it is a very difficult task and has seldom been researched in this com...
We propose a linear time algorithm, called G2DLP, for generating 2D lattice L(n1, n2) paths, equivalent to two-item multiset permutations, with a given number of turns. The usage of turn has three me...
Background/Objectives: Predicting diseases based on the gut microbiome pattern is still difficult because of compositional shortcomings, batch heterogeneity, and scanty modeling of inter-taxon interactions. This study introduces a Dysbiosis-Aware Mul...
Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity (i [...]
The presence of natural fractures can significantly affect the quality of hydraulic fracturing operations in tightsand and shale or oil/gas formations. This paper describes the procedure used to model natural fractures with continuum damage tensor an...
The quality of global cropland products could affect our understanding of the impacts of cropland reclamation on global changes. With the advancement of remote sensing technology, several global land cover products and synergistic datasets have been...
Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is the basis of the distance function, which has a symmetric property. Moreover, finding the resolving set of a gr...
Octahedron sets, which extend beyond the previously defined fuzzy set and soft set concepts to address uncertainty, represent a hybrid set theory that incorporates three distinct systems: interval-valued fuzzy sets, intuitionistic fuzzy sets, and tra...
The Molodtsov-initiated soft set theory plays an important role as a powerful mathematical tool for handling uncertainty. As an extension of the soft set, the fuzzy soft set can be seen to be more generic and flexible than utilizing the soft set only...
Recently, fuzzy multisets have come to the forefront of scientists’ interest and have been used for algebraic structures such as groups, rings, and near rings. In this paper, we first summarize the knowledge about algebraic structure of fuzzy multise...
Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of t...
In this paper, we studied some properties of the neutrosophic multi topological group. For this, we introduced the definition of semi-open neutrosophic multiset, semi-closed neutrosophic multiset, neutrosophic multi regularly open set, neutrosophic m...
The study of algebraic invariants associated with Brauer configuration algebras induced by appropriate multisets is said to be a Brauer analysis of the data that define the multisets. In general, giving an explicit description of such invariants as t...
We present in this paper a new method in detecting anomalies in datasets representing systems behaviour, which is based on comparing a dataset to the data blueprint of the system representing its normal behaviour. This method removes some of the need...
Cayley and nilpotent graphs arise from the interaction between graph theory and algebra and are used to visualize the structures of some algebraic objects as groups and commutative rings. On the other hand, Green and Schroll introduced Brauer graph a...
Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and suffixes of ever...
Cayley hash values are defined by paths of some oriented graphs (quivers) called Cayley graphs, whose vertices and arrows are given by elements of a group
From a broad perspective, we study issues related to implementation, testing, and experimentation in the context of geometric algorithms. Our focus is on the effect of quality of implementation on experimental results. More concisely, we study algori...
Modern sequencing technique has provided a wealth of data on DNA sequences, which has made the analysis and comparison of sequences a very important but difficult task. In this paper, by regarding the dinucleotide as a 2-combination of the multiset...
We define a process calculus to describe multi-agent systems with timeouts for communication and mobility able to handle knowledge. The knowledge of an agent is represented as sets of trees whose nodes carry information; it is used to decide the inte...
Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the propertie...
In this paper, we introduce
This paper is focused on some algebraic and combinatorial properties of a TMTO (Time–Memory Trade-Off) for a chosen plaintext attack against a cryptosystem with a perfect secrecy property. TMTO attacks aim to retrieve the preimage of a given on...
Since the seminal work of Kolmogorov, probability theory has been based on measure theory, where the central components are so-called probability measures, defined as measures with total mass equal to 1. In Kolmogorov’s theory, a probability me...
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