Binary Relations Research Articles

ЭФФЕКТИВНЫЕ ПРОЦЕДУРЫ ФИЛЬТРАЦИИ АЛЬТЕРНАТИВ ТРАНСПОРТНОГО ОБЕСПЕЧЕНИЯ ПОСТАВОК НА ОСНОВЕ СПЕЦИАЛЬНОГО МИНОРИТАРНОГО ПОДХОДА

The report presents a special approach to the formalization of procedures for filtering alternatives in the models of transport provision of supplies. Filtering procedures are developed on the basis of binary relations, and only those alternatives that correspond to minorants in the corresponding strict order relation are removed from consideration. This will significantly reduce the number of alternatives considered so that the selection process can be implemented in real time. Numerical illustrations are given in the format of the following generalized selection criteria: scalar, geometric mean, ideal point.

Coincidence point results on a metric space endowed with a locally T-transitive binary relation employing comparison functions

In this paper, we prove coincidence point results for a pair of self mappings defined on a metric space employing a comparison function and a locally T-transitive binary relation. Our results extend and generalize several known results especially those are contained in Alam and Imdad [Filomat 31 (14) (2017) 4421-4439] and Arif et al. [Miskolc Math. Notes 23 (1) (2022) 71-83]. Finally, we construct some examples to demonstrate the accomplished improvements in our newly proved results in this paper.

Boyd-Wong type functional contractions under locally transitive binary relation with applications to boundary value problems

<abstract><p>The area of metric fixed point theory applied to relational metric spaces has received significant attention since the appearance of the relation-theoretic contraction principle. In recent times, a number of fixed point theorems addressing the various contractivity conditions in the relational metric space has been investigated. Such results are extremely advantageous in solving a variety of boundary value problems, matrix equations, and integral equations. This article offerred some fixed point results for a functional contractive mapping depending on a control function due to Boyd and Wong in a metric space endued with a local class of transitive relations. Our findings improved, developed, enhanced, combined and strengthened several fixed point theorems found in the literature. Several illustrative examples were delivered to argue for the reliability of our findings. To verify the relevance of our findings, we conveyed an existence and uniqueness theorem regarding the solution of a first-order boundary value problem.</p></abstract>

On the Existence of One-Point Time on an Oriented Set

The oriented set notion is the elementary fundamental concept of the theory of changeable sets. In turn, the changeable set theory is closely related to Hilbert's sixth problem. From the formal point of view, any oriented set is a simple relational system with a single reflexive binary relation. Such mathematical structure is the simplest construction, within the framework of which it is possible to give a mathematically strict definition of the time concept. In this regard, the problem of the existence of time with given properties on an oriented set is very interesting. In the present paper, we establish the necessary and sufficient condition for the existence of one-point time on an oriented set. From the intuitive point of view, any one-point time is the time related to the evolution of a system, which consists of a single object (for example, from a single material point). The main result of the paper provides that the one-point time exists on the oriented set if and only if this oriented set is a quasi-chain. Also, using the obtained result, we solve the problem of describing all possible images of linearly ordered sets, which naturally arises in the theory of ordered sets.

A study on new classes of binary soft sets in topological rough approximation space

Soft binary relation is used to define new classes of soft sets, namely BR-soft simply open set and BR-soft simply* alpha open set, in topological rough approximation space over two different universes. The defined set provides information on the missing elements of a BR-soft set and can help in simplifying decision making. Approximation operators are defined and the characteristics of the proposed sets are studied with examples. The relationship between the defined sets and other soft sets is brought out. An accuracy check was done to compare the proposed method with other methods. It is identified that the proposed method is more accurate.

Dual core-nilpotent decomposition and dual binary relation

In this paper, we present the definitions of appreciable index and dual index of a dual real square matrix. Then, we introduce the unique dual core-nilpotent (D-C-N) decomposition that exists universally for all dual real square matrices. By applying the decomposition, we get a characterization of the dual Drazin generalized inverse (D-Drazin), introduce D-Drazin, D-C-N, C-sharp C-N (C-C-N) and G-sharp C-N (G-C-N) binary relations of dual real matrices, and discuss relevant properties of these binary relations. We prove that D-Drazin binary relation is a pre-order, and D-C-N, C-C-N and G-C-N binary relations are partial orders. Furthermore, we discuss relationships among binary relations mentioned above.

Axiomatizing SNOMED CT Disorders: Should There Be Room for Interpretation?

SNOMED CT is a large concept-based terminology designed according to epistemic, semantic and pragmatic principles relevant to clinicians. Its goal is structured clinical reporting in electronic healthcare records (EHRs). The Basic Formal Ontology (BFO) is an ontology designed on the basis of types claimed to exist in reality based on a domain-independent ontological theory. Its goal is faithful representation of reality within that theory. The Ontology for General Medical Science (OGMS) extends the BFO by providing definitions for types relevant within the clinical domain. Combining SNOMED CT with the ontological rigor of BFO and OGMS might improve clinical reporting by, f.i., preventing data entry mistakes and inconsistencies, and make EHRs more comparable. To that end, we are developing a logical framework capable of exploiting what SNOMED CT offers terminologically and realism-based ontologies such as the BFO and the OGMS ontologically by means of bridging axioms compatible with the BFO, and expressed in the same CLIF-dialect as used in its axiomatization in first order logic. In this paper, we report on our attempts to detect in the combinations of binary relations that are used in the definition of SNOMED CT's definitions of disorder concepts patterns which might at least partially automate the construction of such axioms. Our findings suggest that this partial automation is indeed possible, but to a smaller extent than we had hoped for. We compare our approach with a recent proposal that seeks to bring SNOMED CT and BFO closer together by reinterpreting SNOMED CT disorders as clinical occurrents. The proposal has its merit in providing a realist underpinning for that part of SNOMED CT's concept model in terms of the BFO, but is not discriminatory enough for an automatic translation into OGMS. Key problem is the lack of face validity of SNOMED CT disorder terms as compared to the formal definitions they are given and this in absence of textual definitions.

Depth-Bounded Fuzzy Bisimulation for Fuzzy Modal Logic

We introduce depth-bounded fuzzy bisimulation between fuzzy Kripke models. Roughly speaking, a depth-bounded fuzzy bisimulation is a decreasing sequence of fuzzy binary relations whose infimum is a fuzzy bisimulation. We provide logical characterizations of depth-bounded fuzzy bisimulations between fuzzy Kripke models w.r.t. a fuzzy multimodal logic over complete residuated lattices, including fuzzy invariance of formulas of with a modal depth bounded by under the th component of a depth-bounded fuzzy bisimulation, as well as the Hennessy-Milner property of depth-bounded fuzzy bisimulations. We also provide a polynomial-time algorithm for computing the th component of the greatest depth-bounded fuzzy bisimulation between two finite fuzzy Kripke models when the underlying complete residuated lattice is linear.

Shared neighbors rough set model and neighborhood classifiers

Neighborhood relations are established by employing a distance metric and parameters, where the distance metric is utilized to measure the dissimilarities between objects. The information about adjacent objects tends to vary, even though these objects belong to a neighborhood. Taking into account neighborhood information, this paper introduces a similarity measure of shared neighbors, which is determined by the overlapping neighbors in a neighborhood relation. The similarity measure, induced by a neighborhood relation, is superior to the distance metric in quantifying differences, and it is crucial to note that the neighborhood relation can be any binary relation. A neighborhood of shared neighbors is proposed based on the proposed similarity measure, which consists of the most similar neighbors. Subsequently, we propose the shared neighbors rough set model, which is regarded as a framework of fusing neighborhood information. Moreover, an attribute reduction algorithm and a neighborhood classifier of shared neighbors are designed. The experimental results demonstrate the effectiveness of the neighborhood classifier and the shared neighbors rough set model.

Multivalued relation-theoretic weak contractions and applications

Abstract In this article, we discuss the relation theoretic aspects of multivalued weakly contractive mappings to prove fixed point results in the setting of metric spaces endowed with a certain binary relation. Our newly proved results generalize, extend, unify, enrich, sharpen and improve some well-known fixed point theorems of existing literature to the case of multivalued and contractive notion. We also incorporated an example and an application to find the solution of a Volterra-type integral inclusion.

Knowledge-Based Intelligent Text Simplification for Biological Relation Extraction

Relation extraction from biological publications plays a pivotal role in accelerating scientific discovery and advancing medical research. While vast amounts of this knowledge is stored within the published literature, extracting it manually from this continually growing volume of documents is becoming increasingly arduous. Recently, attention has been focused towards automatically extracting such knowledge using pre-trained Large Language Models (LLM) and deep-learning algorithms for automated relation extraction. However, the complex syntactic structure of biological sentences, with nested entities and domain-specific terminology, and insufficient annotated training corpora, poses major challenges in accurately capturing entity relationships from the unstructured data. To address these issues, in this paper, we propose a Knowledge-based Intelligent Text Simplification (KITS) approach focused on the accurate extraction of biological relations. KITS is able to precisely and accurately capture the relational context among various binary relations within the sentence, alongside preventing any potential changes in meaning for those sentences being simplified by KITS. The experiments show that the proposed technique, using well-known performance metrics, resulted in a 21% increase in precision, with only 25% of sentences simplified in the Learning Language in Logic (LLL) dataset. Combining the proposed method with BioBERT, the popular pre-trained LLM was able to outperform other state-of-the-art methods.

Index-MP and MP-index matrices

To extend the concepts of the DMP, MPD and CMP inverses and solve several types of systems of equations, we define three new kinds of square matrices, called the index-MP, MP-index and MP-index-MP matrices. We prove several characterizations for new classes of matrices and their relations with significant generalized inverses. Several types of representations for these new matrices are established. We define new binary relations applying index-MP, MP-index and MP-index-MP matrices and we show that these relations are partial orders on the set including square matrices of index one.

On relation-theoretic F−contractions and applications in F−metric spaces

Abstract The aim is to introduce some relation theoretic variants of F−contraction in an F−metric space endowed with a binary relation R and to prove results for its fixed point. In the sequel, several classes of contractions are sharpened, generalized, and improved. Numerical examples are presented to illustrate the theoretical conclusions. As applications of the main results, we solve a Dirichlet-Neumann initial value problem and two Dirichlet boundary value problems.

On the Divide: Reading Cather Against the Binary

Abstract: This essay argues that Willa Cather’s 1896 short story, “Tommy, the Unsentimental,” paradoxically complicates gender binaries by proliferating binary relations—between East and West, weak and strong, sentimental and unsentimental. In so doing, Cather creates a world in which almost everyone’s gender is non-binary to some extent. Drawing on the work of Eve Kosofsky Sedgwick, Jay Prosser, Jack Halberstam, and Chris Coffman, I contend that Cather anticipates current debates in queer theory by showing how thinking about transgender subjects and sexuality together alters how we understand fundamental terms like “homosexuality.” Finally, I show where the text reaches its limit, unable to shed its rigid taxonomy of “kinds” of people. Instead, we would do well to promote a discourse of “unkindness,” in which changes in gender identity and presentation, like those in Cather’s own life, can be acknowledged.

A New Approach on Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graphs Based on Vertices

Graph is a visual representation of data. In mathematics, graph is a structure which creates the pairwise relation between objects. The objects are known as nodes or vertices and the connection between two nodes are known as links or edges. A graph is a symmetric binary relation on a non-empty set whereas Fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. Bipolar Fuzzy graph is a generalization of graph theory by using bipolar Fuzzy set. The bipolar Fuzzy sets are the extension of Fuzzy sets. Our main objective is to introduce Bipolar Second Degree Perfect Fuzzy Matching for Bipolar Fuzzy Graph based on vertices. Secondly, we proved the necessary conditions under which they are equivalent and also proved that for a particular condition a perfect second-degree fuzzy matching is not a regular bipolar fuzzy graph. Next, we discussed about perfect second-degree Fuzzy matching and second degree fuzzy matching number for bipolar fuzzy graph on the cycle.

Some Logics in the Vicinity of Interpretability Logics

In this paper we shall define semantically some families of propositional modal logics related to the interpretability logic \(\mathbf{IL}\). We will introduce the logics \(\mathbf{BIL}\) and \(\mathbf{BIL}^{+}\) in the propositional language with a modal operator \(\square\) and a binary operator \(\Rightarrow\) such that \(\mathbf{BIL}\subseteq\mathbf{BIL}^{+}\subseteq\mathbf{IL}\). The logic \(\mathbf{BIL}\) is generated by the relational structures \(\left<X,R,N\right>\), called basic frames, where \(\left<X,R\right>\) is a Kripke frame and \(\left<X,N\right>\) is a neighborhood frame. We will prove that the logic \(\mathbf{BIL}^{+}\) is generated by the basic frames where the binary relation \(R\) is definable by the neighborhood relation \(N\) and, therefore, the neighborhood semantics is suitable to study the logic \(\mathbf{BIL}^{+}\) and its extensions. We shall also study some axiomatic extensions of \(\mathsf{\mathbf{BIL}}\) and we will prove that these extensions are sound and complete with respect to a certain classes of basic frames. Finally, we prove that the logic BIL+ and some of its extensions are complete respect with the class of neighborhood frames.

Generalized cut trees for edge-connectivity

We present three cut trees of graphs, each of them giving insights into the edge-connectivity structure. All three cut trees have in common that they are defined with respect to a given binary symmetric relation R on the vertex set of the graph, which generalizes Gomory-Hu trees. Applying these cut trees, we prove the following:•A pair of vertices {v,w} of a graph G is pendant if λ(v,w)=min⁡{d(v),d(w)}. Mader showed in 1974 that every simple graph with minimum degree δ contains at least δ(δ+1)/2 pendant pairs. We improve this lower bound to δn/24 for every simple graph G on n vertices with δ≥5 or λ≥4 or vertex connectivity κ≥3, and show that this is optimal up to a constant factor with regard to every parameter.•Every simple graph G satisfying δ>0 has O(n/δ)δ-edge-connected components. Moreover, every simple graph G that satisfies 0<λ<δ has O((n/δ)2) cuts of size less than min⁡{32λ,δ}, and O((n/δ)⌊2α⌋) cuts of size at most min⁡{α⋅λ,δ−1} for any given real number α≥1.•A cut is trivial if it or its complement in V(G) is a singleton. We provide an alternative proof of the following recent result of Lo et al.: Given a simple graph G on n vertices that satisfies δ>0, we can compute vertex subsets of G in near-linear time such that contracting these vertex subsets separately preserves all non-trivial min-cuts of G and leaves a graph having O(n/δ) vertices and O(n) edges.

Existence and stability of solution for a nonlinear Volterra integral equation with binary relation via fixed point results

The real-world problems that can be resolved by a dynamic mathematical model is an analogous form of a complex integral equation. In this article, we intend to exhibit the solution to a non-homogeneous, nonlinear Volterra integral equation endowed with an arbitrary binary relation utilizing the fixed point solution that is originally proved for a multivalued map and then reduced to a single valued self map. The results proved and the application demonstrated is an added asset to the present literature and can significantly contribute in determining the existence of a solution for a dynamic mathematical model in the form of a Volterra integral equation equipped with an arbitrary binary relation via fixed point findings. Furthermore, the stability of the solution of the Volterra integral equation is verified using the Hyers–Ulam stability concept.

Individuating Powers: On the Regress/Circularity Individuation Arguments against Bird’s Dispositional Monism

According to Bird’s Naïve Dispositional Monism, all properties are powers, and are individuated by their manifestations. Lowe has famously challenged the position with an individuation regress or circularity argument. Bird has then offered a structuralist side-step in the form of Structuralist Dispositional Monism, according to which powers are individuated through the unique position they occupy in an asymmetric power-structure. However, Structuralist Dispositional Monism has been argued to be just as problematic as Naïve Dispositional Monism, if not more so.I argue that the debate is severely flawed to the extent that it relies on Lowe’s standard characterization of metaphysical individuation as a binary relation between objects. I will argue against this characterization in favor of a different one, either as a standard or sui generis explanatory relation of individuality facts. In the former case, Naïve Dispositional Monism is clear of all charges previously raised against it; whereas in the latter case, Structuralist Dispositional Monism works just fine; Structuralist Dispositional Monism may ultimately be argued to the be the superior option. Either way, the status of Dispositional Monism, vis à vis individuation circularities, is not as compromised as some have claimed—and Lowe’s intended way out (viz., allow for some non-power to eventually break the circularity) loses much of its appeal.

МЕТОД АВТОМАТИЗОВАНОЇ КЛАСИФІКАЦІЇ НАДЗВИЧАЙНИХ СИТУАЦІЙ ІЗ СУДНОМ В АКВАТОРІЇ МОРСЬКОГО ПОРТУ

The aim of the study is to develop a method that allows to improve the accuracy of classification of emergencies with a ship in the seaport area. To achieve the research objective, an improved method for automated classification of ship emergencies in the seaport area under conditions of deterministic uncertainty is proposed. The method consists of methods for formalising and processing knowledge on determining the classes of ship emergencies. The method of knowledge formalisation is based on the formation of a set of factors influencing the classification of ship emergencies in the seaport water area based on fuzzy binary relations of non-strict preference. The method of knowledge processing is based on the formation of productive rules for classifying emergencies with a ship in the seaport area according to the predicted or current values of the desired factors in a fuzzy formulation. The determination of the membership functions of several fuzzy variables to linguistic variables is based on the processing of expert data represented by a matrix of binary relations of the values of the membership function of the elements of the domain of determining linguistic variables. A comparative assessment of the classes of recognisable emergencies with a vessel in the seaport water area involves solving a multi-criteria optimisation problem using the hierarchy analysis method. As a mathematical model for determining the classes of emergency situations with a vessel in the seaport waters, the article substantiates a logical-linguistic productive hierarchical model. The process of determining the classes of emergency is described with the help of an algebraic model, which is closest to the linguistic description. In case of inexpediency of synthesis of products, it is proposed to use the method of fuzzy identification to reduce the number of product rules. The proposed method allows to improve the accuracy of classification of emergencies with a ship in the seaport area under conditions of deterministic uncertainty. Keywords: classification, maritime port, hierarchy analysis, fuzzy identification, logicallinguistic production hierarchical model, vessel, class of emergency situations, fuzzy variable, linguistic variable