Triangular Numbers Research Articles

Neutrosophic MARCOS in Decision Making on Smart Manufacturing System

Business firms prefer software-based smart manufacturing systems to monitor and supervise all production activities in a decentralized manner. The choice of software decides the degree of manufacturing robustness. This paper proposes a neutrosophic-based MARCOS (Measurement of Alternatives and Ranking according to COmpromise Solution) method of MCDM with single-valued triangular neutrosophic numbers to solve the software selection problem. The proposed neutrosophic method is applied to hypothetical data to test the efficacy of the method. The results obtained using the proposed method are compared with crisp, fuzzy, and intuitionistic data representations, and suitable inferences are acquired. The proposed method has several industrial implications and it has several scopes of applying to other decision-making scenarios with real data sets.

The determinants of reliable smart grid from experts’ perspective

A smart grid integrates communication networks with the conventional electrical grid. Due to their potential, smart grids are anticipated to achieve widespread deployment. A key component of the success and adoption of smart grids is reliability. Without knowing users’ impressions of the reliability of the smart grid, users will not easily accept and participate in it or its services. However, very few studies address smart grid reliability from the perspective of users. Thus, there is a urgent need to identify key factors that affect smart grid reliability from the user’s viewpoint. The goal of this paper is to examine user perceptions of smart grid reliability and assess their success factors in an effort to close the gap in the literature. This paper propose a model to investigate and determine the most crucial factors that affect the smart grid's reliability based on the Multiple-criteria decision-making (MCDM) method. Firstly, a comprehensive literature analysis was conducted to determine the criteria and sub-criteria used to construct the model; then, the model is constructed using fifteen sub-criteria covering big data, network systems, and grid efficiency criteria; finally, the Fuzzy Analytic Hierarchy Approach (FAHP) and fuzzy triangular numbers are used to evaluate and prioritize the criteria. Twenty smart grid experts were consulted to collect data. The results indicate the significance of the ‘Big Data’ criterion, closely followed by ‘Grid Efficiency’ criterion. Additionally, it is discovered that the sub-criteria of ‘Privacy’ and ‘Interoperability’ had a significant impact on the reliability of the smart grid. The sensitivity analysis shows the variation of factors ranking and the stability and robustness of the model and the results. The research presented in this study has practical applications for academics, engineers, decision-makers, and stakeholders.

Performance Evaluation of Triangular Number Sequence Backoff Algorithm for Constrained Application Protocol

In the of the Internet of Things (IoT) realm, congestion is considered a serious issue affecting network throughput due to the requirement of multiple nodes for message exchange. With free-space optical communications, which can help send a message wirelessly, congestion control mechanisms nowadays depend upon the carrier sense of multiple access with collision avoidance (CSMA/CA), using the so-called Backoff Algorithm (BA). These algorithms,

Fuzzy Clustering With Knowledge Extraction and Granulation

Knowledge-based clustering algorithms can improve traditional clustering models by introducing domain knowledge to identify the underlying data structure. While there have been several approaches to clustering with the guidance of knowledge tidbits, most of them mainly focus on numeric knowledge without considering the uncertain nature of information. To capture the uncertainty of information, pure numeric knowledge tidbits are expanded to knowledge granules in this article. Then, two questions arise: how to obtain granular knowledge and how to use those knowledge granules in clustering. To the end, a novel knowledge extraction and granulation (KEG) method and a granular knowledge-based fuzzy clustering model are proposed in this study. First, inspired by the concept of natural neighbors, an automatic KEG is developed. In KEG, high-density points are filtered from the dataset and then merged with their natural neighbors to form several dense areas, i.e., granular knowledge. Furthermore, the granular knowledge expressed by interval or triangular numbers is leveraged into the clustering algorithm, which is the framework of fuzzy clustering with granular knowledge. To concretize this model into clustering algorithms, the classical fuzzy C-Means clustering algorithm has been selected to incorporate the granular knowledge produced by KEG. Then, the corresponding fuzzy C-Means clustering with interval knowledge granules (IKG-FCM) and triangular knowledge granules (TKG-FCM) are proposed. Experiments on synthetic and real-world datasets demonstrate that IKG-FCM and TKG-FCM always achieve better clustering performance with less time cost, especially on imbalanced data, compared with state-of-the-art algorithms.

On stability of the Erdős–Rademacher problem

Mantel’s theorem states that every n-vertex graph with ⌊n24⌋+t edges, where t>0, contains a triangle. The problem of determining the minimum number of triangles in such a graph is usually referred to as the Erdős–Rademacher problem. Lovász and Simonovits proved that there are at least t⌊n∕2⌋ triangles in each of those graphs. Katona and Xiao considered the same problem under the additional condition that there are no s−1 vertices covering all triangles. They settled the case t=1 and s=2. Solving their conjecture, we determine the minimum number of triangles for every fixed pair of s and t, when n is sufficiently large. Additionally, solving another conjecture of Katona and Xiao, we extend the theory for considering cliques instead of triangles.

On the influence of fuzzy perception of the time passage speed on the solutions of optimization planning problems

The paper considers an approach to the construction of fuzzy structured numerical sets based on the formation of a fuzzy original of a special type with subsequent replication on the number axis. The constructive principle of fuzzy original formalization is to define a fuzzy triangular number with the appropriate support. A variant of the formation of fuzzy numerical sets, formalizing the "fast" and "slow" passage of time, is proposed. The developed technique allows us to propose a solution to the problem associated with the formalization of the subjective perception of the time reference in processes involving a person, to obtain results and evaluate the impact of fuzzy description and taking into account the dynamics of the time reference on the solution of various optimization problems. A general approach to the formation and solution of fuzzy linear optimization problems is considered, the transition from fuzzy to parametric formulation in the Bellman-Zade form is described. Examples of the use of fuzzy flow of time for different statements of tasks that arise when determining the order of the set of tasks within a given time interval with or without additional restrictions on the execution process are considered. An approach is proposed for the correction of the initial time distribution plans, taking into account different rates of time counting. A mathematical model of the fuzzy traveling salesman problem is formulated as a problem of finding a route to visit a given number of cities without repetitions with a minimum travel time with time parameters specified as right fuzzy numbers, the support value in which depends on various external conditions and factors. The results of calculations of solutions of fuzzy optimization problems are obtained. The influence of the speed of the passage of time on the solution of the considered optimization problems is determined.

Fuzzy Semi-Parametric Logistic Quantile Regression Model

In this paper, the fuzzy semi-parametric logistic quantile regression model was studied in the absence of special conditions in the classical regression models. This model becomes more flexible to deal with data for outlier's values and in the absence of a linear regression condition when the data of the dependent variable are restricted and fuzzy data and some of the variables are nonparametric, and the dependent variable in this model represents the fuzzy triangular number.
 The estimation of the semi-parametric logistic quantile regression model has been applied to simulated data when the sample size is (25, 50, 75, 100) and with a repetition of 1000. Where the model is estimated in two steps, the first step is to estimate the parametric part, and the second step is to estimate the non-parametric part by the Nadaraya-Watson estimator through different kernel functions. Depending on the mean squares error and the measure of goodness of fit, the results indicated the best estimate of a model with the Kernel-Cassian function when the quantile of the fuzzy conditional distribution equals 0.2 for all sample sizes .

Structured encryption for triangle counting on graph data

Triangle counting is an important metric on graph analysis for graph data such as social networks. To protect the privacy of graph data, researchers have proposed differential privacy-based triangle counting methods, but the counting results are flawed by estimation errors. A recent study proposes approximate triangle counting on encrypted graph data to achieve triangle counting of the entire graph, but cannot calculate the number of triangles formed between each individual node and its neighbors. In addition, triangle counting on graph is not fully investigated based on other privacy-preserving techniques, such as structured encryption for triangle counting on graph data. To improve the accuracy of triangle counting on graph data, we proposed two types of structured encryption for triangle counting on graph data (STE-TC) with various efficiency-security tradeoffs and combined it with homomorphic encryption to achieve triangle counting between each individual node and its neighbors that can evaluate the importance of this node. We proposed two triangle counting methods in both asymmetric key and symmetric key settings to satisfy different sharing requirements in the cloud. The security analysis and experimental results show that the proposed methods are feasible and practical.

An Intelligent Decision Support Model for Optimal Selection of Machine Tool under Uncertainty: Recent Trends

Many scholars have been interested in the subject of machine tool selection as a result of the growing number of different machines and the continuous advancement of technology associated with these machines. The selection of an unsuitable machine tool may lead to a variety of issues, including limitations on production capacities and productivity indicators when taking into account both time and money from an industrial and practical perspective. The present strategy of selecting machine tools, known as multi-criteria decision-making (MCDM), relies on the subjective viewpoint the vast majority of the time. When selecting an appropriate machining tool, however, it is necessary to take both the subjective and objective points of view into consideration. This is due to the fact that the objective assessment accurately reflects the performance of the machine tools. As a result, the purpose of this work is to provide a strategy for selecting machine tools that are based on an innovative hybrid MCDM framework. The study was conducted under a neutrosophic environment and using triangular neutrosophic numbers (TNNs). In the beginning, the CRiteria Importance through Intercriteria Correlation (CRITIC) method is used to assess and prioritize the criteria set for the study. Then, the Additive Ratio Assessment (ARAS) method is applied to evaluate and rank four machine tools that were selected and used as alternatives in the study. The results indicate that the criteria of maximum spindle speed and linkage accuracy are the most important in determining the best machine tool. Also, the results indicate that the best alternative among the four tools used is FIDLA GTF-28. As a result, the requirements and priorities for research in the future are highlighted.

PERSEPSI GURU DAN SISWA TERHADAP PENGEMBANGAN MEDIA PEMBELAJARAN BERBASIS ANDROID PADA MATERI POLA BILANGAN JENJANG SMP

This study aims to determine the perceptions of students and teachers towards the development of android-based learning media in the matter of number patterns, sub-chapter definition of number patterns, square number patterns, rectangular number patterns and triangular number patterns for grade VIII junior high school students. This research uses descriptive qualitative method. The results showed that students’ perceptions of the development of Android-based learning media in number pattern material obtained a percentage of 1) in the material aspect of 76% in the very feasible category; 2) the display aspect is 77% very decent category; 3) the language aspect gets a percentage score of 75% in the proper category. As for the teacher’s perception, the percentage score 1) on the KD aspect is 60% in the proper category; 2) material aspects of 79% in the very decent category; 3) the display aspect is 86% very decent category; 4) the language aspect gets a percentage score of 88.5% in the very decent category. So that it can be stated that the development of Android-based learning media is very suitable for use in number pattern learning activities.

Improved Merlin–Arthur Protocols for Central Problems in Fine-Grained Complexity

In a Merlin–Arthur proof system, the proof verifier (Arthur) accepts valid proofs (from Merlin) with probability 1, and rejects invalid proofs with probability arbitrarily close to 1. The running time of such a system is defined to be the length of Merlin’s proof plus the running time of Arthur. We provide new Merlin–Arthur proof systems for some key problems in fine-grained complexity. In several cases our proof systems have optimal running time. Our main results include:Certifying that a list of n integers has no 3-SUM solution can be done in Merlin–Arthur time tilde{O}(n). Previously, Carmosino et al. [ITCS 2016] showed that the problem has a nondeterministic algorithm running in tilde{O}(n^{1.5}) time (that is, there is a proof system with proofs of length tilde{O}(n^{1.5}) and a deterministic verifier running in tilde{O}(n^{1.5}) time).Counting the number of k-cliques with total edge weight equal to zero in an n-node graph can be done in Merlin–Arthur time {tilde{O}}(n^{lceil k/2rceil }) (where kge 3). For odd k, this bound can be further improved for sparse graphs: for example, counting the number of zero-weight triangles in an m-edge graph can be done in Merlin–Arthur time {tilde{O}}(m). Previous Merlin–Arthur protocols by Williams [CCC’16] and Björklund and Kaski [PODC’16] could only count k-cliques in unweighted graphs, and had worse running times for small k.Computing the All-Pairs Shortest Distances matrix for an n-node graph can be done in Merlin–Arthur time tilde{O}(n^2). Note this is optimal, as the matrix can have Omega (n^2) nonzero entries in general. Previously, Carmosino et al. [ITCS 2016] showed that this problem has an tilde{O}(n^{2.94}) nondeterministic time algorithm.Certifying that an n-variable k-CNF is unsatisfiable can be done in Merlin–Arthur time 2^{n/2 - n/O(k)}. We also observe an algebrization barrier for the previous 2^{n/2}cdot textrm{poly}(n)-time Merlin–Arthur protocol of R. Williams [CCC’16] for #SAT: in particular, his protocol algebrizes, and we observe there is no algebrizing protocol for k-UNSAT running in 2^{n/2}/n^{omega (1)} time. Therefore we have to exploit non-algebrizing properties to obtain our new protocol.Certifying a Quantified Boolean Formula is true can be done in Merlin–Arthur time 2^{4n/5}cdot textrm{poly}(n). Previously, the only nontrivial result known along these lines was an Arthur–Merlin–Arthur protocol (where Merlin’s proof depends on some of Arthur’s coins) running in 2^{2n/3}cdot textrm{poly}(n) time. Due to the centrality of these problems in fine-grained complexity, our results have consequences for many other problems of interest. For example, our work implies that certifying there is no Subset Sum solution to n integers can be done in Merlin–Arthur time 2^{n/3}cdot textrm{poly}(n), improving on the previous best protocol by Nederlof [IPL 2017] which took 2^{0.49991n}cdot textrm{poly}(n) time.

The maximum number of triangles in a graph and its relation to the size of the Schur multiplier of special p-groups

We give a sharp bound on the number of triangles in a graph with fixed number of edges. We also characterize graphs that achieve the maximum number of triangles. Using the upper bound on number of triangles, we give a sharp bound for the size of the Schur multiplier of special p-group of all ranks. We also improve existing bounds for the size of Schur multiplier of p-groups of class , and for p-groups of coclass r.

ADJACENCY PAIRS IN JOKOWI’S INTERVIEW WITH CNN HOST

- The locution ‘interaction’ could literally apply to several disparate of quite disparate social encounters. An adjacency pairs has the automatic sequences. At all times, they include of the first part and the second part, constructed by another speakers. An expectation of the utterance of a second part of the same pair is generated the utterance of the first part. The example of conversational turn-taking is an adjacency pair. This paper was in control of qualitative descriptive approach. This paper applied the theory of adjacency pairs to Jokowi’s interview with one of CNN host, Christiane Amanpour, on his first 100 days in office after elected as the seventh president of Indonesia. This paper describes about the definition of is the most commonly occurs. is the most commonly occurs. adjacency pairs, the characteristics of adjacency pairs, types of adjacency pairs and elements of adjacency pairs in conversational analysis. There are 44 adjacency pairs on this research. It was found six combinations of common adjacency pairs. The most common occurs was Question-Answer. It was caused by this is an interview where the interviewer offer some interrogation, judgement, and opinion then the interviewee respons all of them.Keywords: Adjacency pairs, Characteristics of adjacency pairs, Conversational analysis, Elements of adjacency pairs, Types of adjacency pairs.

Arrangements of orthogonal circles with many intersections

An arrangement of circles in which circles intersect only in angles of $\pi/2$ is called an arrangement of orthogonal circles. We show that in the case that no two circles are nested, the intersection graph of such an arrangement is planar. The same result holds for arrangement of circles that intersect in an angle of at most $\pi/2$. For the case where circles can be nested we prove that the maximal number of edges in an intersection graph of an arrangement of orthogonal circles lies in between $4n - O\left(\sqrt{n}\right)$ and $\left(4+\frac{5}{11}\right)n$, for $n$ being the number of circles. Based on the lower bound we can also improve the lower bound for the number of triangles in arrangements of orthogonal circles to $(3 + \frac{5}{9})n-O\left(\sqrt{n}\right)$.

The Number of Triangles in Random Intersection Graphs

The Number of Triangles in Random Intersection Graphs

Quadratic Programming and Triangular Numbers Ranking to an Optimal Moroccan Diet with Minimal Glycemic Load

In this work, we suggest a variety of optimal daily diets for people with diabetes in Morocco. To this end, we model the foods glycemic load in term of triangular fuzzy numbers. Then, we model the problem of daily diet in term of fuzzy quadratic optimization programming. To transform this model into a line model, we use a very performance ranking function. To solve the obtained model, we call particles swarm algorithm due to its performance and simplicity. Various experiments were carried out on the basis of feeds available on the Moroccan market and for different sizes of the PSO swarm. The experimental results show that our system proposes optimal diets with a reasonable glycemic load between, acceptable favorable gaps and unfavorable nutrients excesses. We show how to combine the proposed diets to obtain a balanced weekly regime.

Fuzzy Transportation Model Technique to Determine the Minimum Total Cost Using a Novel Ranking Function

The transportation problem (TP) is employed in many different situations, such as scheduling, performance, spending, plant placement, inventory control, and employee scheduling. When all variables, including supply, demand, and unit transportation costs (TC), are precisely known, effective solutions to the transportation problem can be provided. However, understanding how to investigate the transportation problem in an uncertain environment is essential. Additionally, businesses and organizations should seek the most economical and environmentally friendly forms of transportation, considering the significance of environmental issues and strict environmental legislation. This research employs a novel ranking function to solve the transportation problem (TP), where fuzzy triangular numbers represent the fuzzy demand and supply (DAS). The fuzzy model is transformed and compressed to a crisp model (CM), and the results are compared using the northwest corner method and the least cost method. In addition, a numerical example of the fuzzy transportation model (FTM) is shown.

A computational approach to Brauer Witt theorem using Shoda pair theory

A classical theorem due to Brauer and Witt implies that every simple component of the rational group algebra QG of a finite group G is Brauer equivalent to a cyclotomic algebra containing Q in its center. The precise description of this cyclotomic algebra is not available from the proof of the Brauer-Witt theorem and it has been a problem of interest to determine the same in view of its central role in the study of central simple algebras. In this paper, an approach using Shoda pair theory is described, which is quite efficient from computational perspective.

Cohomology and relative Rota-Baxter-Nijenhuis structures on [formula omitted] pairs

A LieYRep pair consists of a Lie-Yamaguti algebra and its representation. In this paper, we establish the cohomology theory of LieYRep pairs and characterize their linear deformations by the second cohomology group. Then we introduce the notion of relative Rota-Baxter-Nijenhuis structures on LieYRep pairs, investigate their properties, and prove that a relative Rota-Baxter-Nijenhuis structure gives rise to a pair of compatible relative Rota-Baxter operators under a suitable condition. Finally, we show the equivalence between r-matrix-Nijenhuis structures and Rota-Baxter-Nijenhuis structures on Lie-Yamaguti algebras.

Mathcal{N} = 2* Schur indices

We find closed-form expressions for the Schur indices of 4d mathcal{N} = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.