(ϵ,δ)-complex anti fuzzy subgroups and their applications by Arshad Ali, Muhammad Haris Mateen, Qin Xin, Turki Alsuraiheed, Ghaliah Alhamzi

“…The complex anti-fuzzy set (CAFS) is an extension of the traditional anti-fuzzy set with a wider range for membership function beyond real numbers to complex numbers with unit disc aims to address the uncertainty of data. …”
Get full text

A Fuzzy Delphi Consensus Methodology Based on a Fuzzy Ranking by Antonio Francisco Roldán López de Hierro, Miguel Sánchez, Daniel Puente-Fernández, Rafael Montoya-Juárez, Concepción Roldán

“…Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. …”
Get full text

The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields by Keiji Nakatsugawa, Motoo Ohaga, Toshiyuki Fujii, Toyoki Matsuyama, Satoshi Tanda

“…This equation, which phenomenologically introduces the quantum numbers <inline-formula><math display="inline"><semantics><msub><mi>I</mi><mi>z</mi></msub></semantics></math></inline-formula> (isospin), <i>S</i> (strangeness), etc., is constructed using group theory with real numbers <inline-formula><math display="inline"><semantics><mi mathvariant="double-struck">R</mi></semantics></math></inline-formula>. …”
Get full text

Optimal Design of a Compound Planetary Reducer Using a Nonlinear Optimization Method by Seongyong Hur, David Kim, Chaehyun Lee, Dongil Choi

“…Using the SLSQP method, optimization results can be obtained as real numbers, making it suitable for use in compound planetary friction reducers with no constraints on the selection of gear dimension. …”
Get full text

Generating word embeddings from an extreme learning machine for sentiment analysis and sequence labeling tasks by Lauren, Paula, Qu, Guangzhi, Yang, Jucheng, Watta, Paul, Huang, Guang-Bin, Lendasse, Amaury

“…Words or phrases from the vocabulary are mapped to vectors of real numbers in a low-dimensional space. In previous work, we proposed using an Extreme Learning Machine (ELM) for generating word embeddings. …”
Get full text

Generalization of the Lehmer problem over incomplete intervals by Zhaoying Liu, Di Han

“…Abstract Let α ≥ 2 $\alpha \geq 2$ , m ≥ 2 $m\geq 2 $ be integers, p be an odd prime with p ∤ m ( m + 1 ) $p\nmid m (m+1 )$ , 0 < λ 1 $0<\lambda _{1} $ , λ 2 ≤ 1 $\lambda _{2}\leq 1$ be real numbers, q = p α > max { [ 1 λ 1 ] , [ 1 λ 2 ] } $q=p^{\alpha }> \max \{ [ \frac{1}{\lambda _{1}} ], [ \frac{1}{\lambda _{2}} ] \}$ . …”
Get full text

Classification of Complex Fuzzy Numbers and Fuzzy Inner Products by Jin Hee Yoon, Taechang Byun, Ji Eun Lee, Keun Young Lee

“…Specfically, the Cauchy-Schwartz inequality for type II is proven in a compact way, not only the one for fuzzy real numbers. In fact, it was already discussed by Hasanhani et al; however, they proved every case in a very complicated way. …”
Get full text

A Map Is a Living Structure with the Recurring Notion of Far More Smalls than Larges by Bin Jiang, Terry Slocum

“…The word endlessly means continuous map scales between two discrete ones, just as there are endless real numbers between 1 and 2. The iterated map system implies that each of the subsequent small-scale maps is a subset of the single large-scale map, not a simple subset but with various constraints to make all geographic features topologically correct.…”
Get full text

What is the Simplest Linear Ramp? by Suman Das, Sumit K. Garg, Chethan Krishnan, Arnab Kundu

“…Abstract We discuss conditions under which a deterministic sequence of real numbers, interpreted as the set of eigenvalues of a Hamiltonian, can exhibit features usually associated to random matrix spectra. …”
Get full text

Extremal values of VDB topological indices over F-benzenoids with equal number of edges by Fengwei Li, Qingfang Ye, Juan Rada

“…The VDB topological index of an $ n $-order graph $ G $ is defined as $ TI(G) = \sum\limits_{1\leq i\leq j\leq n-1}m_{ij}\psi_{ij}, $ where $ \{\psi_{ij}\} $ is a set of real numbers, $ m_{ij} $ is the quantity of edges linking an $ i $-vertex and another $ j $-vertex. …”
Get full text

Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information by Shumaiza, Muhammad Akram, Ahmad N. Al-Kenani, José Carlos R. Alcantud

“…The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon&#8217;s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. …”
Get full text

Nowhere-Zero Unoriented 6-Flows on Certain Triangular Graphs by Yang Fan, Li Liangchen, Zhou Sizhong

“…A nowhere-zero unoriented flow of graph G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. …”
Get full text

Dynamic Energy Modelling as an Alternative Approach for Reducing Performance Gaps in Retrofitted Schools in Denmark by Muhyiddine Jradi

“…It was shown that the retrofit design numbers largely overestimate the attained savings, where the average performance gap between the expected and real numbers for the three schools is around 61% and 136% for annual heating and electricity savings, respectively. …”
Get full text

Development of neutrosophic cubic hesitant fuzzy exponential aggregation operators with application in environmental protection problems by Ateeq Ur Rehman, Muhammad Gulistan, Mumtaz Ali, Mohammed M. Al-Shamiri, Shahab Abdulla

“…In this paper first we establish exponential operational laws in neutrosophic cubic hesitant fuzzy sets, in which the exponents are neutrosophic cubic hesitant fuzzy numbers and bases are positive real numbers. In order to use neutrosophic cubic hesitant fuzzy sets in decision making, we are developing exponential aggregation operators and investigate their properties in the current study. …”
Get full text

Online Signature Verification Systems on a Low-Cost FPGA by Enrique Cantó Navarro, Rafael Ramos Lara, Mariano López García

“…The system is based on an algorithm, which operates on real numbers using the double-precision floating-point IEEE 754 format. …”
Get full text

Some New Midpoint and Trapezoidal-Type Inequalities for General Convex Functions in <i>q</i>-Calculus by Dafang Zhao, Ghazala Gulshan, Muhammad Aamir Ali, Kamsing Nonlaopon

“…In addition, we present some applications of our results to special means of positive real numbers. It is expected that the ideas and techniques may stimulate further research in this field.…”
Get full text

Using the ERFI Function in the Problem of the Shape Optimization of the Compressed Rod by J. Marcinowski, M. Sadowski

“…This approach to many problems can find its solutions, while they are lacking in the real numbers domains. What is more, although these are operations on complex numbers, these solutions have often their real representations, as the numerical example shows. …”
Get full text

Randić energy of digraphs by Roberto Cruz, Juan Monsalve, Juan Rada

“…A VDB topological index φ of D is defined asφ(D)=12∑uv∈E(D)φdu+,dv−, where du+ and dv− denote the outdegree and indegree of vertices u and v, respectively, and φi,j is a bivariate symmetric function defined on nonnegative real numbers. Let Aφ=Aφ(D) be the n×n general adjacency matrix defined as [Aφ]ij=φdvi+,dvj− if vivj∈E(D), and 0 otherwise. …”
Get full text

Solving a Three-Index Transportation Problem under Risk Conditions Using a Genetic Algorithm by Skitsko Volodymyr I., Voinikov Mykola Yu.

“…The article describes the steps of the genetic algorithm to solve a triplanar and triaxial transportation problem, upon the encoding is in real numbers; shows how risks can be considered; presents the steps of the procedure for “returning” a chromosome to the region of feasibility; describes the use of the elitism strategy in order to preserve the best chromosome in the genetic algorithm. …”
Get full text

On p-Laplacian Kirchhoff-Schrödinger-Poisson type systems with critical growth on the Heisenberg group by Shujie Bai, Yueqiang Song, Dušan D. Repovš

“…\end{equation*} $</p> <p>where $ a, b $ are positive real numbers, $ \Omega\subset \mathbb{H}^N $ is a bounded region with smooth boundary, $ 1 &lt; p &lt; Q $, $ Q = 2N + 2 $ is the homogeneous dimension of the Heisenberg group $ \mathbb{H}^N $, $ Q^{\ast} = \frac{pQ}{Q-p} $, $ q\in(2p, Q^{\ast}) $ and $ \Delta_{H, p}u = \mbox{div}(|\nabla_{H} u|^{p-2}\nabla_{H} u) $ is the $ p $-horizontal Laplacian. …”
Get full text