1
|
Zhu W, Li Z, Heidari AA, Wang S, Chen H, Zhang Y. An Enhanced RIME Optimizer with Horizontal and Vertical Crossover for Discriminating Microseismic and Blasting Signals in Deep Mines. SENSORS (BASEL, SWITZERLAND) 2023; 23:8787. [PMID: 37960486 PMCID: PMC10648578 DOI: 10.3390/s23218787] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 10/20/2023] [Accepted: 10/24/2023] [Indexed: 11/15/2023]
Abstract
Real-time monitoring of rock stability during the mining process is critical. This paper first proposed a RIME algorithm (CCRIME) based on vertical and horizontal crossover search strategies to improve the quality of the solutions obtained by the RIME algorithm and further enhance its search capabilities. Then, by constructing a binary version of CCRIME, the key parameters of FKNN were optimized using a binary conversion method. Finally, a discrete CCRIME-based BCCRIME was developed, which uses an S-shaped function transformation approach to address the feature selection issue by converting the search result into a real number that can only be zero or one. The performance of CCRIME was examined in this study from various perspectives, utilizing 30 benchmark functions from IEEE CEC2017. Basic algorithm comparison tests and sophisticated variant algorithm comparison experiments were also carried out. In addition, this paper also used collected microseismic and blasting data for classification prediction to verify the ability of the BCCRIME-FKNN model to process real data. This paper provides new ideas and methods for real-time monitoring of rock mass stability during deep well mineral resource mining.
Collapse
Affiliation(s)
- Wei Zhu
- School of Resources and Safety Engineering, Central South University, Changsha 410083, China; (W.Z.); (Z.L.)
| | - Zhihui Li
- School of Resources and Safety Engineering, Central South University, Changsha 410083, China; (W.Z.); (Z.L.)
| | - Ali Asghar Heidari
- School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran 1417466191, Iran;
| | - Shuihua Wang
- Department of Biological Sciences, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China;
- School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK
| | - Huiling Chen
- Key Laboratory of Intelligent Informatics for Safety & Emergency of Zhejiang Province, Wenzhou University, Wenzhou 325035, China
| | - Yudong Zhang
- School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK
| |
Collapse
|
2
|
Predicting Entrepreneurial Intention of Students: Kernel Extreme Learning Machine with Boosted Crow Search Algorithm. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12146907] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
College students are the group with the most entrepreneurial vitality and potential. How to cultivate their entrepreneurial and innovative ability is one of the important and urgent issues facing this current social development. This paper proposes a reliable, intelligent prediction model of entrepreneurial intentions, providing theoretical support for guiding college students’ positive entrepreneurial intentions. The model mainly uses the improved crow search algorithm (CSA) to optimize the kernel extreme learning machine (KELM) model with feature selection (FS), namely CSA-KELM-FS, to study entrepreneurial intention. To obtain the best fitting model and key features, the gradient search rule, local escaping operator, and levy flight mutation (GLL) mechanism are introduced to enhance the CSA (GLLCSA), and FS is used to extract the key features. To verify the performance of the proposed GLLCSA, it is compared with eight other state-of-the-art methods. Further, the GLLCSA-KELM-FS model and five other machine learning methods have been used to predict the entrepreneurial intentions of 842 students from the Wenzhou Vocational College in Zhejiang, China, in the past five years. The results show that the proposed model can correctly predict the students’ entrepreneurial intention with an accuracy rate of 93.2% and excellent stability. According to the prediction results of the proposed model, the key factors affecting the student’s entrepreneurial intention are mainly the major studied, campus innovation, entrepreneurship practice experience, and positive personality. Therefore, the proposed GLLCSA-KELM-FS is expected to be an effective tool for predicting students’ entrepreneurial intentions.
Collapse
|
3
|
Tool for Predicting College Student Career Decisions: An Enhanced Support Vector Machine Framework. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12094776] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
The goal of this research is to offer an effective intelligent model for forecasting college students’ career decisions in order to give a useful reference for career decisions and policy formation by relevant departments. The suggested prediction model is mainly based on a support vector machine (SVM) that has been modified using an enhanced butterfly optimization approach with a communication mechanism and Gaussian bare-bones mechanism (CBBOA). To get a better set of parameters and feature subsets, first, we added a communication mechanism to BOA to improve its global search capability and balance exploration and exploitation trends. Then, Gaussian bare-bones was added to increase the population diversity of BOA and its ability to jump out of the local optimum. The optimal SVM model (CBBOA-SVM) was then developed to predict the career decisions of college students based on the obtained parameters and feature subsets that are already optimized by CBBOA. In order to verify the effectiveness of CBBOA, we compared it with some advanced algorithms on all benchmark functions of CEC2014. Simulation results demonstrated that the performance of CBBOA is indeed more comprehensive. Meanwhile, comparisons between CBBOA-SVM and other machine learning approaches for career decision prediction were carried out, and the findings demonstrate that the provided CBBOA-SVM has better classification and more stable performance. As a result, it is plausible to conclude that the CBBOA-SVM is capable of being an effective tool for predicting college student career decisions.
Collapse
|
4
|
Yang X, Zhao D, Yu F, Heidari AA, Bano Y, Ibrohimov A, Liu Y, Cai Z, Chen H, Chen X. An optimized machine learning framework for predicting intradialytic hypotension using indexes of chronic kidney disease-mineral and bone disorders. Comput Biol Med 2022; 145:105510. [DOI: 10.1016/j.compbiomed.2022.105510] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Revised: 04/07/2022] [Accepted: 04/07/2022] [Indexed: 11/03/2022]
|
5
|
Chen X, Huang H, Heidari AA, Sun C, Lv Y, Gui W, Liang G, Gu Z, Chen H, Li C, Chen P. An efficient multilevel thresholding image segmentation method based on the slime mould algorithm with bee foraging mechanism: A real case with lupus nephritis images. Comput Biol Med 2022; 142:105179. [DOI: 10.1016/j.compbiomed.2021.105179] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Revised: 12/24/2021] [Accepted: 12/24/2021] [Indexed: 02/01/2023]
|
6
|
Individual Disturbance and Attraction Repulsion Strategy Enhanced Seagull Optimization for Engineering Design. MATHEMATICS 2022. [DOI: 10.3390/math10020276] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The seagull optimization algorithm (SOA) is a novel swarm intelligence algorithm proposed in recent years. The algorithm has some defects in the search process. To overcome the problem of poor convergence accuracy and easy to fall into local optimality of seagull optimization algorithm, this paper proposed a new variant SOA based on individual disturbance (ID) and attraction-repulsion (AR) strategy, called IDARSOA, which employed ID to enhance the ability to jump out of local optimum and adopted AR to increase the diversity of population and make the exploration of solution space more efficient. The effectiveness of the IDARSOA has been verified using representative comprehensive benchmark functions and six practical engineering optimization problems. The experimental results show that the proposed IDARSOA has the advantages of better convergence accuracy and a strong optimization ability than the original SOA.
Collapse
|
7
|
Performance Evaluation of Human Resources Based on Linguistic Neutrosophic Maclaurin Symmetric Mean Operators. Cognit Comput 2022. [DOI: 10.1007/s12559-021-09963-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
|
8
|
Hu J, Liu Y, Heidari AA, Bano Y, Ibrohimov A, Liang G, Chen H, Chen X, Zaguia A, Turabieh H. An effective model for predicting serum albumin level in hemodialysis patients. Comput Biol Med 2022; 140:105054. [PMID: 34847387 DOI: 10.1016/j.compbiomed.2021.105054] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2021] [Revised: 11/13/2021] [Accepted: 11/16/2021] [Indexed: 12/31/2022]
Abstract
Patients on hemodialysis (HD) are known to be at an increased risk of mortality. Hypoalbuminemia is one of the most important risk factors of death in HD patients, and is an independent risk factor for all-cause mortality that is associated with cardiac death, infection, and Protein-Energy Wasting (PEW). It is a clinical challenge to elevate serum albumin level. In addition, predicting trends in serum albumin level is effective for personalized treatment of hypoalbuminemia. In this study, we analyzed a total of 3069 records collected from 314 HD patients using a machine learning method that is based on an improved binary mutant quantum grey wolf optimizer (MQGWO) combined with Fuzzy K-Nearest Neighbor (FKNN). The performance of the proposed MQGWO method was evaluated using a series of experiments including global optimization experiments, feature selection experiments on open data sets, and prediction experiments on an HD dataset. The experimental results showed that the most critical relevant indicators such as age, presence or absence of diabetes, dialysis vintage, and baseline albumin can be identified by feature selection. Remarkably, the accuracy and the specificity of the method were 98.39% and 96.77%, respectively, demonstrating that this model has great potential to be used for detecting serum albumin level trends in HD patients.
Collapse
Affiliation(s)
- Jiao Hu
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Yi Liu
- Department of Nephrology, The First Affiliated Hospital of Wenzhou Medical University, China.
| | - Ali Asghar Heidari
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Yasmeen Bano
- Department of Urology, The First Affiliated Hospital of Wenzhou Medical University, China.
| | - Alisherjon Ibrohimov
- Department of Urology, The First Affiliated Hospital of Wenzhou Medical University, China.
| | - Guoxi Liang
- Department of Information Technology, Wenzhou Polytechnic, Wenzhou, 325035, China.
| | - Huiling Chen
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Xumin Chen
- Department of Nephrology, The First Affiliated Hospital of Wenzhou Medical University, China.
| | - Atef Zaguia
- Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. BOX 11099, Taif, 21944, Saudi Arabia.
| | - Hamza Turabieh
- Department of Information Technology, College of Computers and Information Technology, P.O. Box 11099, Taif, 21944, Taif, Saudi Arabia.
| |
Collapse
|
9
|
Some Single-Valued Neutrosophic Uncertain Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple-Attribute Decision Making. Symmetry (Basel) 2021. [DOI: 10.3390/sym13122322] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The Maclaurin symmetric mean (MSM) operator has a good aggregation effect. It can capture the relationships between multiple input parameters, and the neutrosophic uncertain linguistic numbers can well represent some indeterminate and incomplete information. In this paper, we combine the MSM operator with the singled-valued neutrosophic uncertain linguistic set and propose some MSM operators based on single-valued neutrosophic uncertain linguistic environment, such as single-valued neutrosophic uncertain linguistic Maclaurin symmetric mean(SVNULMSM) operator and single-valued neutrosophic uncertain linguistic generalized Maclaurin symmetric mean(SVNULGMSM) operator. First of all, according to the neutrosophic set and uncertain linguistic numbers, we propose the single-valued neutrosophic uncertain linguistic numbers and give some operating rules. Furthermore, considering the influence of attribute weight on the results, we introduce the weighted SVNULMSM operator and weighted SVNULGMSM operator. Then, we propose a method to deal with MSDM problems and give the specific steps to solve the problem. Finally, an investment example is used to verify the effectiveness of our method, and the superiority of the method is proved by comparing with other methods.
Collapse
|
10
|
Zhang Q, Wang Z, Heidari AA, Gui W, Shao Q, Chen H, Zaguia A, Turabieh H, Chen M. Gaussian Barebone Salp Swarm Algorithm with Stochastic Fractal Search for medical image segmentation: A COVID-19 case study. Comput Biol Med 2021; 139:104941. [PMID: 34801864 DOI: 10.1016/j.compbiomed.2021.104941] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Revised: 10/11/2021] [Accepted: 10/11/2021] [Indexed: 01/11/2023]
Abstract
An appropriate threshold is a key to using the multi-threshold segmentation method to solve image segmentation problems, and the swarm intelligence (SI) optimization algorithm is one of the popular methods to obtain the optimal threshold. Moreover, Salp Swarm Algorithm (SSA) is a recently released swarm intelligent optimization algorithm. Compared with other SI optimization algorithms, the optimization solution strategy of the SSA still needs to be improved to enhance further the solution accuracy and optimization efficiency of the algorithm. Accordingly, this paper designs an effective segmentation method based on a non-local mean 2D histogram and 2D Kapur's entropy called SSA with Gaussian Barebone and Stochastic Fractal Search (GBSFSSSA) by combining Gaussian Barebone and Stochastic Fractal Search mechanism. In GBSFSSSA, the Gaussian Barebone and Stochastic Fractal Search mechanism effectively balance the global search ability and local search ability of the basic SSA. The CEC2017 competition data set is used to prove the algorithm's performance, and GBSFSSSA shows an absolute advantage over some typical competitive algorithms. Furthermore, the algorithm is applied in image segmentation of COVID-19 CT images, and the results are analyzed based on three different metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and feature similarity (FSIM), which can lead to the conclusion that the overall performance of GBSFSSSA is better than the comparison algorithm and can effectively improve the segmentation of medical images. Therefore, it is justified that GBSFSSSA is a reliable and effective method in solving the multi-threshold image segmentation problem.
Collapse
Affiliation(s)
- Qian Zhang
- Wenzhou University of Technology, Wenzhou, 325035, China.
| | - Zhiyan Wang
- School of Artificial Intelligence, Jilin International Studies University, Changchun, 130000, China.
| | - Ali Asghar Heidari
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Wenyong Gui
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Qike Shao
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Huiling Chen
- Department of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, 325035, China.
| | - Atef Zaguia
- Department of Computer Science, College of Computers and Information Technology, Taif University, P.O. BOX 11099, Taif, 21944, Saudi Arabia.
| | - Hamza Turabieh
- Department of Information Technology, College of Computers and Information Technology, PO Box 11099, Taif, 21944, Saudi Arabia.
| | - Mayun Chen
- Department of Pulmonary and Critical Care Medicine, The First Affiliated Hospital of Wenzhou Medical University, Wenzhou, 325000, China.
| |
Collapse
|
11
|
Zhao S, Wang P, Heidari AA, Chen H, He W, Xu S. Performance optimization of salp swarm algorithm for multi-threshold image segmentation: Comprehensive study of breast cancer microscopy. Comput Biol Med 2021; 139:105015. [PMID: 34800808 DOI: 10.1016/j.compbiomed.2021.105015] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Revised: 11/01/2021] [Accepted: 11/01/2021] [Indexed: 11/30/2022]
Abstract
Multi-threshold image segmentation (MIS) is now a well known image segmentation technique, and many researchers have applied intelligent algorithms to it, but these methods suffer from local optimal drawbacks. This paper presented a novel approach to improve the Salp Swarm Algorithm (SSA), namely EHSSA, and applied it to MIS. Knowing the inaccuracies and discussions on implementation of this method, a new efficient mechanism is proposed to improve global search capability of the algorithm and avoid falling into a local optimum. Moreover, the excellence of the proposed algorithm was proved by comparative experiments at IEEE CEC2014. Afterward, the performance of EHSSA was demonstrated by testing a set of images selected from the Berkeley segmentation data set 500 (BSDS500), and the experimental results were analyzed by evaluating the parameters, which proved the efficiency of the proposed algorithm in MIS. Furthermore, EHSSA was applied to the microscopic image segmentation of breast cancer. Medical image segmentation is the study of how to quickly extract objects of interest (human organs) from various images to perform qualitative and quantitative analysis of diseased tissues and improve the accuracy of their diagnosis, which assists the physician in making more informed decisions and patient rehabilitation. The results of this set of experiments also proved its superior performance. For any info about this paper, readers can refer to https://aliasgharheidari.com.
Collapse
Affiliation(s)
- Songwei Zhao
- College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, Zhejiang, 325035, China.
| | - Pengjun Wang
- College of Electrical and Electronic Engineering, Wenzhou University, Wenzhou, 325035, China.
| | - Ali Asghar Heidari
- School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran, Iran.
| | - Huiling Chen
- College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, Zhejiang, 325035, China.
| | - Wenming He
- The Affiliated Hospital of Medical School, Ningbo University, Ningbo, 315020, China.
| | - Suling Xu
- The Affiliated Hospital of Medical School, Ningbo University, Ningbo, 315020, China.
| |
Collapse
|
12
|
Hu J, Heidari AA, Zhang L, Xue X, Gui W, Chen H, Pan Z. Chaotic diffusion‐limited aggregation enhanced grey wolf optimizer: Insights, analysis, binarization, and feature selection. INT J INTELL SYST 2021. [DOI: 10.1002/int.22744] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Jiao Hu
- Department of Computer Science and Artificial Intelligence Wenzhou University Wenzhou China
| | - Ali Asghar Heidari
- Department of Computer Science and Artificial Intelligence Wenzhou University Wenzhou China
| | - Lejun Zhang
- College of Information Engineering Yangzhou University Yangzhou China
| | - Xiao Xue
- College of Computer Science and Technology Henan Polytechnic University Zhengzhou China
| | - Wenyong Gui
- Department of Computer Science and Artificial Intelligence Wenzhou University Wenzhou China
| | - Huiling Chen
- Department of Computer Science and Artificial Intelligence Wenzhou University Wenzhou China
| | - Zhifang Pan
- Zhejiang Engineering Research Center of Intelligent Medicine The First Affiliated Hospital of Wenzhou Medical University Wenzhou China
| |
Collapse
|
13
|
Son NTK, Dong NP, Long HV, Son LH, Khastan A. Linear quadratic regulator problem governed by granular neutrosophic fractional differential equations. ISA TRANSACTIONS 2020; 97:296-316. [PMID: 31399251 DOI: 10.1016/j.isatra.2019.08.006] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2019] [Revised: 07/17/2019] [Accepted: 08/01/2019] [Indexed: 06/10/2023]
Abstract
Quadratic cost functions estimation in the linear optimal control systems governed by differential equations (DEs) or partial differential equations (PDEs) has a well-established discipline in mathematics with many interfaces to science and engineering. During its development, the impact of uncertain phenomena to objective function and the complexity of the systems to be controlled have also increased significantly. Many engineering problems like magnetohydromechanical, electromagnetical and signal analysis for the transmission and propagation of electrical signals under uncertain environment can be dealt with. In this paper, we study the optimal control problem with operating a fractional DEs and PDEs at minimum quadratic objective function in the framework of neutrosophic environment and granular computing. However, there has been no studies appeared on the neutrosophic calculus of fractional order. Hence, we will introduce some derivatives of fractional order, including the neutrosophic Riemann-Liouville fractional derivatives and neutrosophic Caputo fractional derivatives. Next, we propose a new setting of two important problems in engineering. In the first problem, we investigate the numerical and exact solutions of some neutrosophic fractional DEs and neutrosophic telegraph PDEs. In the second problem, we study the optimality conditions together with the simulation of states of a linear quadratic optimal control problem governed by neutrosophic fractional DEs and PDEs. Some key applications to DC motor model and one-link robot manipulator model are investigated to prove the effectiveness and correctness of the proposed method.
Collapse
Affiliation(s)
- Nguyen Thi Kim Son
- Faculty of Natural Science, Hanoi Metropolitan University, Hanoi, Viet Nam.
| | - Nguyen Phuong Dong
- Department of Mathematics, Hanoi Pedagogical University 2, Vinh Phuc, Viet Nam.
| | - Hoang Viet Long
- Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam.
| | - Le Hoang Son
- VNU Information Technology Institute, Vietnam National University, Hanoi, Viet Nam.
| | - Alireza Khastan
- Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran.
| |
Collapse
|
14
|
Xing Y, Zhang R, Zhu X, Bai K. q-Rung orthopair fuzzy uncertain linguistic choquet integral operators and their application to multi-attribute decision making. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-182581] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Yuping Xing
- School of Management and Economic, Beijing Jiaotong University, Beijing, China
| | - Runtong Zhang
- School of Management and Economic, Beijing Jiaotong University, Beijing, China
| | - Xiaomin Zhu
- School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China
| | - Kaiyuan Bai
- School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China
| |
Collapse
|
15
|
Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making. MATHEMATICS 2019. [DOI: 10.3390/math7050389] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other is the LNN Einstein geometry (LNNEWG) operator. Then we present a method for solving decision-making problems based on LNNEWA and LNNEWG operators in the linguistic neutrosophic environment. Finally, we apply an example to verify the feasibility of these two methods.
Collapse
|