Showing papers in "International Journal of Nonlinear Analysis and Applications in 2021"
TL;DR: A novel approach for aspect-based sentiment analysis which utilizes deep ensemble learning, which first builds four deep learning models, namely CNN, LSTM, BiLSTM and GRU, and the outputs of these models are combined using stacking ensemble approach.
Abstract: Sentiment analysis is a subfield of Natural Language Processing (NLP) which tries to process a text to extract opinions or attitudes towards topics or entities. Recently, the use of deep learning methods for sentiment analysis has received noticeable attention from researchers. Generally, different deep learning methods have shown superb performance in sentiment analysis problem. However, deep learning models are different in nature and have different strengths and limitations. For example, convolutional neural networks are useful for extracting local structures from data, while recurrent models are able to learn order dependence in sequential data. In order to combine the advantages of different deep models, in this paper we have proposed a novel approach for aspect-based sentiment analysis which utilizes deep ensemble learning. In the proposed method, we first build four deep learning models, namely CNN, LSTM, BiLSTM and GRU. Then the outputs of these models are combined using stacking ensemble approach where we have used logistic regression as meta-learner. The results of applying the proposed method on the real datasets show that our method has increased the accuracy of aspect-based prediction by 5% to 20% compared to the basic deep learning methods.
17 citations
TL;DR: This work evaluates the performance by a novel approach that implements the transfer learning model on a well-known architecture called ResNet50 and yields better performance using Res net50 compared to other transfer learning techniques.
Abstract: Endometriosis is the anomalous progress of cells at the outer part of the uterus. Generally, this endometrial tissue stripes the uterine cavity. The existence of endometriosis is identified through procedures known as Transvaginal Ultra Sound Scan (TVUS), Magnetic Resonance Imaging (MRI), Laparoscopic procedures, and Histopathological slides. Minimal Invasive Surgery (MIS) Laparo-scopic images are recorded in a small camera. To assist the surgeon in identifying their presence of endometriosis, image quality (characteristics) was enhanced for more visual clarity. Deep learning has the ability in recognising the images for classification. The Convolutional Neural Networks (CNNs) perform classification of images on large datasets. The proposed system evaluates the performance by a novel approach that implements the transfer learning model on a well-known architecture called ResNet50. The proposed system train the model on ResNet50 architecture and yielded a training accuracy of 91%, validation accuracy of 90%, precision of 83%, and recall of 82%, which can be applied for larger datasets with better performance. The presented system yields higher Area Under Curve (AUC) of about 0.78. The proposed method yields better performance using ResNet50 compared to other transfer learning techniques.
11 citations
TL;DR: In this paper, the existence and uniqueness of common coupled fixed point results for three covariant mappings in bipolar metric spaces were established and applied to homotopy theory as well as integral equations.
Abstract: In this paper, we establish the existence and uniqueness of common coupled fixed point results for three covariant mappings in bipolar metric spaces. Moreover, we give an illustration which presents the applicability of the achieved results also we provided applications to homotopy theory as well as integral equations.
11 citations
TL;DR: In this paper, the authors introduce new types of convergence of a sequence in left dislocated and right dislocated metric spaces, and generalize Banach contraction principle in these newly defined generalized metric spaces.
Abstract: In the present paper, we introduce new types of convergence of a sequence in left dislocated and right dislocated metric spaces. Also, we generalize Banach contraction principle in these newly defined generalized metric spaces.
10 citations
TL;DR: In this paper, the authors investigated neutrosophic continuous mappings and gave some properties of these mappings, such as the properties of strong and strongly NE, irresolute NE, and neutro-sophic strongly NE.
Abstract: The aim of this paper is to investigate some new types of neutrosophic continuous mappings like, neutrosophic α∗−continuous mapping (Nα∗ − CM), neutrosophic irresolute α∗−continuous mapping (NIα∗ − CM), and neutrosophic strongly α∗−continuous mapping (NSα∗ − CM) are given and some of their properties are studied. Moreover, new kind of neutrosophic contra continuous mappings is investigated in this work, it is called neutrosophic contra α∗−continuous mapping (NCα∗ − CM).
9 citations
TL;DR: In this paper, the stability analysis of generalized fractional nonlinear systems including the regularized Prabhakar derivative is studied and several criteria for the generalized Mittag-Leffler stability and the asymptotic stability of this system by using the Lyapunov direct method.
Abstract: This work is devoted to study of the stability analysis of generalized fractional nonlinear system including the regularized Prabhakar derivative. We present several criteria for the generalized Mittag-Leffler stability and the asymptotic stability of this system by using the Lyapunov direct method. Further, we provide two test cases to illustrate the effectiveness of results. We apply the numerical method to solve the generalized fractional system with the regularized Prabhakar fractional systems and reveal asymptotic stability behavior of the presented systems by employing numerical simulation.
9 citations
TL;DR: The aim of this research is to initiate a new concept of domination in fuzzy graphs which is called a fuzzy co-even domination number denoted by $gamma_{f c o}(G) .$
Abstract: he aim of this research is to initiate a new concept of domination in fuzzy graphs which is called a fuzzy co-even domination number denoted by $gamma_{f c o}(G) .$ We will touch only a few aspects of the theory to of this definition. Some properties and boundaries of this definition are introduced. The fuzzy co-even domination number of fuzzy certain graphs as fuzzy complete, fuzzy complete bipartite, fuzzy star, fuzzy cycle, fuzzy null, fuzzy path, and fuzzy star are determined. Additionally, this number is computed for the complement of mentioned above fuzzy certain graphs. Finally, this number is also determined for the join to mentioned above fuzzy certain graphs with itself.
8 citations
TL;DR: In this paper, the authors examined the relationship between investment efficiency and financial information excellence and found no evidence on the moderating effect of diversification on the relation between excellence in financial information and efficiency in investment.
Abstract: Objective –This study intends to examine the relationship between investment efficiency and financial information excellence. The study is also examining the moderating impact of sustainability on the relation between excellence in financial information and investment productivity. Methodology –The cumulative measurements are 668 firm-years and are made up of 257 subsamples of underinvestment and 411 sub-samples of overinvestment. This study may find no proof on the moderating effect of diversification on the relation between excellence in financial information and efficiency in investment. In the years 2016 to 2019, our samples are companies listed on the Dhaka Stock Exchange. Findings – The results indicate that financial information reporting quality (both for overinvestment and underinvestment sub-samples) has a positive association with investment performance. Although the evidence is not consistent across sub-samples, the test findings on the relationship between diversification and efficiency of investment appear to indicate a negative and substantial relationship between diversification and efficiency of investment. Research limitations/implications – The study finds no research investigating financial information quality and the productivity of investments. Moreover, it also discusses the regulating consequence for diversification on the correlation concerning financial knowledge and productivity of investment, which has not been examined in current studies as well. Originality/value – This research fills a void in the literature by providing understandings into performs followed by Bangladeshi companies in diversification effects in investment productivity.This study also has major consequences in providing additional proof of the connection between financial information and productivity of investment.
8 citations
TL;DR: This study will give an outline of the particular aspects of machine learning optimization, which have several unique characteristics that are rarely seen in other optimization contexts.
Abstract: Machine learning is fast evolving, with numerous theoretical advances and applications in a variety of domains. In reality, most machine learning algorithms are based on optimization issues. This interaction is also explored in the special topic on machine learning and large-scale optimization. Furthermore, machine learning optimization issues have several unique characteristics that are rarely seen in other optimization contexts. Aside from that, the notions of classical optimization vs machine learning will be discussed. Finally, this study will give an outline of these particular aspects of machine learning optimization.
8 citations
TL;DR: The comparing results of the LRP and LARP models prove that the LARP has a better performance regarding timing and optimal solution, and shows the validity of the robust optimization approach.
Abstract: A Location-Arc Routing Problem (LARP) is a practical problem, while a few mathematical programming models have been considered for this problem. In this paper, a mixed non-linear programming model is presented for a multi-period LARP with the time windows under demand uncertainty. The time windows modeling in the arc routing problem is rarely. To the best our knowledge, it is the first time that the robust LARP model is verified and an optimal solution is presented for it. For this purpose, the CPLEX solver is used for solving the treasury location problems of a bank as a case study. These problems are node-based with close nods and can be transformed into arc-based. Therefore, the method LRP and LARP models can be used to solve these problems. The comparing results of the LRP and LARP models prove that the LARP has a better performance regarding timing and optimal solution. Furthermore, comparing the results of deterministic and robust LARP models for this case study shows the validity of the robust optimization approach.
8 citations
TL;DR: In this paper, the authors investigate solutions of the partial differential equations arising in physics with local fractional derivative operators (LFDOs) and utilize the reduce differential transform method (RDTM) which is based upon the LFDOs.
Abstract: In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising in mathematical physics with local fractional derivative operators (LFDOs). To get approximate solutions of these equations, we utilize the reduce differential transform method (RDTM) which is based upon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. The obtained solutions show that the present method is an efficient and simple tool for solving the linear and nonlinear PDEs within the LFDOs.
TL;DR: In this paper, the authors defined and investigated Mittag-Leffler-Hyers-Ulam and Ulam-Rassias stability of the Prabhakar fractional integral equation.
Abstract: In this paper, we define and investigate Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of Prabhakar fractional integral equation
TL;DR: In this paper, the spectral collocation method was proposed to solve linear and nonlinear stochastic It^o-Volterra integral equations (SVIEs) using the Legendre Gauss type quadrature.
Abstract: The purpose of this paper is to propose the spectral collocation method to solve linear and nonlinear stochastic It^o-Volterra integral equations (SVIEs). The proposed approach is different from other numerical techniques as we consider the Legendre Gauss type quadrature for estimating It^o integrals. The main characteristic of the presented method is that it reduces SVIEs into a system of algebraic equations. Thus, we can solve the problem by Newton's method. Furthermore, the convergence analysis of the approach is established. The method is computationally attractive, and to reveal the accuracy, validity, and efficiency of the proposed method, some numerical examples and convergence analysis are included.
TL;DR: In this article, the arrow domination is introduced with its inverse as a new type of domination in finite graphs and its inverse is shown to be the minimum cardinality over all arrow dominating sets in a finite graph.
Abstract: The arrow domination is introduced in this paper with its inverse as a new type of domination Let $G$ be a finite graph, undirected, simple and has no isolated vertex, a set $D$ of $V(G)$ is said an arrow dominating set if $|N(w)cap (V-D)|=i$ and $|N(w)cap D|geq j$ for every $w in D$ such that $i$ and $j$ are two non-equal positive integers The arrow domination number $gamma_{ar}(G)$ is the minimum cardinality over all arrow dominating sets in $G$ Essential properties and bounds of arrow domination and its inverse when $i=1$ and $j=2$ are proved Then, arrow domination number is discussed for several standard graphs and other graphs that formed by join and corona operations
TL;DR: This research throws light on understanding the basic concepts of sentiment analysis and then showcases a model which performs deep learning for classification for a movie review and airline sentiment data set.
Abstract: Leveraging text mining for sentiment analysis, and integrating text mining and deep learning are the main purposes of this paper. The presented study includes three main steps. At the first step, pre-processing such as tokenization, text cleaning, stop word, stemming, and text normalization has been utilized. Secondly, feature from review and tweets using Bag of Words (BOW) method and Term Frequency $_$Inverse Document Frequency is extracted. Finally, deep learning by dense neural networks is used for classification. This research throws light on understanding the basic concepts of sentiment analysis and then showcases a model which performs deep learning for classification for a movie review and airline$_$ sentiment data set. The performance measure in terms of precision, recall, F1-measure and accuracy were calculated. Based on the results, the proposed method achieved an accuracy of $95.38%$ and $93.84%$ for a movie review and Airline$_$ sentiment, respectively.
TL;DR: The statistical population is consist of 35 managers and basic technology senior experts in the Internet of Things (IOT) field, marketing and information technology experts who have been selected by Snow Ball method (chain reference) to the theoretical saturation limit.
Abstract: Many industry leaders predict that the industrial Internet will create unprecedented levels of growth and productivity over the coming decades. Business leaders, governments, academic environments, and technology vendors are working hard together to realize and restrain this powerful potential. In this research, the combined method has been used. In the qualitative part, the foundation data method or grounded theory with a systematic approach which attributed to Strauss and Corbin has been used for data analysis and has been designed with three open, axial and selective coding techniques in Maxqda model software. Then, the questionnaire was designed in 6 dimensions: causal, axial phenomenon, prevailing context, intervening conditions and consequences in 50 items to confirm the dimensions, components and indicators. The statistical population is consist of 35 managers and basic technology senior experts in the Internet of Things (IOT) field, marketing and information technology experts who have been selected by Snow Ball method (chain reference) to the theoretical saturation limit. In the quantitative part, after identifying the relevant dimensions, components and indicators, the questionnaire was provided to managers and experts. The results were confirmed by independent t-test. Prioritization of dimensions and components has been done by AHP technique. Reliability of interviews with Cohen's Kappa coefficient and inter-rater reliability method, content validity of the questionnaire using content validity ratio (CVR), content validity index (CVI), apparent validity with item impact scores and reliability with Cronbach's alpha and halving method has been approved.
TL;DR: In this article, the Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper, the results obtained by FSHPM are in acceptable concurrence with the specific arrangement of the problem.
Abstract: The Sumudu homotopy perturbation method (SHPM) is applied to solve fractional order nonlinear differential equations in this paper.The current technique incorporates two notable strategies in particular Sumudu transform (ST) and homotopy perturbation method (HPM). The proposed method’s hybrid property decreases the number of the quantity of computations and materials needed. In this method, illustration examples evaluate the accuracy and applicability of the mentioned procedure. The outcomes got by FSHPM are in acceptable concurrence with the specific arrangement of the problem.
TL;DR: In this article, the concept of orthogonal contractive mappings and fixed point theorems for such contractions are established in orthogonality bounded complete metric spaces via the notion of $tau-distances.
Abstract: In this paper, we introduce the concept of orthogonal contractive mappings and prove some fixed point theorems for such contractions. We establish our results in orthogonal bounded complete metric spaces via the notion of $tau-$distances. Moreover, an application to a differential equation is given.
TL;DR: In this article, the effects of adding or removing an edge and removing a vertex from a graph are studied on the order of minimum total pitchfork dominating set $gamma{pf}^{t} (G)$ and the inverse total pitch fork dominating set$gamma_{pf]^{-t}(G)$.
Abstract: Let $G=(V, E)$ be a finite, simple, and undirected graph without isolated vertex. We define a dominating $D$ of $V(G)$ as a total pitchfork dominating set, if $1leq|N(t)cap V-D|leq2$ for every $t in D$ such that $G[D]$ has no isolated vertex. In this paper, the effects of adding or removing an edge and removing a vertex from a graph are studied on the order of minimum total pitchfork dominating set $gamma_{pf}^{t} (G)$ and the order of minimum inverse total pitchfork dominating set $gamma_{pf}^{-t} (G)$. Where $gamma_{pf}^{t} (G)$ is proved here to be increasing by adding an edge and decreasing by removing an edge, which are impossible cases in the ordinary total domination number.
TL;DR: In this article, the impact of diffusion of innovation model on behavioral intention in adopting social media marketing with the moderator role of subjective norms in Iranian users was analyzed by making use of an online exploration, which gathered data from 253 experienced social-media users in Iran.
Abstract: Social media has become a new orientation and attitude for businesses today. Tools and methods for communicating with the customers have changed enormously with the revelation of social media and it has become a channel and an instrument that marketers can extend their marketing campaigns to a wider range of consumers. The research purpose of this article is to analyze the impact of diffusion of innovation model on behavioral intention in adopting social media marketing with the moderator role of subjective norms in Iranian users. By making use of an online exploration, this study gathers data from 253 experienced social-media users in Iran. We have utilized partial least squares structural equation modeling to examine the links between items of diffusion of innovation model, social media marketing adoption, behavioral intention and subjective norms. The results revealed that diffusion of innovation influence was found as a nominative determinant of users’ behavioral intention to adopting social media marketing while behavioral intentions were also found to have positive significant association towards users’ behavioral intention to adopt social media marketing. In addition, the results of the empirical study showed that subjective norms moderated the relation between diffusion of innovation and customer behavioral intention.
TL;DR: In this paper, the application of a socialist cooperative game for propensity to cooperate and improve agriculture's cumulative net benefit and stimulate the balanced use of groundwater is proposed to prevent groundwater level drawdown and compensate for part of the groundwater reserve deficit in the Dezful-Andimeshk plain, southwest of Iran.
Abstract: The increase in exploitation from aquifers in an unbalanced way to meet the growing demands of agriculture has led to a decrease in the groundwater levels and as a result, an increase in the cumulative groundwater-reservoir deficit. In the long run, this will also reduce profits from agriculture due to declining water table levels and rising water extraction costs. In this article, is proposed the application of a socialist cooperative game for propensity to cooperate and improve agriculture's cumulative net benefit and stimulate the balanced use of groundwater. The purpose of this approach is to prevent groundwater level drawdown and compensate for part of the groundwater-reservoir deficit in the Dezful-Andimeshk plain, southwest of Iran. In this study, the consumer behavior, as one of the main factors in groundwater resources management has been investigated. This method has been derived from the socialist cooperative game theory, taking the consumer as an effective factor on water table drawdown, and envisioned in the form of an eco-socialism model. Results revealed that maximum water table drawdown will be reduced by 21%, and as a result, 16 million cubic meters (MCM) of groundwater reservoir deficit will be compensated and the net benefit from agricultural activities will also increase by 26%.
TL;DR: An improved convolutional neural network is used to detect automatically the nutrients present in a leaf using Internet of Thing based image acquisition and nutrition analyser devices to show an improved detection accuracy than other deep learning models.
Abstract: In this paper, the study detects the nutritional deficiencies from these leaves using Internet of Thing (IoT) based image acquisition and nutrition analyser devices. The former captures the color of the leaf and the latter helps in finding the nutrients in each zone based on the image captured by the device. The study uses an improved convolutional neural network to detect automatically the nutrients present in a leaf. The type of leaf is considered from the plants including coriander, tomato, pepper, chili, etc. The Convolutional Neural Network (CNN) is used to extract the patterns of leaf images from the data capturing IoT devices and nutrition analyser device. The system stores and process the data in cloud, where the CNN integrated in Virtual Machines enables the process of input data and process it and sends the report to the authority. A total of 3000 images are collected out of various disorders in five different plants. A 5 fold cross-validation is conducted on training and testing dataset. The system is tested in terms of accuracy, sensitivity, specificity, f-measure, geometric mean and percentage error. The comparison made with existing models shows an improved detection accuracy by CNN than other deep learning models.
TL;DR: As illustrated by the preceeding network approach, public sentiment on neural networks and IoT is critical for the public sector, the public interest, and a special event in an emergency (IoT).
Abstract: The community's rise, public opinion network's popularity, and emergency personnel's advancement have changed drastically. Individuals can now go online from any place and through communications systems to share their opinions and attitudes more efficiently and more often. As illustrated by the preceeding network approach, public sentiment on neural networks and IoT is critical for the public sector, the public interest, and a special event in an emergency (IoT). In terms of data security and anonymity, the proposed program is not safe and has environmental problems. Network public opinion's approach is based on FPGAs and machine education. FPGAs (Field Programmable Gate Array) Instant perspectives, possible future themes, knowledge exchange, excellent content and Team variance are used to build machine learning. In this popular sentiment network, several disasters have seriously threatened the security of our community. Public views on disaster networks in all type of internet media, such as internet news, blogs and webpages, are inextricably connected with society. This plays into unprecedented stress the ability of the government to deal with crises and their consequences.
TL;DR: The study's finding reaffirms the need for routine baseline screening for this marker and as there is more chance of co-infection with these hepatitis viruses due to enhanced immunodeficiency by HIV and shared routes of transmission.
Abstract: Hepatitis-related liver diseases are a leading cause of mortality and morbidity among people with HIV/ AIDS taking highly active antiretroviral therapy due to shared transmission routes. An estimated 2–4 million HIV-infected persons have chronic HBV co-infection, and 4–5 million have HCV co-infection worldwide and 14,000 new infections each day. The purpose of this study was to determine the prevalence and associated factors of HBV and HCV co-infection in HIV-positive patients. A cross-sectional study was conducted among 235 HIV/ AIDS patients seeking medical care at special clinics of two public hospitals in Lahore, Pakistan, from February 2018 to May 2018. A structured questionnaire was used to collect information on socio-demographic and clinical characteristics of HIV/ AIDS patients after obtaining their written informed consent. Chi-square, Fisher's exact, and two independent sample t-tests as appropriate were used to find the association between risk factors and HBV, HCV co-infection with HIV. Further, a forward stepwise logistic regression model was used to evaluate the predictors of HBV and HCV co-infection with HIV. P-value < 0.05 was regarded as significant. Of 235 HIV-positive patients, 9% were co-infected with HBV, 41 were HCV co-infected, and 6% had HBV-HCV triple infection. The highest prevalence of HBV (55%), HCV co-infection (70%), and HBV-HCV triple infection (85%) were observed in intravenous drug users followed by heterosexual routes. Male, hypertensive, alcohol consumers, and smokers were statistically significantly associated with HBV co-infection $(P-value < 0.05)$. The factors include being male, never married, having $< 1$ year of HIV diagnosis, having $< 200$ CD4 counts (cell/mm3), presence of physical disability, having been infected through sexual routes, injecting drug user, alcohol consumer, and smoker were statistically significantly associated with HCV co-infection $(P-value < 0.05)$. Whereas the factors; heterosexual transmission, intravenous drug use, alcohol use, smoking, and presence of physical disability were statistically significantly associated with HBV, HCV triple infection $(P < 0.05)$. The adjusted odds ratio obtained by fitted logistic regression model showed that HIV transmission routes (both hetero and homo) and never married had lesser odds of HCV co-infection whereas the person with HIV transmission through intravenous drug use, who smoke and aged more than 30 years, had greater odds of HCV co-infection. Co-infection with hepatitis B and C virus is common among this studied sample of HIV-infected patients. The study's finding reaffirms the need for routine baseline screening for this marker and as there is more chance of co-infection with these hepatitis viruses due to enhanced immunodeficiency by HIV and shared routes of transmission. It highlights the need for timely initiation of HAART. Furthermore, those found to be negative should be immunized with HBV and HCV vaccines to improve.
TL;DR: This new modification can increase the invulnerability of the Hill Cipher against future attacks during transmission of information between agencies in this age of information technology.
Abstract: Secure message transformation promote the creation of various cryptography systems to enable receivers to interpret the transformed information. In the present age of information technology, the secure transfer of information is the main study of most agencies. In this study, a particular symmetric cryptography system, Hill Cipher method, is enhanced with the help of encryption and decryption algorithms of the asymmetric RSA cryptography system to avoid certain problems. Previous results show that the original Hill algorithms are still insufficient because of their weakness to known plaintext attack, and a modification of the Hill Cipher cryptography system is therefore presented to increase its invulnerability. The enhancement focuses on implementing the RSA algorithms over the Hill Cipher to increase its security efficiency. The suggested method relies on the security of the RSA and Hill Cipher cryptosystems to find the private decryption keys, and thus is much more secure and powerful than both methods applied separately. Also secure and dynamic generation of the Hill Cipher matrix instead of using static matrix are proposed. This new approach is composed of a public key cryptosystem that has a shared secret key (between participants only), public key (announced to all), and two private keys (for each person). Therefore, this new modification can increase the invulnerability of the Hill Cipher against future attacks during transmission of information between agencies in this age of information technology
TL;DR: In this article, a new iterative method of successive approximations based on Haar wavelets is proposed for solving three-dimensional nonlinear Fredholm integral equations, and the convergence of the method is verified.
Abstract: In this paper, a new iterative method of successive approximations based on Haar wavelets is proposed for solving three-dimensional nonlinear Fredholm integral equations. The convergence of the method is verified. The error estimation and numerical stability of the proposed method are provided in terms of Lipschitz condition. Conducting numerical experiments confirm the theoretical results of the proposed method and endorse the accuracy of the method.
TL;DR: In that paper the fuzzy equality co-neighborhood domination and denoted by $gamma_{en}(G)$ for a new definition of domination was described for the fuzzy graph.
Abstract: In that paper the fuzzy equality co-neighborhood domination and denoted by $gamma_{en}(G)$ for a new definition of domination was described for the fuzzy graph. This new definition was studied in a strong fuzzy graph and constraints were found for many several graphs. Complementary strong fuzzy graphs of the same graphs were examined and studied in detail.
TL;DR: In this article, the authors prove a new common fixed point in a general topological space with a $tau-distance and deduce two common fixed points theorems for two new classes of contractive selfmappings in complete bounded metric spaces.
Abstract: In this paper, we prove a new common fixed point in a general topological space with a $tau-$distance. Then we deduce two common fixed point theorems for two new classes of contractive selfmappings in complete bounded metric spaces. Moreover, an application to a system of differential equations is given.
TL;DR: This article introduces the interval-valued intuitionistic fuzzy set (textbf{IVIFS}), and introduces two multiple attribute group decision-making methods ( textbf{MAGDM}) based on such operators.
Abstract: In this article, we introduce the interval-valued intuitionistic fuzzy set (textbf{IVIFS}), which are generalized forms of intuitionistic fuzzy set (textbf{IFS}) and fuzzy set, this is because in intuitionistic fuzzy sets the non-membership function also applies to evaluations, and these sets are useful for modelling ambiguous concepts that abound in real problems. Here we try to look for new methods for more practical solutions in optimization problems for various sciences such as computer science, mathematics, engineering, medicine, psychology, climate and etc. First, with the introduction of t-norm Frank, an action we construct some Frank aggregation operators on interval-valued intuitionistic fuzzy numbers (textbf{IVIFN}s), including the Frank weighted averaging operator, Frank-ordered weighted averaging operator, Frank hybrid weighted averaging operator, Frank geometric weighted averaging operator, Frank geometric-ordered weighted averaging operator, and Frank geometric hybrid weighted averaging operator. Also, examine some of the characteristics of these operators. In the following, we introduce two multiple attribute group decision-making methods (textbf{MAGDM}) based on such operators. Finally, we provide illustrative examples of these methods.