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Prediction intervals of loan rate for mortgage data based on bootstrapping technique: A comparative study 基于自举技术的抵押贷款数据贷款利率预测区间的比较研究
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022027
Donglin Wang, Rencheng Sun, Lisa Green
{"title":"Prediction intervals of loan rate for mortgage data based on bootstrapping technique: A comparative study","authors":"Donglin Wang, Rencheng Sun, Lisa Green","doi":"10.3934/mfc.2022027","DOIUrl":"https://doi.org/10.3934/mfc.2022027","url":null,"abstract":"<p style='text-indent:20px;'>The prediction interval is an important guide for financial organizations to make decisions for pricing loan rates. In this paper, we considered four models with bootstrap technique to calculate prediction intervals. Two datasets are used for the study and <inline-formula><tex-math id=\"M1\">begin{document}$ 5 $end{document}</tex-math></inline-formula>-fold cross validation is used to estimate performance. The classical regression and Huber regression models have similar performance, both of them have narrow intervals. Although the RANSAC model has a slightly higher coverage rate, it has the widest interval. When the coverage rates are similar, the model with a narrower interval is recommended. Therefore, the classical and Huber regression models with bootstrap method are recommended to calculate the prediction interval.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"60 1","pages":"280-289"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85847242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Fuzzy approximation based on $ tau- mathfrak{K} $ fuzzy open (closed) sets 基于$ tau- mathfrak{K} $模糊开(闭)集的模糊逼近
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023010
Priti, A. Tripathi
{"title":"Fuzzy approximation based on $ tau- mathfrak{K} $ fuzzy open (closed) sets","authors":"Priti, A. Tripathi","doi":"10.3934/mfc.2023010","DOIUrl":"https://doi.org/10.3934/mfc.2023010","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"20 1","pages":"558-572"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82366259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ideal convergence in modified IFNS and $ mathcal{L} $-fuzzy normed space 修正IFNS和$ mathcal{L} $-模糊赋范空间的理想收敛性
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023044
Vakeel A. Khan, Mikail Et, Izhar Ali Khan
{"title":"Ideal convergence in modified IFNS and $ mathcal{L} $-fuzzy normed space","authors":"Vakeel A. Khan, Mikail Et, Izhar Ali Khan","doi":"10.3934/mfc.2023044","DOIUrl":"https://doi.org/10.3934/mfc.2023044","url":null,"abstract":"This paper aims to present the concept of $ I $ &amp; $ I^* $ convergence and $ s_p $- $ I $ convergence along with the $ I $ Cauchy criterion in $ mathcal{L} $-fuzzy normed space (in short $ mathcal{L} $-FNS). Characterizations of these notions in $ mathcal{L} $-FNS have been shown in the paper. This paper also presents how these notions are related to each other in $ mathcal{L} $-FNS. We have also given certain important counter-examples to establish the relationships between them. In addition, we introduce the $ mathcal{L} $ -fuzzy limit points and $ mathcal{L} $-fuzzy cluster points of a sequence in $ mathcal{L} $-FNS.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135559814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some new fractional integral inequalities for $ (h_ {1}, h_ {2})- $convex functions $ (h_ {1}， h_{2})- $凸函数的一些新的分数积分不等式
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023040
Xiaoyue Han, Run Xu
{"title":"Some new fractional integral inequalities for $ (h_ {1}, h_ {2})- $convex functions","authors":"Xiaoyue Han, Run Xu","doi":"10.3934/mfc.2023040","DOIUrl":"https://doi.org/10.3934/mfc.2023040","url":null,"abstract":"In this paper, some Hermite-Hadamard integral inequalities and Hermite-Hadamard-Fejér integral inequalities involving Atangana-Baleanu fractional integral operators via $ (h_ {1}, h_ {2})- $convex functions and $ (h_ {1}, h_ {2})- $concave functions are established. Then, according to an integral equation with Atangana-Baleanu fractional integral operators, some Hermite-Hadamard integral inequalities for second order differentiable convex maps are given.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135699860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation 具有有界变分函数的Stancu型修正$ q $-Gamma算子的收敛速度
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022002
H. Karsli, P. Agrawal
{"title":"Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation","authors":"H. Karsli, P. Agrawal","doi":"10.3934/mfc.2022002","DOIUrl":"https://doi.org/10.3934/mfc.2022002","url":null,"abstract":"<p style='text-indent:20px;'>Recently, Karsli [<xref ref-type=\"bibr\" rid=\"b15\">15</xref>] estimated the convergence rate of the <inline-formula><tex-math id=\"M2\">begin{document}$ q $end{document}</tex-math></inline-formula>-Bernstein-Durrmeyer operators for functions whose <inline-formula><tex-math id=\"M3\">begin{document}$ q $end{document}</tex-math></inline-formula>-derivatives are of bounded variation on the interval <inline-formula><tex-math id=\"M4\">begin{document}$ [0, 1] $end{document}</tex-math></inline-formula>. Inspired by this study, in the present paper we deal with the convergence rate of a <inline-formula><tex-math id=\"M5\">begin{document}$ q $end{document}</tex-math></inline-formula>- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [<xref ref-type=\"bibr\" rid=\"b17\">17</xref>], for the functions <inline-formula><tex-math id=\"M6\">begin{document}$ varphi $end{document}</tex-math></inline-formula> whose <inline-formula><tex-math id=\"M7\">begin{document}$ q $end{document}</tex-math></inline-formula>-derivatives are of bounded variation on the interval <inline-formula><tex-math id=\"M8\">begin{document}$ [0, infty ). $end{document}</tex-math></inline-formula> We present the approximation degree for the operator <inline-formula><tex-math id=\"M9\">begin{document}$ left( { mathfrak{S}}_{n, ell, q}^{(alpha , beta )} { varphi}right)(mathfrak{z}) $end{document}</tex-math></inline-formula> at those points <inline-formula><tex-math id=\"M10\">begin{document}$ mathfrak{z} $end{document}</tex-math></inline-formula> at which the one sided q-derivatives<inline-formula><tex-math id=\"M11\">begin{document}$ {D}_{q}^{+}{ varphi(mathfrak{z}); and; D} _{q}^{-}{ varphi(mathfrak{z})} $end{document}</tex-math></inline-formula> exist.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"21 1","pages":"601-615"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75357827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Lyapunov type inequalities for nonlinear fractional Hamiltonian systems in the frame of conformable derivatives 适形导数框架下非线性分数阶哈密顿系统的Lyapunov型不等式
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023004
Qi Zhang, J. Shao
{"title":"Lyapunov type inequalities for nonlinear fractional Hamiltonian systems in the frame of conformable derivatives","authors":"Qi Zhang, J. Shao","doi":"10.3934/mfc.2023004","DOIUrl":"https://doi.org/10.3934/mfc.2023004","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A review of definitions of fractional differences and sums 分数差和定义的复习
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022013
Qiushuang Wang, R. Xu
{"title":"A review of definitions of fractional differences and sums","authors":"Qiushuang Wang, R. Xu","doi":"10.3934/mfc.2022013","DOIUrl":"https://doi.org/10.3934/mfc.2022013","url":null,"abstract":"Given the increasing importance of discrete fractional calculus in mathematics, science engineering and so on, many different concepts of fractional difference and sum operators have been defined. In this paper, we mainly reviews some definitions of fractional differences and sum operators that emerged in the fields of discrete calculus. Moreover, some properties of those operators are also analyzed and compared with each other, including commutation rules, linearity, Leibniz rules, etc.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"45 1","pages":"136-160"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89854411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Shape preserving properties of $ (mathfrak{p}, mathfrak{q}) $ Bernstein Bèzier curves and corresponding results over $ [a, b] $ $ (mathfrak{p}， mathfrak{q}) $ Bernstein b<e:1>曲线的保形性质及其在$ [a, b] $上的结果
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022041
V. Sharma, Asif Khan, M. Mursaleen
{"title":"Shape preserving properties of $ (mathfrak{p}, mathfrak{q}) $ Bernstein Bèzier curves and corresponding results over $ [a, b] $","authors":"V. Sharma, Asif Khan, M. Mursaleen","doi":"10.3934/mfc.2022041","DOIUrl":"https://doi.org/10.3934/mfc.2022041","url":null,"abstract":"<p style='text-indent:20px;'>This article deals with shape preserving and local approximation properties of post-quantum Bernstein bases and operators over arbitrary interval <inline-formula><tex-math id=\"M3\">begin{document}$ [a, b] $end{document}</tex-math></inline-formula> defined by Khan and Sharma (Iran J Sci Technol Trans Sci (2021)). The properties for <inline-formula><tex-math id=\"M4\">begin{document}$ (mathfrak{p}, mathfrak{q}) $end{document}</tex-math></inline-formula>-Bernstein bases and Bézier curves over <inline-formula><tex-math id=\"M5\">begin{document}$ [a, b] $end{document}</tex-math></inline-formula> have been given. A de Casteljau algorithm has been discussed. Further we obtain the rate of convergence for <inline-formula><tex-math id=\"M6\">begin{document}$ (mathfrak{p}, mathfrak{q}) $end{document}</tex-math></inline-formula>-Bernstein operators over <inline-formula><tex-math id=\"M7\">begin{document}$ [a, b] $end{document}</tex-math></inline-formula> in terms of Lipschitz type space having two parameters and Lipschitz maximal functions.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"97 1","pages":"691-703"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91053183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability analysis of fractional order modelling of social media addiction 社交媒体成瘾分数阶模型的稳定性分析
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2022040
Pradeep Malik, Deepika
{"title":"Stability analysis of fractional order modelling of social media addiction","authors":"Pradeep Malik, Deepika","doi":"10.3934/mfc.2022040","DOIUrl":"https://doi.org/10.3934/mfc.2022040","url":null,"abstract":"<p style='text-indent:20px;'>In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point <inline-formula><tex-math id=\"M1\">begin{document}$ E_{0} $end{document}</tex-math></inline-formula>, endemic equilibrium point <inline-formula><tex-math id=\"M2\">begin{document}$ E_{*} $end{document}</tex-math></inline-formula>, and basic reproduction number <inline-formula><tex-math id=\"M3\">begin{document}$ R_0 $end{document}</tex-math></inline-formula> have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"6 1","pages":"670-690"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70219010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal investment strategy for the DC pension plan based on jump diffusion model and S-shaped utility 基于跳跃扩散模型和s型效用的DC养老金计划最优投资策略
Mathematical foundations of computing Pub Date : 2023-01-01 DOI: 10.3934/mfc.2023007
Jiaxin Lu, Hua Dong
{"title":"Optimal investment strategy for the DC pension plan based on jump diffusion model and S-shaped utility","authors":"Jiaxin Lu, Hua Dong","doi":"10.3934/mfc.2023007","DOIUrl":"https://doi.org/10.3934/mfc.2023007","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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