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 begin{document}$ 5 $end{document}-fold cross validation is used to estimate performance. The classical regression and Huber regression models have similar performance, both of them have narrow intervals. Although the RANSAC model has a slightly higher coverage rate, it has the widest interval. When the coverage rates are similar, the model with a narrower interval is recommended. Therefore, the classical and Huber regression models with bootstrap method are recommended to calculate the prediction interval.
The prediction interval is an important guide for financial organizations to make decisions for pricing loan rates. In this paper, we considered four models with bootstrap technique to calculate prediction intervals. Two datasets are used for the study and begin{document}$ 5 $end{document}-fold cross validation is used to estimate performance. The classical regression and Huber regression models have similar performance, both of them have narrow intervals. Although the RANSAC model has a slightly higher coverage rate, it has the widest interval. When the coverage rates are similar, the model with a narrower interval is recommended. Therefore, the classical and Huber regression models with bootstrap method are recommended to calculate the prediction interval.
{"title":"Prediction intervals of loan rate for mortgage data based on bootstrapping technique: A comparative study","authors":"Donglin Wang, Rencheng Sun, Lisa Green","doi":"10.3934/mfc.2022027","DOIUrl":"https://doi.org/10.3934/mfc.2022027","url":null,"abstract":"<p style='text-indent:20px;'>The prediction interval is an important guide for financial organizations to make decisions for pricing loan rates. In this paper, we considered four models with bootstrap technique to calculate prediction intervals. Two datasets are used for the study and <inline-formula><tex-math id=\"M1\">begin{document}$ 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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
This paper aims to present the concept of $ I $ & $ 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.
{"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 $ & $ 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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified and estimated the convergence properties using of modulus of continuity, Lipschitz- type space, and Ditzian-Totik modulus of continuity. After that, the weighted approximation result is also given. Finally, some results related to the A-statistical convergence of the operators are obtained.
{"title":"Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators","authors":"Chandra Prakash, D. K. Verma, N. Deo","doi":"10.3934/mfc.2022034","DOIUrl":"https://doi.org/10.3934/mfc.2022034","url":null,"abstract":"In this paper, we are dealing with Cheney-Sharma Chlodovsky Durrmeyer operators and studying their approximation properties. The Bohman-Korovkin theorem is verified and estimated the convergence properties using of modulus of continuity, Lipschitz- type space, and Ditzian-Totik modulus of continuity. After that, the weighted approximation result is also given. Finally, some results related to the A-statistical convergence of the operators are obtained.","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73438969","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}
Recently, Karsli [15] estimated the convergence rate of the begin{document}$ q $end{document}-Bernstein-Durrmeyer operators for functions whose begin{document}$ q $end{document}-derivatives are of bounded variation on the interval begin{document}$ [0, 1] $end{document}. Inspired by this study, in the present paper we deal with the convergence rate of a begin{document}$ q $end{document}- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [17], for the functions begin{document}$ varphi $end{document} whose begin{document}$ q $end{document}-derivatives are of bounded variation on the interval begin{document}$ [0, infty ). $end{document} We present the approximation degree for the operator begin{document}$ left( { mathfrak{S}}_{n, ell, q}^{(alpha , beta )} { varphi}right)(mathfrak{z}) $end{document} at those points begin{document}$ mathfrak{z} $end{document} at which the one sided q-derivativesbegin{document}$ {D}_{q}^{+}{ varphi(mathfrak{z}); and; D} _{q}^{-}{ varphi(mathfrak{z})} $end{document} exist.
Recently, Karsli [15] estimated the convergence rate of the begin{document}$ q $end{document}-Bernstein-Durrmeyer operators for functions whose begin{document}$ q $end{document}-derivatives are of bounded variation on the interval begin{document}$ [0, 1] $end{document}. Inspired by this study, in the present paper we deal with the convergence rate of a begin{document}$ q $end{document}- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [17], for the functions begin{document}$ varphi $end{document} whose begin{document}$ q $end{document}-derivatives are of bounded variation on the interval begin{document}$ [0, infty ). $end{document} We present the approximation degree for the operator begin{document}$ left( { mathfrak{S}}_{n, ell, q}^{(alpha , beta )} { varphi}right)(mathfrak{z}) $end{document} at those points begin{document}$ mathfrak{z} $end{document} at which the one sided q-derivativesbegin{document}$ {D}_{q}^{+}{ varphi(mathfrak{z}); and; D} _{q}^{-}{ varphi(mathfrak{z})} $end{document} exist.
{"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})} $end{document}</tex-math></inline-formula> exist.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75357827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point begin{document}$ E_{0} $end{document}, endemic equilibrium point begin{document}$ E_{*} $end{document}, and basic reproduction number begin{document}$ R_0 $end{document} have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.
In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point begin{document}$ E_{0} $end{document}, endemic equilibrium point begin{document}$ E_{*} $end{document}, and basic reproduction number begin{document}$ R_0 $end{document} have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.
{"title":"Stability analysis of fractional order modelling of social media addiction","authors":"Pradeep Malik, Deepika","doi":"10.3934/mfc.2022040","DOIUrl":"https://doi.org/10.3934/mfc.2022040","url":null,"abstract":"<p style='text-indent:20px;'>In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point <inline-formula><tex-math id=\"M1\">begin{document}$ 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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
{"title":"Study on the well-posedness of stochastic Boussinesq equations with Navier boundary conditions","authors":"Chengfeng Sun, Shan Jiang, Hui Liu","doi":"10.3934/mfc.2023033","DOIUrl":"https://doi.org/10.3934/mfc.2023033","url":null,"abstract":"","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70220863","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}
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