Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923An Improved Method Estimating and Performing Confidence Interval and Hypothesis
Test in a Fuzzy Simple Linear Regression Model With non-fuzzy Inputs And Fuzzy outputsAn Improved Method Estimating and Performing Confidence Interval and Hypothesis
Test in a Fuzzy Simple Linear Regression Model With non-fuzzy Inputs And Fuzzy outputs1321476910.22055/jamm.2019.23961.1505FAMohammad Ghasem AkbariDepartment of Statistics, University of Birjand, Birjand, Iran0000-0001-5064-8065Gholamreza HesamianDepartment of Statistics, Payame Noor University, IranJournal Article20171105In this paper, an existing method to estimate coefficients of a fuzzy regression model with non-fuzzy inputs and fuzzy out-puts as well as its method to perform a fuzzy hypothesis test and a fuzzy confidence interval are recalled. Then, the disadvantages and shortcoming of this method are examined and criticized by analyzing several numerical examples. By introducing an appropriate alternative approach to estimating coefficients and applying conventional fuzzy hypotheses in a fuzzy environment, we try to improve the method in the structure and decision making to accept or reject fuzzy hypotheses. For this purpose, employing a common distance measure and Bootstrap technique, the required test statistics are defined as non-fuzzy criteria. Then, by comparing the p-value obtained from the test statistics and a given significance, unlike the existing one, one can easily decide to accept or reject the null hypothesis. Also, using some applied examples, the possible advantageous of the proposed approach in hypothesis testing and confidence interval for fuzzy coefficients are compared and discussed.In this paper, an existing method to estimate coefficients of a fuzzy regression model with non-fuzzy inputs and fuzzy out-puts as well as its method to perform a fuzzy hypothesis test and a fuzzy confidence interval are recalled. Then, the disadvantages and shortcoming of this method are examined and criticized by analyzing several numerical examples. By introducing an appropriate alternative approach to estimating coefficients and applying conventional fuzzy hypotheses in a fuzzy environment, we try to improve the method in the structure and decision making to accept or reject fuzzy hypotheses. For this purpose, employing a common distance measure and Bootstrap technique, the required test statistics are defined as non-fuzzy criteria. Then, by comparing the p-value obtained from the test statistics and a given significance, unlike the existing one, one can easily decide to accept or reject the null hypothesis. Also, using some applied examples, the possible advantageous of the proposed approach in hypothesis testing and confidence interval for fuzzy coefficients are compared and discussed.https://jamm.scu.ac.ir/article_14769_a78320d96493744ac78e4f3e789b7f8b.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Estimation of reliability in multicomponent stress-strength model based on Gompertz distributionEstimation of reliability in multicomponent stress-strength model based on Gompertz distribution33521477010.22055/jamm.2019.24238.1519FAShahram YagoobzadehDepartment of Statistics, Payame Noor University, Tehran, Iran0000-0002-8794-2222Journal Article20171128In this research article,we estimate the multicomponent stress–strength reliability of a system when strength and stress variates are drawn from an exponentiated Weibull distribution with different shape parameters and , and common scale parameter , respectively. The reliability is estimated using the best single observation percentile method and maximum liklihood method of estimation when samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets we illustrate the procedure.<br /> Keywords: Stress–Strength, Reliability, Maximum likelihood estimation, Best single observation percentile estimation, Mean square error, Confidence intervals, Gompertz distribution.In this research article,we estimate the multicomponent stress–strength reliability of a system when strength and stress variates are drawn from an exponentiated Weibull distribution with different shape parameters and , and common scale parameter , respectively. The reliability is estimated using the best single observation percentile method and maximum liklihood method of estimation when samples drawn from strength and stress distributions. The reliability estimators are compared asymptotically. The small sample comparison of the reliability estimates is made through Monte Carlo simulation. Using real data sets we illustrate the procedure.<br /> Keywords: Stress–Strength, Reliability, Maximum likelihood estimation, Best single observation percentile estimation, Mean square error, Confidence intervals, Gompertz distribution.https://jamm.scu.ac.ir/article_14770_84a4e339faa798c7d5f4326bfcdee769.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Analysis of Spatial-Temporal data: the Case Study of Zanjan Daily mean Wind Speed DataAnalysis of Spatial-Temporal data: the Case Study of Zanjan Daily mean Wind Speed Data53761477110.22055/jamm.2019.26917.1624FAAli ShahnavazDepartment of Statistics. Science and Research Branch. Islamic Azad University. Tehran. IranAli M. MosammamDepartment of Statistics. University of Zanjan. Zanjan. IranMohammad Hassan BehzadiDepartment of Statistics. Science and Research Branch. Islamic Azad University. Tehran. IranJournal Article20180829In this paper, we first study the theory of the spatial-temporal half spectral modelling and describe some properties of recently proposed half spectral models. Next, we propose an estimation method for the estimation of spatial-temporal covariance functions in the half-spectral setting. To assess the performance of the proposed half-spectral models, we conduct two simulations. in which we compare the proposed fitting approach with respect to the other classical estimation methods. The proposed methods have great success in fitting parametric space-time covariance functions specifically for massive data sets. Finally, we apply the proposed methods for a real daily wind speed data in Zanjan, Iran.In this paper, we first study the theory of the spatial-temporal half spectral modelling and describe some properties of recently proposed half spectral models. Next, we propose an estimation method for the estimation of spatial-temporal covariance functions in the half-spectral setting. To assess the performance of the proposed half-spectral models, we conduct two simulations. in which we compare the proposed fitting approach with respect to the other classical estimation methods. The proposed methods have great success in fitting parametric space-time covariance functions specifically for massive data sets. Finally, we apply the proposed methods for a real daily wind speed data in Zanjan, Iran.https://jamm.scu.ac.ir/article_14771_21c15c6af4c4d4a622cc3320d2e6b452.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Modeling seasonal changes and death rate of hive bee in honey bee colonyModeling seasonal changes and death rate of hive bee in honey bee colony77921477210.22055/jamm.2019.26669.1613FAShahin BagheriDepartment of Applied Mathematics, Tarbiat Modares University, Tehran, Iran.Mehdi MirzaieDepartment of Applied Mathematics, Tarbiat Modares University, Tehran, IranRezvan SalehiDepartment of Applied Mathematics, Tarbiat Modares University, Tehran, Iran.Journal Article20180801Honey bee is the insect that mainly pollens agricultural products. In recent decades, colony failure rates as a global concern have increased. Some mathematical models have been proposed. In one of the first models the impact of bee death rates on population dynamics was studied and then the food availability and the rate of broods added to the model. Here we improve the model by considering seasonal changes and death rate of hive bees. Our results show that death rates higher than 0.41 lead to colony collapse. At higher death rates, despite of colony failure, food stored in colony and this is instance of colony collapse. Additionally, the model predicts the minimum food needed for colony in various death rates.Honey bee is the insect that mainly pollens agricultural products. In recent decades, colony failure rates as a global concern have increased. Some mathematical models have been proposed. In one of the first models the impact of bee death rates on population dynamics was studied and then the food availability and the rate of broods added to the model. Here we improve the model by considering seasonal changes and death rate of hive bees. Our results show that death rates higher than 0.41 lead to colony collapse. At higher death rates, despite of colony failure, food stored in colony and this is instance of colony collapse. Additionally, the model predicts the minimum food needed for colony in various death rates.https://jamm.scu.ac.ir/article_14772_6a3bada222bce8488a905dcb8ce21654.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Modelling of chaos in smooth piecewise dynamical systems with one discontinuous pointModelling of chaos in smooth piecewise dynamical systems with one discontinuous point931051477310.22055/jamm.2019.26024.1588FAMehdi PourbaratDepartment of Mathematics, Shhid Beheshti University, Tehran, IranNeda AbbasiMahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, IranRoya MakrooniDepartment of Mathematics, University of Sistan and Baluchestan, Zahedan, IranJournal Article20180526In this paper, we provide conditions on the smooth piecewise dynamical systems that guarantee the existence of Devaney chaos. In fact, we show that if f is a generalized semi-baker map with two branches and its derivative greater than or equal √2, then the dynamical system related to that is chaotic in the sense of Devaney. Such conditions on the dynamical systems with more than one discontinues point essentially does not satisfy this result.In this paper, we provide conditions on the smooth piecewise dynamical systems that guarantee the existence of Devaney chaos. In fact, we show that if f is a generalized semi-baker map with two branches and its derivative greater than or equal √2, then the dynamical system related to that is chaotic in the sense of Devaney. Such conditions on the dynamical systems with more than one discontinues point essentially does not satisfy this result.https://jamm.scu.ac.ir/article_14773_c5481d490ef17b67d259a9de14be11f7.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923A new mixed integer model and iterative solution approach for scheduling and planning of multi product oil pipelineA new mixed integer model and iterative solution approach for scheduling and planning of multi product oil pipeline1061251477410.22055/jamm.2019.24365.1527FANeda BeheshtiDepartment of Applied Mathematics, Amir Kabir University of Technology, Tehran, IranSeyed Ali MirhassaniDepartment of Applied Mathematics, Amir Kabir University of Technology, Tehran, IranJournal Article20171218The problem of pipeline planning is one of the most complex problems in the field of applied and industrial problems. Multi product pipeline planning and inventory management in distribution centers has to consider the pipeline limitations as well as the operational restrictions. Another important issue is the customer demands that must be satisfy on time. Providing effective mathematical models, that cover different aspects of this problem, as well as appropriate solving methods helps to planner to achieve the optimal scheduling of pipelines. Many researchers have been working on models to provide efficient models and develop appropriate methods for solving this problem. In this paper, a new mixed integer optimization model (MILP) is proposed for scheduling and planning multiple product pipelines that connect a refinery to a distribution center. The advantage of this model is its formulation method, which attempts to reduce the number of binary variables used in the model and reduce the complexity of the mathematical model. For this purpose, the problem has first been formulated without taking into account some operational constraints and during the model's solving, by applying an iterative algorithm, these restrictions are added to the model step by step. Finally, to validate models and solving methods, by implementing the proposed models and solution methods on real pipeline systems (based on information from Iran Telecom and Oil Pipelines), the outputs in terms of solving time and quality solution and objective function value are evaluated.The problem of pipeline planning is one of the most complex problems in the field of applied and industrial problems. Multi product pipeline planning and inventory management in distribution centers has to consider the pipeline limitations as well as the operational restrictions. Another important issue is the customer demands that must be satisfy on time. Providing effective mathematical models, that cover different aspects of this problem, as well as appropriate solving methods helps to planner to achieve the optimal scheduling of pipelines. Many researchers have been working on models to provide efficient models and develop appropriate methods for solving this problem. In this paper, a new mixed integer optimization model (MILP) is proposed for scheduling and planning multiple product pipelines that connect a refinery to a distribution center. The advantage of this model is its formulation method, which attempts to reduce the number of binary variables used in the model and reduce the complexity of the mathematical model. For this purpose, the problem has first been formulated without taking into account some operational constraints and during the model's solving, by applying an iterative algorithm, these restrictions are added to the model step by step. Finally, to validate models and solving methods, by implementing the proposed models and solution methods on real pipeline systems (based on information from Iran Telecom and Oil Pipelines), the outputs in terms of solving time and quality solution and objective function value are evaluated.https://jamm.scu.ac.ir/article_14774_7f876d0c965df7cf10eb3a33235017b5.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923A generalized SBM super-efficiency in fuzzy data envelopment analysisA generalized SBM super-efficiency in fuzzy data envelopment analysis1261451477510.22055/jamm.2019.21655.1422FAMozhgan Mansouri KaleibarDepartment of Mathematics, Semnan University, Semnan, IranAli AshrafiDepartment of Mathematics, Semnan University, Semnan, IranJournal Article20170405The slacks-based measure super-efficiency model is presented for ranking SBM's efficient decision making units. Fuzzy data envelopment analysis models have been introduced to evaluate uncertain inputs and outputs for decision making units (DMUs). In this methods, mostly used α-cut procedure. Also, sample fuzzy decision making units in these methods cannot be assessed. This paper proposes generalized fuzzy super-efficiency model which includes, old fuzzy DEA models, and evaluates the sample decision making units. This scheme embraces evaluation method based on vector. As an empirical example, the proposed method is applied to the flexible manufacturing system data to rank efficient units.The slacks-based measure super-efficiency model is presented for ranking SBM's efficient decision making units. Fuzzy data envelopment analysis models have been introduced to evaluate uncertain inputs and outputs for decision making units (DMUs). In this methods, mostly used α-cut procedure. Also, sample fuzzy decision making units in these methods cannot be assessed. This paper proposes generalized fuzzy super-efficiency model which includes, old fuzzy DEA models, and evaluates the sample decision making units. This scheme embraces evaluation method based on vector. As an empirical example, the proposed method is applied to the flexible manufacturing system data to rank efficient units.https://jamm.scu.ac.ir/article_14775_43939b8a05d7e99bf5709f7147a2ca8e.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923A generalized convex quadratic programming to solve fuzzy linear systemA generalized convex quadratic programming to solve fuzzy linear system1461701477610.22055/jamm.2019.26438.1605FAOmid Solaymani FardDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranNaser AkhoundiDepartment of Applied Mathematics, Damghan University, Damghan, IranMohadeseh RamezanZadehDepartment of Applied Mathematics, Damghan University, Damghan, IranMorteza GachpazanDepartment of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20180704The linear systems are one of the most important tools for modeling real-world phenomena. Because the real-world phenomena are always associated with uncertainty, solving the fuzzy linear system have a great importance. One of the proposed methods to find the exact and approximate solutions of a fuzzy linear system is using the least squares method. In this method, by choosing an arbitrary meter and solving a quadratic programming, they provide an approximate (or exact) solution for the fuzzy linear system. In this paper, at first, we prove that under some conditions and not depending on the selected meter the quadratic programming is convex. Therefore, by considering three different meters and solving several examples, we compare the obtained approximate solutions.The linear systems are one of the most important tools for modeling real-world phenomena. Because the real-world phenomena are always associated with uncertainty, solving the fuzzy linear system have a great importance. One of the proposed methods to find the exact and approximate solutions of a fuzzy linear system is using the least squares method. In this method, by choosing an arbitrary meter and solving a quadratic programming, they provide an approximate (or exact) solution for the fuzzy linear system. In this paper, at first, we prove that under some conditions and not depending on the selected meter the quadratic programming is convex. Therefore, by considering three different meters and solving several examples, we compare the obtained approximate solutions.https://jamm.scu.ac.ir/article_14776_12b46a50aacfef6089f164fbca82d677.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Generalization of the concept of equitable efficiency in multiobjective optimization problemsGeneralization of the concept of equitable efficiency in multiobjective optimization problems1711901477710.22055/jamm.2019.26673.1614FADavoud ForoutanniaDepartment of Mathematics, Vali Asr University of Rafsanjan, Rafsanjan, IranMina MeratiDepartment of Mathematics, Vali Asr University of Rafsanjan, Rafsanjan, IranJournal Article20180802The main purpose of the paper is to generalize the concept of equitable efficiency by introducing the concept of equitable A-efficiency, where A is an arbitrary matrix with non-negative entries. Two conditions are provided to ensure that the relation of equitable A-dominance is an equitable rational preference relation. Furthermore the structure of equitably A-efficient set is investigated and is proved that the set of equitably A-efficient solutions is contained within the set of efficient. Hence to reduce Pareto-optimal solutions, we can use equitably A-efficient solutions.The main purpose of the paper is to generalize the concept of equitable efficiency by introducing the concept of equitable A-efficiency, where A is an arbitrary matrix with non-negative entries. Two conditions are provided to ensure that the relation of equitable A-dominance is an equitable rational preference relation. Furthermore the structure of equitably A-efficient set is investigated and is proved that the set of equitably A-efficient solutions is contained within the set of efficient. Hence to reduce Pareto-optimal solutions, we can use equitably A-efficient solutions.https://jamm.scu.ac.ir/article_14777_a189f2adc9afc8b0d37a6fb3397371e1.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Dominance Graph of Binary WordsDominance Graph of Binary Words1912051477810.22055/jamm.2019.26702.1616FAFarzad ShaveisiDepartment of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran0000-0001-9138-6321Soheila NasouriDepartment of Mathematics, Razi University, Kermanshah, IranJournal Article20180805The dominance graph of the binary words, which is denoted by (Γ_n ) ⃗ , is a directed graph whose vertex set is the set of all binary words of length n. Setting B_1 (w)={1≤i≤n┤| w_i=1}, for every vertex 〖w_1 w_2…w〗_n, we join two vertices v and w by an arc if B_1 (w) is contained in B_1 (v). In this paper, we study some graphical parameters of this graph. For example, after computing the distance of every two vertices and the eccentricity of any vertex, it is proved that the diameter and the radius of the underlying graph of (Γ_n ) ⃗ equals 3 and 2, respectively. Also, it is proved that this graph has 〖 3〗^n-3(2^n-1) edges. Then we prove that both of the clique nmber and the chromatic number of the dominance graph of binary words of length n are n-1. Among other results, it is shown that the edge chromatic number and the maximum degree of vertices are equal to 2^(n-1)-2. Finally, by a combinatorial method, the independence number of this graph is determined, too.The dominance graph of the binary words, which is denoted by (Γ_n ) ⃗ , is a directed graph whose vertex set is the set of all binary words of length n. Setting B_1 (w)={1≤i≤n┤| w_i=1}, for every vertex 〖w_1 w_2…w〗_n, we join two vertices v and w by an arc if B_1 (w) is contained in B_1 (v). In this paper, we study some graphical parameters of this graph. For example, after computing the distance of every two vertices and the eccentricity of any vertex, it is proved that the diameter and the radius of the underlying graph of (Γ_n ) ⃗ equals 3 and 2, respectively. Also, it is proved that this graph has 〖 3〗^n-3(2^n-1) edges. Then we prove that both of the clique nmber and the chromatic number of the dominance graph of binary words of length n are n-1. Among other results, it is shown that the edge chromatic number and the maximum degree of vertices are equal to 2^(n-1)-2. Finally, by a combinatorial method, the independence number of this graph is determined, too.https://jamm.scu.ac.ir/article_14778_b460607ff30451796447b02bd9491699.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923Revisiting Narayana's Approach to the Chung-Feller TheoremRevisiting Narayana's Approach to the Chung-Feller Theorem2062121477910.22055/jamm.2019.27150.1640FASeyed Mohsen Ghoraishi SharakiDepartment of mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20180923Using cyclic permutations, Narayana investigated the relation between the area under north-east paths from the origin to the point (n,n) and the number of the flaws of the paths. His result implies a proof to the Chung-Feller Theorem. In this paper by revising the Narayana's approach, we offer short proofs to the theorems of Narayana and Chung-Feller.Using cyclic permutations, Narayana investigated the relation between the area under north-east paths from the origin to the point (n,n) and the number of the flaws of the paths. His result implies a proof to the Chung-Feller Theorem. In this paper by revising the Narayana's approach, we offer short proofs to the theorems of Narayana and Chung-Feller.https://jamm.scu.ac.ir/article_14779_473e876733969f0635a1e0d9443ecb3b.pdfShahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80889220190923s- R - continuous functionss- R - continuous functions2132251478010.22055/jamm.2019.26434.1606FAMasoumeh EtebarDepartment of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, IranJournal Article20180625A new class of continuous functions, namely s - R - continuous<br /> functions, is introduced. The relations of s - R - continuity with<br /> continuity and other variants of continuity are discussed. Basic<br /> Properties of s - R - continuous functions are studied. <br /> Conditions are established under which every weakly theta_cl -continuous<br /> function is s - R - continuous.A new class of continuous functions, namely s - R - continuous<br /> functions, is introduced. The relations of s - R - continuity with<br /> continuity and other variants of continuity are discussed. Basic<br /> Properties of s - R - continuous functions are studied. <br /> Conditions are established under which every weakly theta_cl -continuous<br /> function is s - R - continuous.https://jamm.scu.ac.ir/article_14780_ded870f03a4d037038b49589108f1036.pdf