Pub Date : 2018-02-08DOI: 10.1504/IJMOR.2018.10010214
R. Hassanzadeh, I. Mahdavi, N. Mahdavi-Amiri, A. Tajdin
We propose an approach for computing the product of various fuzzy numbers using α-cuts. A regression model is used to obtain the membership function of the product. Then, we make use of the approach to compute solutions of fully fuzzy linear systems. We also show how to compute solutions of fully fuzzy linear systems with various fuzzy variables. Examples are worked out to illustrate the approach.
{"title":"An α-cut approach for fuzzy product and its use in computing solutions of fully fuzzy linear systems","authors":"R. Hassanzadeh, I. Mahdavi, N. Mahdavi-Amiri, A. Tajdin","doi":"10.1504/IJMOR.2018.10010214","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010214","url":null,"abstract":"We propose an approach for computing the product of various fuzzy numbers using α-cuts. A regression model is used to obtain the membership function of the product. Then, we make use of the approach to compute solutions of fully fuzzy linear systems. We also show how to compute solutions of fully fuzzy linear systems with various fuzzy variables. Examples are worked out to illustrate the approach.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126037390","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}
Pub Date : 2018-02-08DOI: 10.1504/IJMOR.2018.10010221
Vijay Vir Singh, Hamisu I. Ayagi
The present paper focuses on the study of complex system consisting of three units super priority, priority and ordinary unit under preemptive resume repair policy. Three units connected with an automatic changeover switch and human operator is handling the system. Together with the failure in super priority, priority and ordinary unit, the other important failures like deliberate failure and switch failure have been considered for study of mathematical model. All failure rates are assumed constant and follow exponential distribution however, the repair rate for partially failed state follow general distribution and complete failed states are repaired using Gumbel-Hougaard family copula (a joint probability distribution of general distribution and negative exponential distribution). The system is analysed using supplementary variable technique and Laplace transform. The various popular measures of reliability such as availability, reliability, mean time to failure (MTTF) and profit function has been calculated for particular values of failure and repair rates. Sensitivity analysis for different traditional measures has also been done. Computed results have been highlighted by tables and graphs.
{"title":"Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel-Hougaard family copula","authors":"Vijay Vir Singh, Hamisu I. Ayagi","doi":"10.1504/IJMOR.2018.10010221","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010221","url":null,"abstract":"The present paper focuses on the study of complex system consisting of three units super priority, priority and ordinary unit under preemptive resume repair policy. Three units connected with an automatic changeover switch and human operator is handling the system. Together with the failure in super priority, priority and ordinary unit, the other important failures like deliberate failure and switch failure have been considered for study of mathematical model. All failure rates are assumed constant and follow exponential distribution however, the repair rate for partially failed state follow general distribution and complete failed states are repaired using Gumbel-Hougaard family copula (a joint probability distribution of general distribution and negative exponential distribution). The system is analysed using supplementary variable technique and Laplace transform. The various popular measures of reliability such as availability, reliability, mean time to failure (MTTF) and profit function has been calculated for particular values of failure and repair rates. Sensitivity analysis for different traditional measures has also been done. Computed results have been highlighted by tables and graphs.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123319286","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}
Pub Date : 2018-02-08DOI: 10.1504/IJMOR.2018.10010212
A. Hamadameen, Nasruddin Hassan
A study on multiobjective stochastic linear programming (MSLP) problems with partial information on probability distribution is conducted. A method is proposed to utilise the concept of dominated solution for the multiobjective linear programming (MLP) problems, and find a pareto optimal solution (POS) without converting the MLP problem into its unique linear programming (LP) problem. An algorithm is proposed along with a numerical example which illustrated the practicability of the proposed algorithm. Comparison of results with existing methods shows the efficiency of the proposed method based on the analysis of results performed.
{"title":"Pareto optimal solution for multiobjective stochastic linear programming problems with partial uncertainty","authors":"A. Hamadameen, Nasruddin Hassan","doi":"10.1504/IJMOR.2018.10010212","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010212","url":null,"abstract":"A study on multiobjective stochastic linear programming (MSLP) problems with partial information on probability distribution is conducted. A method is proposed to utilise the concept of dominated solution for the multiobjective linear programming (MLP) problems, and find a pareto optimal solution (POS) without converting the MLP problem into its unique linear programming (LP) problem. An algorithm is proposed along with a numerical example which illustrated the practicability of the proposed algorithm. Comparison of results with existing methods shows the efficiency of the proposed method based on the analysis of results performed.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125181933","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}
Pub Date : 2018-02-08DOI: 10.1504/IJMOR.2018.10010217
Dilbagh Panchal, Umesh Jamwal, P. Srivastava, Kushal Kamboj, Rohit Sharma
The aim of this research work is to propose a fuzzy methodology-based integrated framework for the failure analysis of the transmission system of the TATA Company-made heavy commercial vehicle. Under the failure analysis failure mode effect analysis (FMEA) approaches has been applied and the critical components of the considered system were identified on the basis of their risk priority number (RPN). The identification of critical components on the basis of RPN score results in confusion to system analyst as it becomes difficult to allocate appropriate risk priorities under same RPN scores. Also, importance among the probability of occurrence of failure (Of), severity (S), probability of non-detection (Od) are assumed to be of same importance, however, in real practical application there exists relative importance among these three factors. Therefore, to overcome such types of limitations of FMEA approach a fuzzy decision making system (FDMS) and grey relation analysis (GRA) approaches were applied. The ranking results so obtained were compared for better and intelligent decision making of risky components and the results were further supplied to maintenance management/reliability engineer of the considered system for planning and implementing the suitable maintenance policy accordingly.
{"title":"Fuzzy methodology application for failure analysis of transmission system","authors":"Dilbagh Panchal, Umesh Jamwal, P. Srivastava, Kushal Kamboj, Rohit Sharma","doi":"10.1504/IJMOR.2018.10010217","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010217","url":null,"abstract":"The aim of this research work is to propose a fuzzy methodology-based integrated framework for the failure analysis of the transmission system of the TATA Company-made heavy commercial vehicle. Under the failure analysis failure mode effect analysis (FMEA) approaches has been applied and the critical components of the considered system were identified on the basis of their risk priority number (RPN). The identification of critical components on the basis of RPN score results in confusion to system analyst as it becomes difficult to allocate appropriate risk priorities under same RPN scores. Also, importance among the probability of occurrence of failure (Of), severity (S), probability of non-detection (Od) are assumed to be of same importance, however, in real practical application there exists relative importance among these three factors. Therefore, to overcome such types of limitations of FMEA approach a fuzzy decision making system (FDMS) and grey relation analysis (GRA) approaches were applied. The ranking results so obtained were compared for better and intelligent decision making of risky components and the results were further supplied to maintenance management/reliability engineer of the considered system for planning and implementing the suitable maintenance policy accordingly.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126194026","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}
Pub Date : 2018-02-08DOI: 10.1504/IJMOR.2018.10010216
Nirbhay Mathur, P. Srivastava, A. Paul
The objective of this paper is a wide survey of recent optimisation techniques in the field of fuzzy transportation problems. The authors have reviewed papers on various techniques to solve fuzzy transportation problems. We have considered the algorithms discussed in research papers within the last decade so as to know the present scenario. A comparative study of methods with own critical comments as remarks has been included.
{"title":"Algorithms for solving fuzzy transportation problem","authors":"Nirbhay Mathur, P. Srivastava, A. Paul","doi":"10.1504/IJMOR.2018.10010216","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010216","url":null,"abstract":"The objective of this paper is a wide survey of recent optimisation techniques in the field of fuzzy transportation problems. The authors have reviewed papers on various techniques to solve fuzzy transportation problems. We have considered the algorithms discussed in research papers within the last decade so as to know the present scenario. A comparative study of methods with own critical comments as remarks has been included.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125912927","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}
Pub Date : 2018-02-08DOI: 10.1504/IJMOR.2018.10010218
Geeta Sachdev
A pair of symmetric dual second-order multi-objective fractional programming programs is formulated. Various duality results are established for this pair which further helps to study minimax mixed integer programming problems. Symmetric duality theorem is established under pseudobonvexity and multiplicative separability assumptions on the functions involved.
{"title":"Symmetric duality for multi-objective second-order fractional programs","authors":"Geeta Sachdev","doi":"10.1504/IJMOR.2018.10010218","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010218","url":null,"abstract":"A pair of symmetric dual second-order multi-objective fractional programming programs is formulated. Various duality results are established for this pair which further helps to study minimax mixed integer programming problems. Symmetric duality theorem is established under pseudobonvexity and multiplicative separability assumptions on the functions involved.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126078957","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}
Pub Date : 2018-01-12DOI: 10.1504/IJMOR.2018.10009201
M. S. Tabass, G. M. Borzadran
Generalisations of maximum entropy principle (MEP) and minimum discrimination information principle (MDIP) are described by Kapur and Kesavan (1989) . In this paper, we used generalised entropies and replaced Shannon entropy with Tsallis entropy when α = 2 . The generalisation has been achieved by the entropy maximisation postulate and examining its consequences . The inverse principles which are inherent in the maximum α entropy and minimum discrimination α entropy are made in the new methodology.
{"title":"The generalised maximum α entropy principle","authors":"M. S. Tabass, G. M. Borzadran","doi":"10.1504/IJMOR.2018.10009201","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10009201","url":null,"abstract":"Generalisations of maximum entropy principle (MEP) and minimum discrimination information principle (MDIP) are described by Kapur and Kesavan (1989) . In this paper, we used generalised entropies and replaced Shannon entropy with Tsallis entropy when α = 2 . The generalisation has been achieved by the entropy maximisation postulate and examining its consequences . The inverse principles which are inherent in the maximum α entropy and minimum discrimination α entropy are made in the new methodology.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126820455","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}
Pub Date : 2017-11-02DOI: 10.1504/IJMOR.2017.10008668
Sunil Kawale, Yogita Sanas
Trade credit is a regular component of market transactions. It arises when a seller allows a buyer to delay making payments for purchased goods or services. Such a contract has attracted the attention of many researchers and practitioners in recent years. In this review article, an attempt is made to present a complete up-to-date survey of published inventory literature under trade credit. This paper addresses the researches with delay in payment and presents pertinent information about developments and extensions of such models to provide an up-to-date review of the studies conducted. It is also an attempt to prepare this paper in a different view of the diagram so that new researchers can easily understand how and what is the development of inventory under trade credit? This can also be the starting point of further research.
{"title":"A review on inventory models under trade credit","authors":"Sunil Kawale, Yogita Sanas","doi":"10.1504/IJMOR.2017.10008668","DOIUrl":"https://doi.org/10.1504/IJMOR.2017.10008668","url":null,"abstract":"Trade credit is a regular component of market transactions. It arises when a seller allows a buyer to delay making payments for purchased goods or services. Such a contract has attracted the attention of many researchers and practitioners in recent years. In this review article, an attempt is made to present a complete up-to-date survey of published inventory literature under trade credit. This paper addresses the researches with delay in payment and presents pertinent information about developments and extensions of such models to provide an up-to-date review of the studies conducted. It is also an attempt to prepare this paper in a different view of the diagram so that new researchers can easily understand how and what is the development of inventory under trade credit? This can also be the starting point of further research.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125479601","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}
Pub Date : 2017-11-02DOI: 10.1504/IJMOR.2017.10008666
S. Jana, C. Nahak
In this paper, we study equilibrium problems and mixed equilibrium problems on Hadamard manifolds. Using the KKM technique, we establish the existence of solutions of the stated problems under the generalised monotonicity assumptions on the functions involved. We construct some examples to justify our work in Hadamard manifold. We also investigate the proximal point algorithm to solve mixed equilibrium problems on Hadamard manifolds. Our results and ideas may stimulate further research in this fascinating and interesting field of nonlinear space.
{"title":"Equilibrium and mixed equilibrium problems on Hadamard manifolds","authors":"S. Jana, C. Nahak","doi":"10.1504/IJMOR.2017.10008666","DOIUrl":"https://doi.org/10.1504/IJMOR.2017.10008666","url":null,"abstract":"In this paper, we study equilibrium problems and mixed equilibrium problems on Hadamard manifolds. Using the KKM technique, we establish the existence of solutions of the stated problems under the generalised monotonicity assumptions on the functions involved. We construct some examples to justify our work in Hadamard manifold. We also investigate the proximal point algorithm to solve mixed equilibrium problems on Hadamard manifolds. Our results and ideas may stimulate further research in this fascinating and interesting field of nonlinear space.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129959646","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}
Pub Date : 2017-11-02DOI: 10.1504/IJMOR.2017.10008665
Reeta Bhardwaj, T. Singh, Vijay Kumar
In this communication, the queuing system has two different types of queues namely primary and secondary queue. The existence of secondary queue is possible only when server has limited services to provide, and the system has a characteristic of service surrender facility. The paper deals with the analytical study of such system in which the parameter of the primary queue is probabilistic while parameter of the secondary queue is considered totally uncertain. We are the first to apply fuzzy logic to deal with the secondary queue. The average waiting time in the system by a customer and service wastage rate has been explored in our study through fuzzy arithmetic using α-cut. The service wastage rate is helpful in finding the level of amount of instability in the system when the secondary queue is in existence and is fuzzified.
{"title":"Analysis of service surrender queue model in fuzzy system","authors":"Reeta Bhardwaj, T. Singh, Vijay Kumar","doi":"10.1504/IJMOR.2017.10008665","DOIUrl":"https://doi.org/10.1504/IJMOR.2017.10008665","url":null,"abstract":"In this communication, the queuing system has two different types of queues namely primary and secondary queue. The existence of secondary queue is possible only when server has limited services to provide, and the system has a characteristic of service surrender facility. The paper deals with the analytical study of such system in which the parameter of the primary queue is probabilistic while parameter of the secondary queue is considered totally uncertain. We are the first to apply fuzzy logic to deal with the secondary queue. The average waiting time in the system by a customer and service wastage rate has been explored in our study through fuzzy arithmetic using α-cut. The service wastage rate is helpful in finding the level of amount of instability in the system when the secondary queue is in existence and is fuzzified.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116159215","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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