Multi-Objective Stochastic Programming in Fuzzy Environments最新文献

Fuzzy Linear Multi-Objective Stochastic Programming Models 模糊线性多目标随机规划模型

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch003

{"title":"Fuzzy Linear Multi-Objective Stochastic Programming Models","authors":"","doi":"10.4018/978-1-5225-8301-1.ch003","DOIUrl":"https://doi.org/10.4018/978-1-5225-8301-1.ch003","url":null,"abstract":"In this chapter, fuzzy goal programming (FGP) technique is presented to solve fuzzy multi-objective chance constrained programming (CCP) problems having parameters associated with the system constrains following different continuous probability distributions. Also, the parameters of the models are presented in the form of crisp numbers or fuzzy numbers (FNs) or fuzzy random variables (FRVs). In model formulation process, the imprecise probabilistic problem is converted into an equivalent fuzzy programming model by applying CCP methodology and the concept of cuts of FNs, successively. If the parameters of the objectives are in the form of FRVs then expectation model of the objectives are employed to remove the probabilistic nature from multiple objectives. Afterwards, considering the fuzzy nature of the parameters involved with the problem, the model is converted into an equivalent crisp model using two different approaches. The problem can either be decomposed on the basis of tolerance values of the parameters; alternatively, an equivalent deterministic model can be obtained by applying different defuzzification techniques of FNs. In the solution process, the individual optimal value of each objective is found in isolation to construct the fuzzy goals of the objectives. Then the fuzzy goals are transformed into membership goals on the basis of optimum values of each objective. Then priority-based FGP under different priority structures or weighted FGP is used for achievement of the highest membership degree to the extent possible to achieve the ideal point dependent solution in the decision-making context. Finally, several numerical examples considering different types of probability distributions and different forms of FNs are considered to illustrate the developed methodologies elaborately.","PeriodicalId":404955,"journal":{"name":"Multi-Objective Stochastic Programming in Fuzzy Environments","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126539759","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

Introduction and Historical Background 简介及历史背景

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch001

引用次数: 0

On Solving Fuzzy Multi-Objective Multi-Choice Stochastic Transportation Problems 求解模糊多目标多选择随机运输问题

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch009

{"title":"On Solving Fuzzy Multi-Objective Multi-Choice Stochastic Transportation Problems","authors":"","doi":"10.4018/978-1-5225-8301-1.ch009","DOIUrl":"https://doi.org/10.4018/978-1-5225-8301-1.ch009","url":null,"abstract":"This chapter presents solution procedures for solving unbalanced multi-objective multi-choice stochastic transportation problems in a hybrid fuzzy uncertain environment. In this chapter, various types of unbalanced multi-objective fuzzy stochastic transportation models are considered with the assumption that the parameters representing supplies of the products at the origins and demands of the products at the destinations, capacity of the conveyances, associated with the system constraints are either fuzzy numbers (FNs) or fuzzy random variables (FRVs) with some known continuous fuzzy probability distributions. The multi-choice cost parameters are considered as FNs. In this chapter, two objectives are considered: total transportation cost and total transportation time. As the transportation cost mainly depends on fuel prices and since fuel prices are highly fluctuating, the cost parameters are taken as multi-choice cost parameters with possibilistic uncertain nature. The time of transportation mainly depends on vehicle conditions, quality of roads, and road congestion. Due to these uncertain natures, the parameters representing time of transportation are also taken as fuzzy uncertain multi-choice parameters. In this transportation model, these objectives are minimized satisfying the constraints: product availability constraints, requirement of the product constraints, and capacity of the conveyance constraints. Numerical examples are provided for the sake of illustration of the methodology presented in this chapter, and also achieved solutions are compared with the solutions obtained by some existing methodologies to establish its effectiveness.","PeriodicalId":404955,"journal":{"name":"Multi-Objective Stochastic Programming in Fuzzy Environments","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126536921","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

Development of Fuzzy Multi-Objective Stochastic Fractional Programming Models 模糊多目标随机分式规划模型的发展

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch004

{"title":"Development of Fuzzy Multi-Objective Stochastic Fractional Programming Models","authors":"","doi":"10.4018/978-1-5225-8301-1.ch004","DOIUrl":"https://doi.org/10.4018/978-1-5225-8301-1.ch004","url":null,"abstract":"In this chapter, two methodologies for solving multi-objective linear fractional stochastic programming problems containing fuzzy numbers (FNs) and fuzzy random variables (FRVs) associated with the system constraints are developed. In the model formulation process, the fuzzy probabilistic constraints are converted into equivalent fuzzy constraints by applying chance constrained programming (CCP) technique in a fuzzily defined probabilistic decision-making situation. Then two techniques, -cut and defuzzification methods, are used to convert the model into the corresponding deterministic model. In the method of using -cut for FNs, the tolerance level of FNs is considered, and the constraints are reduced to constraints with interval coefficients. Alternatively, in using defuzzification method, FNs are replaced by their defuzzified values. Consequently, the constraints are modified into constraints in deterministic form. In the next step, the constraints with interval coefficients are customized into its equivalent form by using the convex combination of each interval. If the parameters of the objectives are triangular FNs, then on the basis of their tolerance ranges each objective is decomposed into three objectives with crisp coefficients. Then each objective is solved independently to find their best and worst values and those values are used to construct membership function of each objective. Finally, the compromise solution of multi-objective linear fractional CCP problems is obtained by applying any of the approaches: priority-based fuzzy goal programming (FGP) method, Zimmermann's approach, -connective process, or minimum bounded sum operator technique. To demonstrate the efficiency of the above-described techniques, two illustrative examples, studied previously, are solved, and the solutions are compared with the existing methodology.","PeriodicalId":404955,"journal":{"name":"Multi-Objective Stochastic Programming in Fuzzy Environments","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126732857","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 Multi-Objective Stochastic Models for Municipal Solid Waste Management 城市生活垃圾管理的模糊多目标随机模型

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch008

{"title":"Fuzzy Multi-Objective Stochastic Models for Municipal Solid Waste Management","authors":"","doi":"10.4018/978-1-5225-8301-1.ch008","DOIUrl":"https://doi.org/10.4018/978-1-5225-8301-1.ch008","url":null,"abstract":"With rising urbanization and change in lifestyle and food habits of human beings, the amount of municipal solid wastes (MSWs) are now being increasing day by day, and the composition of wastes are now also being changed. Therefore, it is now becoming essential to develop a consistent mathematical model for managing those wastes in a systematic manner. In this context, fuzzy chance constrained programming (FCCP) model becomes useful to handle wastes efficiently through the process of selecting sorting stations, treatment facilities, etc. through an efficient way so that the net system cost of sorting and transporting the wastes would be minimized, and the revenue generated from different sorting stations and different treatment facilities would be to maximized. From that view point, in this chapter, a fuzzy chance constrained programming (CCP) model is developed for MSW management. Most of the parameters involved with this model are imprecisely defined and probabilistically uncertain. So, the parameters of the objectives are considered as FNs, and the right side parameters of the probabilistic constraints involve normally distributed fuzzy random variables (FRVs). To resolve the cases arising due to the multiple occurrences of fuzzy goals, a fuzzy goal programming (FGP) has been adopted. To expound the potential use of the approach, a modified version of a case example, studied previously, is considered and solved. The achieved model solution is discussed elaborately to illustrate the proposed methodology for MSW management.","PeriodicalId":404955,"journal":{"name":"Multi-Objective Stochastic Programming in Fuzzy Environments","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126289266","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

Fundamental Concepts 基本概念

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch002

引用次数: 0

Fuzzy Multi-Objective Programming With Joint Probability Distribution 联合概率分布的模糊多目标规划

Multi-Objective Stochastic Programming in Fuzzy Environments Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-8301-1.ch007

{"title":"Fuzzy Multi-Objective Programming With Joint Probability Distribution","authors":"","doi":"10.4018/978-1-5225-8301-1.ch007","DOIUrl":"https://doi.org/10.4018/978-1-5225-8301-1.ch007","url":null,"abstract":"In this chapter, a fuzzy goal programming (FGP) model is employed for solving multi-objective linear programming (MOLP) problem under fuzzy stochastic uncertain environment in which the probabilistic constraints involves fuzzy random variables (FRVs) following joint probability distribution. In the preceding chapters, the authors explain about linear, fractional, quadratic programming models with multiple conflicting objectives under fuzzy stochastic environment. But the chance constraints in these chapters are considered independently. However, in practical situations, the decision makers (DMs) face various uncertainties where the chance constraints occur jointly. By considering the above fact, the authors presented a solution methodology for fuzzy stochastic MOLP (FSMOLP) with joint probabilistic constraint following some continuous probability distributions. Like the other chapters, chance constrained programming (CCP) methodology is adopted for handling probabilistic constraints. But the difference is that in the earlier chapters chance constraints are considered independently, whereas in this chapter all the chance constraints are taken jointly. Then the transformed problem involving possibilistic uncertainty is converted into a comparable deterministic problem by using the method of defuzzification of the fuzzy numbers (FNs). Objectives are now solved independently under the set of modified system constraints to obtain the best solution of each objective. Then the membership function for each objective is constructed, and finally, a fuzzy goal programming (FGP) model is developed for the achievement of the highest membership goals to the extent possible by minimizing group regrets in the decision-making context.","PeriodicalId":404955,"journal":{"name":"Multi-Objective Stochastic Programming in Fuzzy Environments","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133479021","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