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interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期75卷 217-229页

作者： Zhang, Xiaolu Xu, Zeshui Southeast Univ Sch Econ & Management Nanjing 211189 Jiangsu Peoples R China Sichuan Univ Sch Business Chengdu 610065 Sichuan Peoples R China

The aim of this study is to employ the main structure of LINMAP (LINear programming technique for Multidimensional Analysis of Preference) to propose an interval programming method for solving multi-attribute group decision making (MAGDM) problems in which the ratings of alternatives are taken as hesitant fuzzy elements (HFEs) and all pair-wise comparison judgments over alternatives are represented by interval numbers. The contribution of this study is fivefold: (1) we define the new consistency and inconsistency indices;(2) we construct an interval programming model to determine the hesitant fuzzy positive ideal solution and the optimal weights of attributes, and at the same time present a decision algorithm;(3) we discuss several special cases of the proposed model in detail;(4) we show that compared with intuitionistic fuzzy LINMAP method (Li et al., 2010), the proposed approach reveals more useful information including the interval preference information, and does not need to transform HFEs into intuitionistic fuzzy numbers but directly deals with MAGDM problems and thus obtains better final decision results;and (5) we demonstrate the applicability and implementation process of the proposed approach by using an energy project selection example. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Hesitant fuzzy set Multi-attribute group decision making Incomplete preference interval programming

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interval programming for the redundancy allocation with choices of redundancy strategy and component type under uncertainty: Erlang time to failure distribution

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APPLIED MATHEMATICS AND COMPUTATION 2014年第0期244卷 413-421页

作者： Soltani, Roya Sadjadi, Seyed Jafar Tavakkoli-Moghaddam, Reza Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Coll Engn Sch Ind Engn Tehran Iran Univ Tehran Coll Engn Res Inst Energy Management & Planning Tehran Iran Res Ctr Org Proc Improvement Sari Iran

Engineering design problems involve meeting system's performance requirements such as reliability which is in close relation to appropriate selection of components and determination of a system level architecture. In this paper a new nonlinear redundancy allocation model with the choice of redundancy strategy and component types is presented. The redundancy strategies can be in forms of active and cold standby. Also there is a choice for no redundancy strategy. We assume that time to failure follows Erlang distribution which is parameterized in terms of shape and scale parameters which are usually determined deterministically. In this paper we release the deterministic assumption of the scale parameter since in reality the estimation of this parameter accompanies with uncertainty. Also, the cost and weights are not known exactly due to estimation uncertainties and fluctuations. The uncertain proposed model maximizes the system's reliability, which is converted into a deterministic multi-objective model maximizing left bound and center of intervals. Finally, a numerical example is presented to show the performance of the proposed method. (C) 2014 Elsevier Inc. All rights reserved.

关键词： interval programming System engineering Reliability optimization Redundancy allocation Erlang time to failure

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interval programming Model for the Journal Selection Problem

Interval Programming Model for the Journal Selection Problem

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International Conference on Advanced Research on Computer Science and Information Engineering

作者： Zhou, Yueyi Lib Hangzhou Dianzi Univ Hangzhouzhou 310018 Peoples R China

The problem of choosing a set of journals to order or to cancel is significant in applications of operations research to library decision making. This paper describes a zero-one interval linear programming approach th... 详细信息

ISBN: (纸本)9783642214011

关键词： journal selection problem interval programming satisficing solution

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An interval programming method of earth-moon trajectory for manned lunar exploration mission under interval uncertainty

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2024年第11期238卷 1103-1119页

作者： Yang, Luyi Li, Haiyang Zhang, Jin Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha Peoples R China China Astronauts Res & Training Ctr Beijing Peoples R China Hunan Key Lab Intelligent Planning & Simulat Aeros Changsha Peoples R China Natl Univ Def Technol Coll Aerosp Sci & Engn Hunan Key Lab Intelligent Planning & Simulat Aeros 256 Deya Rd Changsha 410073 Hunan Peoples R China

There are always uncertainties in practical engineering, and the design of the optimal Earth-Moon trajectory under uncertainties significantly reduces flight risk for the manned lunar exploration mission (MLEM). This paper proposes an interval programming method to optimize the trans-lunar trajectory under interval uncertainties. Firstly, the influence of the trans-lunar injection uncertainties (TLI) is investigated, finding that the reached orbit at the perilune is very sensitive to the impulse errors at TLI. Then, the design methods of the Earth-Moon trajectory and the trajectory correction maneuver (TCM) are presented. Based on the mathematical tool of the interval possibility degree, the interval programming model is built to transform the uncertain optimization problem into a deterministic one, and then a multi-layer optimization scheme is proposed to solve it. The uncertain objectives and constraints' interval bounds are calculated in the inner loop, and the design variables are searched and optimized in the outer loop. The proposed method is used to design the Earth-Moon trajectories of both manned and unmanned spacecraft. The designed trajectories are insensitive to the uncertainties and are validated by the Monte Carlo simulations.

关键词： manned lunar exploration mission trans-lunar trajectory interval uncertainties interval programming multi-layer optimization scheme

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An interval programming approach for the bilevel linear programming problem under fuzzy random environments

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SOFT COMPUTING 2014年第5期18卷 995-1009页

作者： Ren, Aihong Wang, Yuping Xue, Xingsi Xidian Univ Sch Comp Sci & Technol Xian 710071 Peoples R China

In this paper, we address a class of bilevel linear programming problems with fuzzy random variable coefficients in objective functions. To deal with such problems, we apply an interval programming approach based on the -level set to construct a pair of bilevel mathematical programming models called the best and worst optimal models. Through expectation optimization model, the best and worst optimal problems are transformed into the deterministic problems. By means of the Kth best algorithm, we obtain the best and worst optimal solutions as well as the corresponding range of the objective function values. In this way, more information can be provided to the decision makers under fuzzy random circumstances. Finally, experiments on two examples are carried out, and the comparisons with two existing approaches are made. The results indicate the proposed approaches can get not only the best optimal solution (ideal solution) but also the worst optimal solution, and is more reasonable than the existing approaches which can only get a single solution (ideal solution).

关键词： Bilevel linear programming Fuzzy random variables interval programming Level sets Expectation optimization model

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Pareto approach for DEA cross efficiency evaluation based on interval programming

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017年第4期33卷 2375-2389页

作者： Huang, Yan Wang, Ying-Ming Fuzhou Univ Decis Sci Inst Fuzhou 350116 Fujian Peoples R China Fujian Agr & Forestry Univ Coll Comp & Informat Sci Fuzhou Fujian Peoples R China

Efficiency assessment by using data envelopment analysis (DEA) in interval environment is studied. Two parameters with regard to the input and output are introduced to characterize the variability of the production possibility sets. The extended production facets with different production possibility sets are determined. The inclusion relation between different extended production facets is discussed, and self-evaluation models are constructed to calculate the interval efficiency of the decisionmaking units (DMUs) with the optimal production facet. By setting self-evaluation as a target, the aggressive and benevolent cross-efficiency models are established based on the likelihood between the values of self-evaluation and peer evaluation. The analysis of the models yields the interval cross-efficiency matrices and the weight allocation method that is more advantageous to the DMU for aggregating the interval cross-efficiency matrices. An example is used to illustrate the applications of the models.

关键词： interval programming Pareto optimal DEA cross-efficiency

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Optimal ABC inventory classification using interval programming

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2015年第11期46卷 1944-1952页

作者： Rezaei, Jafar Salimi, Negin Delft Univ Technol Fac Technol Policy & Management Delft Netherlands Eindhoven Univ Technol Fac Ind Engn & Innovat Sci NL-5600 MB Eindhoven Netherlands

Inventory classification is one of the most important activities in inventory management, whereby inventories are classified into three or more classes. Several inventory classifications have been proposed in the literature, almost all of which have two main shortcomings in common. That is, the previous methods mainly rely on an expert opinion to derive the importance of the classification criteria which results in subjective classification, and they need precise item parameters before implementing the classification. While the problem has been predominantly considered as a multi-criteria, we examine the problem from a different perspective, proposing a novel optimisation model for ABC inventory classification in the form of an interval programming problem. The proposed interval programming model has two important features compared to the existing methods: it provides optimal results instead of an expert-based classification and it does not require precise values of item parameters, which are not almost always available before classification. Finally, by illustrating the proposed classification model in the form of numerical example, conclusion and suggestions for future works are presented.

关键词： optimisation ABC inventory classification interval programming

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An interval programming approach for developing economic order quantity model with imprecise exponents and coefficients

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APPLIED MATHEMATICAL MODELLING 2014年第15-16期38卷 3917-3928页

作者： Omrani, Hashem Keshavarz, Mehdi Urmia Univ Technol Dept Ind Engn Orumiyeh Iran

This paper develops an economic order quantity (EOQ) model with uncertain data. For modelling the uncertainty in real-world data, the exponents and coefficients in demand and cost functions are considered as interval data and then, the related model is designed. The proposed model maximises the profit and determines the price, marketing cost and lot sizing with the interval data. Since the model parameters are imprecise, the objective value is imprecise, too. So, the upper and lower bounds are specially formulated for the problem and then, the model is transferred to a geometric program. The resulted geometric program is solved by using the duality approach and the lower and upper bounds are found out for the objective function and variables. Two numerical examples and sensitivity analysis are further used to illustrate the performance of the proposed model. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Lot sizing EOQ interval programming Geometric programming

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An interval programming Approach for Multi-period and Multi-product Aggregate Production Planning by Considering the Decision Maker's Preference

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2018年第3期20卷 1015-1026页

作者： Zhu, Bin Hui, Jizhuang Zhang, Fuqiang He, Li Changan Univ Natl Engn Lab Highway Maintenance Equipment Xian 710064 Shaanxi Peoples R China

This paper presents an interval programming approach for solving a typical multi-period and multi-product aggregate production planning (MPMP-APP) problem. Firstly, a MPMP-APP model based on interval programming is developed, in which the decision maker's risk preference is taken into consideration. Next, to solve the MPMP-APP model based on interval numbers, the original uncertain objective function is replaced by two crisp objective functions which are equivalent to minimizing the interval value and the deviation of the uncertain objective function, respectively, and uncertain constraints are transformed into their corresponding crisp equivalents by using the possibility degree based on six possible relations between two intervals. And then, the linear weighted sum method is adopted to transform the above two-objective model into a single one which can be solved by LINGO software. Finally, an industrial example is used to illustrate the validity and flexibility of the proposed method. It is expected that this study can provide a useful reference for decision makers to make a rational production plan in uncertain environment.

关键词： Production planning Uncertainty modeling interval programming Risk preference

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Optimal design of system reliability using interval programming and genetic algorithms

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COMPUTERS & INDUSTRIAL ENGINEERING 1996年第1-2期31卷 237-240页

作者： Gen, M Cheng, RW Department of Industrial & Systems Engineering Ashikaga Institute of Technology Ashikaga 326 Japan

In this paper, we examine the optimal design problem of system reliability with uncertain coefficients and formulate it as an interval programming model. Genetic algorithms are applied to the problem. The basic idea of the proposed method is first to transform the interval programming model into an equivalent bicriteria programming model and then to find the Pareto solutions of the bicriteria programming problem using genetic algorithms. Numerical examples are given to demonstrate the efficiency of the proposed approach.

关键词： reliability optimization interval programming bicriteria programming and genetic algorithm

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