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2nd International Conference of Mathematical Modelling and Scientific Computation (ICMMSC 2012)

作者： Biswas, Animesh Bose, Koushik Univ Kalyani Dept Math Kalyani 741235 W Bengal India

ISBN: (纸本)9783642289255

This paper presents a fuzzy programming procedure to solve nonlinear fractional programming problems in which the parameters involved in objective function are considered as fuzzy numbers. At first a multiobjective fuzzy nonlinear programming model is constructed by considering the numerator and denominator part, individually, of the fractional objective. Then by using tolerance ranges of the fuzzy parameters, the problem is decomposed and each decomposed objectives is solved independently within the feasible region to find the upper and lower tolerance values of the fuzzy objective goals in the decision making environment. Finally a Taylor's series linear approximation technique is applied to linearize the membership goals and thereby obtaining most satisfactory decision in the decision making arena. A numerical example is solved and the solution is compared with existing approach to establish the efficiency of the proposed methodology.

关键词： Fractional programming Quadratic programming fuzzy programming Triangular fuzzy number fuzzy goal programming Taylor's series approximation

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An enhanced NSGA-II algorithm for fuzzy bi-objective assembly line balancing problems

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 123卷 189-208页

作者： Babazadeh, Hossein Alavidoost, M. H. Zarandi, M. H. Fazel Sayyari, S. T. Univ Sci & Technol Dept Ind Engn Tehran Iran Amirkabir Univ Technol Dept Ind Engn Tehran Iran

Due to immense role of an efficient assembly line in today's manufacturing systems, the consideration of this paper is devoted to address the straight and U-shaped assembly line balancing problems. Assembly Line Balancing Problem (ALBP) considers conflicting objective functions that should be optimized simultaneously subject to set of constraints. To this end, this paper spends endeavor to develop a new fuzzy linear programming model. Having dealt with uncertain nature of the real production system, triangular fuzzy numbers (TFNs) are employed in order to represent uncertainty and vagueness associated with the task processing times. The proposed model can be regarded as a basis of fuzzy programming for further practical development in assembly line problems. To solve the problem, an efficient Multi Objective Genetic Algorithm (MOGA) is proposed. For this purpose, having respected several special characteristics of both fuzzy straight and U-shaped assembly line balancing problems for algorithm segments, including initial generation, encoding and decoding schemes, and GA's operations, an new approach is proposed to promote population diversity and search efficiency. Finally, the proposed algorithm is evaluated though several benchmarks as well as that of exact method. The obtained results proved high efficiency of our method over other approaches suggested in the literature.

关键词： fuzzy programming Multi-objective genetic algorithm Assembly line balancing NSGA-II

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MODELING fuzzy DATA ENVELOPMENT ANALYSIS UNDER ROBUST INPUT AND OUTPUT DATA

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RAIRO-OPERATIONS RESEARCH 2018年第2期52卷 619-643页

作者： Bai, Xuejie Zhang, Feng Liu, Yankui Hebei Agr Univ Coll Sci Baoding 071001 Hebei Peoples R China Hebei Univ Coll Math & Informat Sci Baoding 071002 Hebei Peoples R China Hebei Univ Coll Math & Informat Sci Key Lab Machine Learning & Computat Intelligence Baoding 071002 Peoples R China

This paper offers a fuzzy optimization framework for data envelopment analysis (DEA) to evaluate the relative efficiency of decision making units (DMUs) with parametric interval-valued fuzzy variable-based inputs and outputs. The parametric interval-valued fuzzy variable-based inputs and outputs is employed to capture the uncertainty of data on the basis of professional judgements or empirical estimations. The DEA problem is formulated as fuzzy expectation model with credibility constraints. When the inputs and outputs are mutually independent parametric interval-valued triangular fuzzy variables, we investigate the parametric equivalent representations of expectation objective function and chance constraints. In order to find the optimal solution of our DEA model, a domain decomposition method is proposed. Finally, the numerical example on the sustainable supplier evaluation and selection problem is provided to demonstrate the efficiency of the proposed DEA model and domain decomposition method.

关键词： Data envelopment analysis fuzzy programming parametric interval-valued fuzzy variable lambda selection variable domain decomposition method

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A multi-objective assembly line balancing problem with worker's skill and qualification considerations in fuzzy environment

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APPLIED INTELLIGENCE 2018年第8期48卷 2137-2156页

作者： Salehi, Maryam Maleki, Hamid Reza Niroomand, Sadegh Shiraz Univ Technol Fac Math Shiraz Iran Firouzabad Inst Higher Educ Dept Ind Engn Firouzabad Fars Iran

In this study a new multi-objective assembly line balancing problem is studied. Objectives like the number of stations, the equipment purchasing cost, the worker time dependent wage, and worker dependent dis-quality level of the stations is to be minimized simultaneously with worker allocation and equipment assignment possibilities. The problem also is formulated in a fuzzy environment. To solve such problem, a new hybrid fuzzy interactive approach is proposed in two stages. In the first stage, the fuzzy formulation is converted to a crisp multi-objective formulation using a credibility-based chance constrained programming approach. Then in the second stage, the obtained crisp multi-objective formulation is solved by a new hybrid fuzzy programming approach. To evaluate the proposed approach, two generated examples and a case study from garment production industries are used for computational experiments. The extensive computational study prove the superiority of the proposed approach over the well-known approaches of the literature.

关键词： Assembly line balancing problem Multi-objective optimization fuzzy programming Chance-constrained modeling Case study

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Cost Models and Cost Factors of Road Freight Transportation: A Literature Review and Model Structure

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fuzzy INFORMATION AND ENGINEERING 2019年第3期11卷 257-278页

作者： Izadi, Amir Nabipour, Mohammad Titidezh, Omid Shomal Univ Dept Civil Engn Amol Iran

This paper presents a detailed comparative review of cost models and cost factors published in a number of studies on freight transportation. It attempts to determine and categorise cost factors from a different point of views in the reviewed studies which include cost factors (operational costs, value of time and external costs), study area (Europe, the United States, North America and Asia) and cost models (activity-based costing (ABC), statistical models, surveys, data mining, GIS, meta-analysis and Mathematical models). The results are assessed by comparison with the reviewed studies. The paper also proposed two model structures;(1) Road freight transportation costs (2) Road freight transportation cost estimating methods and data gathering. These models are designed to identify any gaps between the types of cost or any inconsistencies in cost factors and consist of an overall structure and multiple substructures.

关键词： Cost factors cost models fuzzy programming model structure operational costs road freight transportation costs

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Interval Goal programming Approach to Multiobjective fuzzy Goal programming Problem with Interval Weights

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Procedia Technology 2013年 10卷 587-595页

作者： Shyamal Sen Bijay Baran Pal Department of Mathematics B.K.C. College Kolkata-700108 West Bengal India Department of Mathematics University of Kalyani Kalyani-741235 West Bengal India

This article presents interval goal programming (IGP) approach for solving linear multiobjective fuzzy goal programming problem with interval weights. In the proposed approach, interval weights for achievement of fuzzy goals to their aspired levels on the basis of their relative importance are considered in an uncertain environment. In the model formulation of the problem, the membership functions for each of the fuzzy goals are defined first. Then, the membership functions are transformed into membership goals by assigning the highest membership value (unity) and introducing under-and over-deviational variables to each of them. In the solution process, the interval weights (derived from pairwise interval judgment matrix) associated with the unwanted deviational variables is introduced in the goal achievement function for minimizing them to reach the aspired goal levels of the problem. To illustrate the proposed approach, a numerical example is solved.

关键词： Interval arithmetic interval programming pairwise comparison matrix fuzzy programming fuzzy goal programming goal programming

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Models and Algorithm for the Orienteering Problem in a fuzzy Environment

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INTERNATIONAL JOURNAL OF fuzzy SYSTEMS 2018年第3期20卷 861-876页

作者： Ni, Yaodong Chen, Yi Ke, Hua Ralescu, Dan A. Univ Int Business & Econ Sch Informat Technol & Management Beijing 100029 Peoples R China Nanyang Technol Univ Nanyang Business Sch Div Informat Technol & Operat Management Singapore Singapore Tongji Univ Sch Econ & Management Shanghai Peoples R China Univ Cincinnati Dept Math Sci Cincinnati OH USA

The orienteering problem is a classical decision-making problem that can model many applications in logistics, tourism , and several other fields. In the orienteering problem, a graph is given, in which each vertex is associated with a score and the travel time along each edge is provided. The goal of this problem is to find a path that maximizes the sum of the collected scores, such that the total travel time along the path is below a given time limit. In the real world, the scores and the travel time may be uncertain, especially when the historical data are not sufficient. In this paper, we study the orienteering problem in a fuzzy environment and represent the scores and the travel time as fuzzy variables. Based on credibility theory, three fuzzy programming models under different decision criteria are proposed. For cases where the fuzzy variables are of some specific types, crisp equivalents of the models are constructed. In order to solve the proposed models, we design a hybrid intelligent algorithm integrating fuzzy simulation with genetic algorithm. A series of numerical experiments are performed to show the effectiveness and robustness of our hybrid intelligent algorithm.

关键词： fuzzy programming Orienteering problem Credibility theory fuzzy simulation Genetic algorithm

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Use of Nonlinear Membership Functions and the Water Stress Index for the Environmentally Conscious Management of Urban Water Systems: Application to the City of Morelia

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ACS SUSTAINABLE CHEMISTRY & ENGINEERING 2018年第6期6卷 7752-7760页

作者： Medina-Gonzalez, Sergio A. Guadalupe Rojas-Torres, Ma Ponce-Ortega, Jose M. Espuna, Antonio Guillen-Gosalbez, Gonzalo Univ Politecn Cataluna Chem Engn Dept EEBE Av Eduard Maristany 16Edifici 1Planta 6 Barcelona 08019 Spain Univ La Cienega Estado Michoacan de Ocampo Chem Engn Dept Ave Univ 3000 Sahuayo Michoacan Mexico Univ Michoacana Chem Engn Dept Morelia Michoacan 58060 Mexico Imperial Coll London CPSE London SW7 2AZ England

This article proposes a multiobjective optimization strategy based on a fuzzy formulation for the sustainable design and planning of water supply chains in urban areas that considers simultaneously economic and environmental objectives. Harvested rainwater and reclaimed water are considered as alternative sources to reduce freshwater consumption while maximizing water revenues and minimizing land usage. As opposed to other models that attempt to minimize water consumption, this work seeks to minimize the water stress index, which quantifies the impact of freshwater consumption with respect to the specific location where the withdrawals take place. We illustrate the capabilities of this approach through its application to a real case study based on the city of Morelia in Mexico, in which we show that the use of alternative water sources along with an appropriate water distribution plan can reduce the impact over natural reservoirs.

关键词： fuzzy programming Multiobjective optimization Water stress index Cause-effect relationship

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The optimistic-pessimistic revenue distribution in the presence of imprecise data

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OPSEARCH 2018年第2期55卷 288-301页

作者： Lashani, Esfandyar Aryavash, Kourosh Islamic Azad Univ Doroud Branch Dept Math Doroud Iran

In many situations, a common revenue or benefit must be distributed amongst a set of beneficiary decision making units (DMUs) with imprecise data represented by fuzzy or stochastic data. A fair revenue distribution can certainly increase the motivation of DMUs for improving their performances. The share of each DMU must be determined according to its eligibility. To access a fair distribution, we use an optimistic-pessimistic approach of data envelopment analysis which considers both weaknesses and strengths of DMUs. This method determines the share of each DMU according to a combination of its minimum and maximum possible shares which are respectively obtained under the pessimistic and optimistic approaches.

关键词： Data envelopment analysis Optimistic-pessimistic Revenue distribution Chance constrained programming fuzzy programming

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A Penalty Function Based fuzzy Goal programming Procedure for Solving Multiobjective Decision Making Problems

A Penalty Function Based Fuzzy Goal Programming Procedure fo...

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IEEE International Conference on fuzzy Systems

作者： Mousumi Kumar Bijay Baran Pal Department of Mathematics Alipurduar College Department of Mathematics University of Kalyani

ISBN: (纸本)9781479900213

This paper presents how fuzzy penalty functions can be grafted to the fuzzy goal programming formulation of a multiobjective decision making problem for making proper decisions in uncertain environment. In the proposed approach, the fuzzily described objectives are first characterized by the associated membership functions. The membership functions are then transformed into membership goals by assigning the highest degree (unity) as the aspiration level and introducing under- and over-deviational variables to each of them. In the model formulation, the penalty functions in terms of degree of achievement of membership values in different ranges are introduced to the framework of the model for minimizing deviations from the goal levels to the extent possible for arriving at most satisfactory solution in the decision making context. In the solution process, the minsum fuzzy goal programming method is employed to achieve the solution on the basis of relative weights of importance of achieving the aspired goal levels in the decision making horizon. A numerical example is provided to illustrate the efficient use of the approach.

关键词： fuzzy set theory fuzzy programming fuzzy goal programming Goal programming Membership function Penalty function

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