Fuzzy Stochastic Linear Programming Research Articles

Optimal Modeling of Sustainable Land Use Planning under Uncertain at a Watershed Level: Interval Stochastic Fuzzy Linear Programming with Chance Constraints

In this paper, an uncertain interval stochastic fuzzy chance constraint land use optimal allocation method is proposed and applied to solve the problem of land use planning in river basins. The UISFCL-LUP method is an aggregation of interval parametric programming, fuzzy linear programming and chance constraint programming which can cope with uncertain problems such as interval value, fuzzy set and probability. In this paper, the uncertain mathematical method is explored and studied in the optimal allocation of land use in the next two planning periods of Nansihu Lake Basin in China. Moreover, it was proved that ISFCL-LUP can deal with the uncertainty of interval, membership function and probability representation and can also be used to solve the land use planning and land use strategy analysis under uncertain conditions. On the basis of model calculations, we obtained the optimal allocation results for six types of land use in four regions over two planning periods based on different environmental constraints. The results show that the optimized λ value (that is, the degree of satisfaction with all the model conditions) is in the range of [0.54, 0.79] and the corresponding system benefits are between [18.4, 20.4] × 1012 RMB and [96.7, 109.3] × 1012 RMB. The results indicate that land managers can make judgments based on the different socio-economic development needs of different regions and determine strategic land use allocation plans under uncertain conditions. At the same time, the model obtained interval solutions under different system satisfaction and constraint violation probabilities, which helps land managers to analyze the importance of land system optimization and sustainable development more deeply.

WEIGHTED ADDITIVE MODEL AND CHANCE CONSTRAINED TECHNIQUE FOR SOLVING NONSYMMETRICAL STOCHASTIC FUZZY MULTIOBJECTIVE LINEAR PROGRAM

The problems of linear programming are developing from time to time, and its complexity is constantly growing. Various problems can be viewed as a multi-objective fuzzy linear programming, multi-objective stochastic linear programming or a combination of both. This research is focused on examining Multi-Objective Fuzzy Stochastic Linear Programming (MOFSLP) with each of the objective functions has a different level of importance to decision makers, or better known as the nonsymmetrical model. The objective function of the linear program contains fuzzy parameters, while the constraint function contains the fuzzy parameters and random variables. The purpose of this study is to develop an algorithm to transform the MOFSLP be a Program of linear Single-Objective Deterministic Linear Programming (SODLP) so that it can be solved using simplex method. In the process of transforming MOFSLP to SODLP, several approaches have been used. They are; weighted additive model, analytic hierarchy process and chance constrained technique. An example of numerical computations has been provided at the end of the discussion in order to illustrate how the algorithm works. The resulted Model and algorithm are expected to help companies in the decision making process.

A faucet closed-loop supply chain network design considering used faucet exchange plan

Abstract Many companies established a closed-loop supply chain to increase their supply chain profit and sustainability. The goal of this study is to design a faucet closed-loop supply chain network, in which forward supply chain is explained is aimed to increase the profit and environmental savings, and used faucet exchange plan is presented in the reverse chain. A mixed integer linear programming model under demand uncertainty is developed. A single-objective, multi-product and multi-period model is proposed for this network. The objective function maximizes the total profit along with optimization of the flow within facilities. Moreover, a fuzzy linear programming and fuzzy stochastic linear programming model describes the proposed network's decisions. Finally, to validate the proposed model, a real case study is performed on Tehrandoosh Company and the model solutions are analyzed. The obtained results show the performance of the presented network. In which, considering the exchange plan would lead to 58 percent increase in the total profit of the supply chain. Furthermore, this study provided efficient and reliable managerial solutions for the faucet industry decision makers.

An interval type-2 fuzzy stochastic approach for regional-scale electric power system under parameter uncertainty

ABSTRACTIn this study, an interval type-2 fuzzy stochastic linear programming method (IT2FSLP) is developed to support regional-scale electric power system (REM) planning. The IT2FSLP-REM model is based on an integration of interval type-2 fuzzy sets boundary programming and stochastic linear programming techniques enable it to have robust abilities to the deal with uncertainties expressed as type-2 fuzzy intervals and probabilistic distributions within a general optimization framework. Moreover, it can reflect dynamic decisions for energy supply and energy conversion processes, as well as provide capacity expansion options with multiple periods. The developed model is applied to a case of planning regional-scale energy and environmental systems to demonstrate its applicability. Based on a two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs among economic cost, environmental requirements, and energy-supply security. Thus, the lower and upper solutions of IT2FSLP-REM would then help energy authorities adjust or justify allocation patterns of regional energy resources and services.

Inexact rough-interval type-2 fuzzy stochastic optimization model supporting municipal solid waste management under uncertainty

ABSTRACTIn this study, an inexact rough-interval type-2 fuzzy stochastic linear programming (IRIT2FSLP) approach is developed for addressing uncertainties presented as rough-interval, type-2 fuzzy and random variables. The proposed method is applied to the case of a long-term municipal solid waste management system. The IRIT2FSLP approach is an extension of the inexact interval linear programming for handling nonlinear stochastic optimization problems where rough-interval and type-2 fuzzy parameters are integrated into a general framework. The results indicate that IRIT2FSLP normally leads to rough-interval solutions. Comparisons of the proposed model with scenarios without rough-interval and type-2 fuzzy parameters are also conducted. The results indicate the significant impact of dual-uncertain information on the system, which implies the reliability of IRIT2FSLP in handling waste flow allocation.

Fuzzy stochastic linear programming-based approach for multiple departures single destination multiple travelling salesman problem

The multiple departures single destination multiple travelling salesmen problem (MDmTSP) is a problem in which two or more salesmen start from any node of departure and finish their tour by reaching a single specific destination node. In many real-life problems, the decision should be made according to information which is both possibilistically imprecise and probabilistically uncertain. Although consistency indexes provide a union nexus between possibilistic and probabilistic representation of uncertainty, there are no reliable transformations between them. A means to this end is fuzzy stochastic linear programming. In this paper, a realistic environment for MDmTSP with fuzzy stochastic distance between nodes is investigated. To justify the proposed approach and to illustrate its efficiency in real-life problems, a case of employees’ bus transport routing problem (EBTRP) is presented.

An approach for linear programming under randomness and fuzziness: a case of discrete random variables with fuzzy probabilities

This paper presents a new approach for solving stochastic fuzzy linear programming problems. The random variables in the constraints and in the objective function are discrete with triangular fuzzy probabilities. The D-cut method is applied to the triangular membership functions of the fuzzy probabilities. For the constraints, the chance-constrained approach is utilised, whether according to strict dominance relation or dominance relation. The mean-variance criterion is exploited in the objective function, whereas four different cases are considered. The model, for the general case, which takes the form of mixed zero-one non-linear programme, is illustrated by a numerical example.

A semi-infinite analysis-based inexact two-stage stochastic fuzzy linear programming approach for water resources management

A semi-infinite analysis-based inexact two-stage stochastic fuzzy linear programming approach is proposed for water resources management problems. Semi-infinite analysis is incorporated into the modelling framework to handle infinite α -cuts to the membership functions of fuzzy parameters. Compared to the existing methods in which only limited α -cuts are divided under an assumption that these could represent all fuzzy information of the function, the proposed approach could be more reliable in terms of full consideration of fuzzy membership functions. The obtained optimal results from this approach present robustness according to a case study. By assigning different confidence levels, five groups of optimal solutions are obtained. It is indicated that higher confidence levels would relate to more reliable allocation strategies, as well as higher and more stable system benefits. However, with the increases in violation risks, the intervals of the optimal system benefit become wider, reflecting the impact of high risks combined with high benefits.

Solving linear programming problems under fuzziness and randomness environment using attainment values

In this paper, the author presents a model to measure attainment values of fuzzy numbers/fuzzy stochastic variables. These new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem. Numerical comparisons are provided to illustrate the effectiveness of the proposed method.

Fuzzy stochastic linear programming: Survey and future research directions

In many real-life problems one has to base decision on information which is both fuzzily imprecise and probabilistically uncertain. Although consistency indexes providing a union nexus between possibilistic and probabilistic representation of uncertainty exist, there are no reliable transformations between them. This calls for new paradigms for incorporating the two kinds of uncertainty into mathematical models. Fuzzy stochastic linear programming is an attempt to fulfill this need. It deals with modelling and problem solving issues related to situations where randomness and fuzziness co-occur in a linear programming framework. In this paper we provide a survey of the essential elements, methods and algorithms for this class of linear programming problems along with promising research directions. Being a survey, the paper includes many references to both give due credit to results in the field and to help readers obtain more detailed information on issues of interest.

A suggested approach for possibility and necessity dominance indices in stochastic fuzzy linear programming

This paper presents a suggested approach for solving a stochastic fuzzy linear programming problem. This approach utilizes two possibility and two necessity dominance indices that have been introduced by Dubois and Prade [D. Dubois, H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information Sciences 30 (1983) 183–224]. The chance-constrained approach and the α -cut are used to transform the stochastic fuzzy problem to its deterministic-crisp equivalent, according to each of the four dominance indices. A numerical example is given.

Using different dominance criteria in stochastic fuzzy linear multiobjective programming: A case of fuzzy weighted objective function

In this paper, a stochastic fuzzy linear multiobjective programming problem is introduced and transformed to a stochastic fuzzy linear programming problem by utilizing a suggested approach of weighted objective function. In each objective, the given weight as well as the coefficients are considered fuzzy numbers with similar or different types. In each constraint, the right-hand side is a random variable with known distribution function while both the left-hand side coefficients and the tolerance measures are considered fuzzy numbers with similar or different types. Also, all random variables are considered independent. Therefore, the chance-constrained approach with different dominance criteria is used to transform the stochastic fuzzy linear multiobjective programming problem to its equivalent deterministic-crisp linear programming problem. A comparison between different dominance criteria is illustrated by a numerical example.

Linear programming under randomness and fuzziness

This paper is concerned with the use of fuzzy sets theory, well suited for nuanced human behavior, to extend the applicability of linear programming in a way to let both randomness and fuzziness uncertainties be taken into account. A fuzzy stochastic linear programming problem is considered and ways to handle it suggested. The basic idea behind our approaches is to translate the original problem in deterministic terms via tools provided by fuzzy sets theory to get a classical one. Some conditions for the resulting problems to be solved without extra computational effort are stressed and illustrative examples given.