Fuzzy Simulation Algorithm Research Articles

Efficient fuzzy simulations for estimating the failure credibility of engineering structures under fuzzy environment

Efficiently and accurately solving the failure credibility of a structural system plays a significant role in the engineering field under fuzzy environment. A more precise failure credibility can help assess the safety degree of the system, and then reduce the occurrence of security accidents. At present, the extended fuzzy first-order and second-moment method (EFFOSM) is effective to analyze failure credibility for some occasions. However, when it comes to complicated performance functions and fuzzy inputs, the accuracy of EFFOSM is greatly reduced and its efficiency also needs to be improved. To overcome the above shortcomings, this paper proposes two types of novel fuzzy simulation algorithms, namely uniform discretization algorithm (UDA) and bisection simulation algorithm (BSA). For the system involving frequently-encountered continuous and strictly monotone performance functions of regular LR fuzzy interval inputs, these two algorithms are designed to estimate failure credibility with higher efficiency and accuracy. Subsequently, with the aid of the linearization and regularization procedures in EFFOSM, the application of UDA and BSA is extended to non-monotone performance functions of irregular LR fuzzy intervals. To evaluate and verify the performance of the proposed two algorithms, their comparisons with EFFOSM are conducted through some numerical examples and practical problems. The results show that the proposed two algorithms outperform EFFOSM in terms of accuracy and efficiency, and also have wider application range for estimating the failure credibility of strictly monotone performance functions involving regular LR fuzzy interval inputs. Meanwhile, BSA is slightly better than UDA for the less runtime.

Optimal Replenishment Policies and Trade Credit for Integrated Inventory Problems in Fuzzy Environment

In this highly volatile, uncertain, complex, and ambiguous (VUCA) environment, a fuzzy inventory optimization problem is a hot topic that received the most attention from both academicians and practitioners. In this paper, the authors have studied the integrated inventory problems under trade credit in fuzzy environments, where the demand rate and deterioration rate are taken here as triangular fuzzy numbers. Accordingly, three types of fuzzy programming models as fuzzy expected cost minimization model, fuzzy α-cost minimization model, and credibility maximization model are built according to different management goals. Since the problem is shown to be NP-hard, this research focuses on proposing a hybrid intelligent algorithm by integrating fuzzy simulation, neural network, and genetic algorithm for solving these models. Then, some numerical examples are presented to illustrate the benefits of the models and evaluate the efficiency of the algorithms. The computational experiments show that the trade credit strategy has a positive impact on improving the supply chain’s performance and reducing its total cost. In addition, the maximum relative error of the objective values is less than 1%, which implies that the hybrid intelligent algorithm is robust to the parameter settings and effective in solving our models. Finally, the practical implications are discussed and useful managerial insights are given.

On Fuzzy Simulations for Expected Values of Functions of Fuzzy Numbers and Intervals

Based on existing fuzzy simulation algorithms, this article presents two innovative techniques for approximating the expected values of fuzzy numbers' monotone functions, which is of utmost importance in fuzzy optimization literature. In this regard, the stochastic discretization algorithm of Liu and Liu (2002) is enhanced by updating the discretization procedure for the simulation of the membership function and the calculation formula for the expected values. This is achieved through initiating a novel uniform sampling process and employing a formula for discrete fuzzy numbers, respectively, as the generated membership function in the stochastic discretization algorithm would adversely affect its accuracy to some extent. What is more, considering that the bisection procedure involved in the numerical integration algorithm of Li (2015) is time-consuming and also, not necessary for the specified types of fuzzy numbers, a special numerical integration algorithm is proposed, which can simplify the simulation procedure by adopting the analytical expressions of α-optimistic values. Subsequently, concerning the extensive applications of regular fuzzy intervals, several theorems are introduced and proved as an extended effort to apply the improved stochastic discretization algorithm and the special numerical integration algorithm to the issues of fuzzy intervals. Throughout this article, a series of numerical experiments are conducted from which the superiority of both the two novel techniques over others are conspicuously displayed in aspects of accuracy, stability, and efficiency.

Safety analysis for the posfust reliability model under possibilistic input and fuzzy state

The structural input can be simply classified as probabilistic one and possibilistic one, and the structural state can be divided into binary state and fuzzy state. Combining different kinds of structural input and state, the reliability analysis model can be sorted into four types, i.e., the one based on probabilistic input and binary state (probist), the one based on probabilistic input and fuzzy state (profust), the one based on possibilistic input and binary state (posbist) and the one based on possibilistic input and fuzzy state (posfust). Various researches about the former three reliability models have been developed, whereas the study on the posfust reliability model is rare. Due to this fact, the fuzzy failure credibility is established to measure the safety degree of the posfust model, and it is a fuzzy safety index defined by the definite integral of the failure membership function. Then, to estimate the defined fuzzy failure credibility efficiently, two adaptive Kriging based methods are proposed. The first one is based on the definition of the fuzzy failure credibility, in which the lower and upper bounds of performance function are mainly concerned by the strategy of constructing the Kriging model. The second one combines the adaptive Kriging and fuzzy simulation algorithm, and it is based on the relationship between the defined fuzzy failure credibility and the failure credibility in the posbist reliability model. Several examples are provided to verify the rationality of the established fuzzy failure credibility, and the efficiency and accuracy of the proposed methods.

Antenna Array Aperture Resource Management of Opportunistic Array Radar for Multiple Target Tracking

In this paper, an antenna array aperture resource management scheme of opportunistic array radar (OAR) based on chance-constraint programming (CCP) is proposed for multiple target tracking (MTT). In the multi-target tracking scenario, multiple beams need to be synthesized to illuminate the targets. According to the predicted distance of targets, the OAR can intelligently segment the antenna array aperture, and select the optimal combination of array elements to synthesize the satisfactory beams with the element-level antenna steering. Owing to the unique array arrangement and work mode of opportunistic array, the element number in working modes is uncertain. To represent the uncertainty, a fuzzy CCP model is introduced. The element number in working modes is viewed as a fuzzy variable. The maximum tracking error, which is denoted by Bayesian Cramer-Rao lower bound(BCRLB), of the targets is regarded as the objective function. The fuzzy simulation algorithm is embedded into genetic algorithm (GA) to compose a hybrid intelligent optimization algorithm to solve the CCP problem. The simulation results verify the validity and practicability of the antenna array aperture resource allocation scheme.

An Integrated Fuzzy Simulation-Optimization Model for Supporting Low Impact Development Design under Uncertainty

Seeking cost-effective design of urban hydrological facilities and drainage systems is an important task for many city planners. However, such a process has always been complicated with intrinsic uncertainties. This work presented an integrated fuzzy simulation-optimization model (FSOM) for supporting Low Impact Development (LID) design under model uncertainties. Various LID implementation schemes involving green roof, bio-retention cell, and permeable pavement were simulated through an urban hydrological model. Three model parameters were assumed as fuzzy sets. In a case study, fuzzy simulation (FS) and genetic algorithm (GA) were employed to search the optimal schemes of LIDs under various confidence levels of satisfying flood control constraints. Comparison of FSOM to traditional deterministic and stochastic models were also carried out. It was shown that FSOM could offer a flexible way of defining and assessing uncertainties associated with hydrological modeling and generate solutions that were comparable to those from either deterministic or stochastic models. However, FSOM also showed limitation of high computational requirement.

A model for project team formation in complex engineering projects under uncertainty

PurposeThis paper aims to develop a model for selecting project team members. In this model, while knowledge sharing among individuals is maximized, the project costs and the workload balance among employees are also optimized.Design/methodology/approachThe problem of project team formation is formulated as a fuzzy multi-objective 0-1 integer programming model. Afterward, to deal with uncertainty in the decision-making on the candidates’ abilities and the project requirements, the fuzzy multi-objective chance-constrained programming approach is adopted. Finally, by combining the non-dominated sorting genetic algorithm II and the fuzzy simulation algorithms, a method is proposed to solve the problem.FindingsThe computational results of the proposed model in a case study of project team formation in a large Iranian company from the shipbuilding industry evidently demonstrated its effectiveness in providing Pareto-optimal solutions for the team composition.Originality/valueSeemingly for the first time, this paper develops a model to optimize knowledge sharing and improve the project efficiency through the selection of appropriate project team members.

Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty

Absolute deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. The existing mean-absolute deviation models are devoted to either stochastic portfolio optimization or fuzzy one. However, practical investment decision problems often involve the mixture of randomness and fuzziness such as stochastic returns with fuzzy information. Thus it is necessary to model portfolio selection problem in such a hybrid uncertain environment. In this paper, we employ random fuzzy variable to describe the stochastic return on individual security with ambiguous information. We first define the absolute deviation of random fuzzy variable and then employ it as risk measure to formulate mean-absolute deviation portfolio optimization models. To find the optimal portfolio, we design random fuzzy simulation and simulation-based genetic algorithm to solve the proposed models. Finally, a numerical example for synthetic data is presented to illustrate the validity of the method.

Fuzzy Multi-objective Expected Value Optimization Models for Locating an Automotive Service Enterprise

Automotive service enterprise location is an interesting and important issue in the logistic field. In practice, some factors of its facility location allocation (FLA) problem, i.e., customer demands, allocations, even locations of customers and facilities, are usually changing, and thus FLA problem features with uncertainty. To account for this uncertainty, some researchers have addressed the fuzzy time and cost issues for locating an automotive service enterprise. However, a decision-maker hopes to minimize the transportation time of customers meanwhile minimizing their transportation cost when locating a facility. Also, they prefer to arrive at the destination within the specific time and cost. To handle this issue via a more practical manner, by taking the vehicle inspection station as a typical automotive service enterprise example, this work presents a fuzzy multi-objective expected value optimization approach to address it. Moreover, some region constraints can greatly influence FLA and travel velocity is also an uncertain variable due to the influence of some unpredictable factors in the location process. To do so, this work builds two practical fuzzy multi-objectives programming models of its location with regional constraints, fuzzy inspection demand, and varying velocity. A hybrid algorithm integrating fuzzy simulation, neural networks (NN), and Genetic Algorithms (GA), namely a random weight based multi-objective NN-GA, is proposed to solve the proposed models. A numerical example is given to illustrate the proposed models and the effectiveness of the proposed algorithm.

Fuzzy multi-objective chance-constrained programming model for hazardous materials transportation

Hazardous materials transportation is an important and hot issue of public safety. Based on the shortest path model, this paper presents a fuzzy multi-objective programming model that minimizes the transportation risk to life, travel time and fuel consumption. First, we present the risk model, travel time model and fuel consumption model. Furthermore, we formulate a chance-constrained programming model within the framework of credibility theory, in which the lengths of arcs in the transportation network are assumed to be fuzzy variables. A hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed for finding a satisfactory solution. Finally, some numerical examples are given to demonstrate the efficiency of the proposed model and algorithm.

3Es System Optimization under Uncertainty Using Hybrid Intelligent Algorithm: A Fuzzy Chance-Constrained Programming Model

Harmonious development of 3Es (economy-energy-environment) system is the key to realize regional sustainable development. The structure and components of 3Es system are analyzed. Based on the analysis of causality diagram, GDP and industrial structure are selected as the target parameters of economy subsystem, energy consumption intensity is selected as the target parameter of energy subsystem, and the emissions of COD, ammonia nitrogen, SO2, andNOXand CO2emission intensity are selected as the target parameters of environment system. Fixed assets investment of three industries, total energy consumption, and investment in environmental pollution control are selected as the decision variables. By regarding the parameters of 3Es system optimization as fuzzy numbers, a fuzzy chance-constrained goal programming (FCCGP) model is constructed, and a hybrid intelligent algorithm including fuzzy simulation and genetic algorithm is proposed for solving it. The results of empirical analysis on Shandong province of China show that the FCCGP model can reflect the inherent relationship and evolution law of 3Es system and provide the effective decision-making support for 3Es system optimization.

A Numerical-Integration-Based Simulation Algorithm for Expected Values of Strictly Monotone Functions of Ordinary Fuzzy Variables

Fuzzy simulation is used to approximate the expected values of functions of fuzzy variables, which plays an important role in the solution algorithms of fuzzy optimization problems. The traditional discretization-based simulation algorithms fail to return a satisfactory approximation within an acceptable computation time, which hinders the applications of fuzzy optimization methods in large-size or even middle-size problems. In this paper, we first prove some equivalent formulas for the expected values of strictly monotone functions of ordinary fuzzy variables. Then, we propose a new fuzzy simulation algorithm based on the numerical integration technique. Finally, we present some numerical examples to make comparisons between the traditional approach and our approach. The results show that our approach has higher performances on the reliability, stability, and computation time.

PSS solution evaluation considering sustainability under hybrid uncertain environments

In order to deal with resource shortage and environmental deterioration, product service system (PSS) are proposed as a sustainable development concept. Careful evaluation in the earlier design stages must be performed before putting a PSS design solution into practice in order to guarantee the sustainability. Due to the reason that sustainability involves many factors and PSS is a complex system with long lifespan, the sustainability criteria will be of great quantity and various measurements. This paper aims to deal with two issues: (1) how to choose the sustainability criteria (2) and how to deal with uncertain factors when measuring these criteria. The zigzag mapping process is adopted to help decision makers to obtain criteria from the customer domain to function domain. The customer domain is modified to include the economic, environmental and social aspects of sustainability. To deal with uncertain factors, the Information Axiom is extended in the hybrid uncertain environments characterized by fuzziness and randomness co-existing. The design range is modeled as a fuzzy variable and the system range is modeled as a random variable. Thus the information content calculating involves integrals with fuzzy boundaries. A fuzzy simulation algorithm is constructed to calculate this kind of integrals. Two case studies are illustrated to highlight the effectiveness and accuracy of the proposed approach. The results show that the proposed method could reflect the judgements of decision makers more precisely, and make use of evaluation information more comprehensively. The results also show that use-oriented PSS is easy to be influenced by the social aspect of sustainability, while product-oriented PSS is easy to be influenced by the economic aspect of sustainability.

Fuzzy cost-profit tradeoff model for locating a vehicle inspection station considering regional constraints

Facility location allocation (FLA) is one of the important issues in the logistics and transportation fields. In practice, since customer demands, allocations, and even locations of customers and facilities are usually changing, the FLA problem features uncertainty. To account for this uncertainty, some researchers have addressed the fuzzy profit and cost issues of FLA. However, a decision-maker needs to reach a specific profit, minimizing the cost to target customers. To handle this issue it is essential to propose an effective fuzzy cost-profit tradeoff approach of FLA. Moreover, some regional constraints can greatly influence FLA. By taking a vehicle inspection station as a typical automotive service enterprise example, and combined with the credibility measure of fuzzy set theory, this work presents new fuzzy cost-profit tradeoff FLA models with regional constraints. A hybrid algorithm integrating fuzzy simulation and genetic algorithms (GA) is proposed to solve the proposed models. Some numerical examples are given to illustrate the proposed models and the effectiveness of the proposed algorithm.

A simulation-based fuzzy possibilistic programming model for coal blending management with consideration of human health risk under uncertainty

In this research, a simulation-based fuzzy possibilistic programming (SFPP) model was advanced through integrating California puff (CALPUFF), fuzzy sets theory and inexact optimization within a general framework. It has advantages in uncertainty reflection, pollutant dispersion modeling, and the management of coal blending and the related human health risks. The developed SFPP model was solved through a direct search approach which coupled fuzzy simulation and Genetic Algorithm (GA). This approach can not only handle a coupled simulation–optimization problem considering uncertainties that can be expressed as fuzzy sets, but also provided the additional information (i.e. possibility of constraint satisfaction) indicating that how likely a decision maker can believe the decision results. It also can reduce the chances of being trapped in local optima as GA converges to global optima. Moreover, the employed direct search method can avoid the approximation error originating from surrogate simulators and enhance the confidence level of the generated optimal solutions. The developed model was applied to the planning of coal blending in Gaojing and Shijingshan power plants in the west of Beijing. The results indicated that the developed SFPP model was useful for generating a series of coal blending schemes under different acceptable possibility levels, ensuring that the risk to human health reduce to an acceptable level, identifying desired coal blending strategies for decision makers, and considering a proper balance between system costs and acceptable possibility levels.

The Minimum Weight Dominating Set Problem under Hybrid Uncertain Environments

The minimum weight dominating set problem (MWDSP) has been a popular research topic in recent years. The weights of vertexes may be considered as cost, time, or opponent’s payoff, which are uncertain in most cases. This paper discusses MWDSP under hybrid uncertain environments where the weights of vertexes are random fuzzy variables. First, random fuzzy theory is introduced to describe these hybrid uncertain variables. Then we propose three decision models based on three different decision criteria to solve MWDSP under hybrid uncertain environments. To solve the proposed models, we present a hybrid intelligent algorithm where random fuzzy simulation and genetic algorithm are embedded. Numerical experiments are performed in the last to show the robustness and effectiveness of the presented hybrid intelligent algorithm.

Fuzzy Chance-Constrained Multiobjective Portfolio Selection Model

This paper addresses the problem of portfolio selection with fuzzy parameters from a perspective of chance-constrained multiobjective programming. The key financial criteria used here are conventional, namely, return, risk, and liquidity; however, we use short- and long-term variants of return rather than a single measure of an investor's expectations in respect thereof. The proposed model aims to achieve the maximal return (short term as well as long term) and liquidity of the portfolio. It does so at a credibility, which is no less than the confidence levels defined by the investor. Further, to capture uncertain behavior of the financial markets more realistically, fuzzy parameters used here are such as those characterized by general functional forms. To solve the problem, we rely on a specially developed algorithm that hybridizes fuzzy simulation and real-coded genetic algorithm. Numerical experiments are included to showcase the applicability and efficiency of the model in a real investment environment.

Determination of target values of engineering characteristics in QFD using a fuzzy chance-constrained modelling approach

Quality function deployment (QFD) is a method used for the manufacturing process of a product or service that is devoted to transforming customer requirements (CRs) into appropriate engineering characteristics (ECs) by specifying the importance of the ECs and then setting their target values. Confronting the inherent vagueness or impreciseness in the QFD process, we embed the fuzzy set theory into QFD. A fuzzy chance-constrained modelling approach with core philosophies of fuzzy expected value model and fuzzy chance-constrained programming is used in this paper. Thus, a novel fuzzy chance-constrained programming model whose objective is to minimize the fuzzy expected cost is proposed to determine the target values of the ECs with risk control to ensure satisfying CRs. Meanwhile, when considering the importance of the ECs, we adopt a more reasonable dispose which is to aggregate the relationships between the CRs and the ECs, and the correlations among the ECs. In order to solve the presented model, a hybrid intelligent algorithm is designed by integrating fuzzy simulation and genetic algorithm. Finally, an example of a motor car design is given to demonstrate the feasibility and effectiveness of the devised modelling approach and algorithm.

Integrated inventory problem under trade credit in fuzzy random environment

This paper is concerned with an integrated inventory problem under trade credit where both the demand rate and deteriorating rate are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The objective of this paper is to determine the optimal inventory policy by optimizing simultaneously the replenishment cycle length and trade credit period. At first, three decision criteria are given: (1) expected value criterion, (2) chance-constrained criterion and (3) chance maximization criterion. Then, after building the fuzzy random models based on the above decision criterion, a hybrid intelligent algorithm by integrating fuzzy random simulation and genetic algorithm is employed to deal with these models. At the end, three numerical examples are given to illustrate the benefits of the models and show the effectiveness of the algorithms.

Transshipment problem with fuzzy customer demands and fuzzy inventory costs

We consider a supply chain consisting of a supplier and locations selling an innovative product. These locations could collaborate together by transshipment which is known as product transferring adopted mainly to reduce inventory costs and to improve customer service level. In this research, we are interested in the transshipment problem where the customer demands, the holding and the shortage costs are uncertain and represented by fuzzy sets. Our objectives are to propose a transshipment policy that takes into account the fuzziness of the mentioned parameters and to derive the approximate replenishment quantities. In order to achieve these objectives, we propose a transshipment decision process considering decision makers attitudes towards risks and a hybrid algorithm based on fuzzy simulation and genetic algorithm designed to determine the approximate replenishment quantities.