Part family formation for GT applications based on fuzzy mathematics

Group Technology (GT) is one of the key issues in a successful implementation of flexible manufacturing systems ( FMSs). The objective of GT is, through the use of a part-family (PF) formation scheme, to reduce unnecessary variation proliferation. A part family is a group of parts presenting similar geometry and/or requiring a similar production process. Traditional schemes such as classification and coding and production flow analysis do not consider uncertainty or impreciseness in PF formation. In order to incorporate the uncertainty which is inherent in the measurement of similarities between parts, fuzzy mathematics is employed in this research. Two different approaches of fuzzy cluster analysis, fuzzy classification and fuzzy equivalence, are introduced in the process of part-family formation. In addition, a dynamic part-family assignment procedure is presented using the methodology of fuzzy pattern recognition to assign new parts to existing PFs. A computer program is developed, and several rotational parts from a local company have been tested with satisfactory results. In this paper the theoretical foundation is detailed, along with real world examples.     

Evaluating system behavior through Dynamic Master Logic Diagram (DMLD) modeling

In this paper, the Dynamic Master Logic Diagram (DMLD) is introduced for representing full-scale time-dependent behavior and uncertain behavior of complex physical systems. Conceptually, the DMLD allows one to decompose a complex system hierarchically to model and to represent: (1) partial success/failure of the system, (2) full-scale logical, physical and fuzzy connectivity relations, (3) probabilistic, resolutional or linguistic uncertainty, (4) multiple-state system dynamics, and (5) floating threshold and transition effects. To demonstrate the technique, examples of using DMLD to model, to diagnose and to control dynamic behavior of a system are presented. A DMLD-based expert system building tool, called Dynamic Reliability Expert System (DREXs), is introduced to automate the DMLD modeling process.     

Automatic creation of Markov models for reliability assessment of safety instrumented systems

After the release of new international functional safety standards like IEC 61508, people care more for the safety and availability of safety instrumented systems. Markov analysis is a powerful and flexible technique to assess the reliability measurements of safety instrumented systems, but it is fallible and time-consuming to create Markov models manually. This paper presents a new technique to automatically create Markov models for reliability assessment of safety instrumented systems. Many safety related factors, such as failure modes, self-diagnostic, restorations, common cause and voting, are included in Markov models. A framework is generated first based on voting, failure modes and self-diagnostic. Then, repairs and common-cause failures are incorporated into the framework to build a complete Markov model. Eventual simplification of Markov models can be done by state merging. Examples given in this paper show how explosively the size of Markov model increases as the system becomes a little more complicated as well as the advancement of automatic creation of Markov models.     

Uncertainty quantification in dynamic system risk assessment: a new approach with randomness and fuzzy theory

Quantifying uncertainty during risk analysis has become an important part of effective decision-making and health risk assessment. However, most risk assessment studies struggle with uncertainty analysis and yet uncertainty with respect to model parameter values is of primary importance. Capturing uncertainty in risk assessment is vital in order to perform a sound risk analysis. In this paper, an approach to uncertainty analysis based on the fuzzy set theory and the Monte Carlo simulation is proposed. The question then arises as to how these two modes of representation of uncertainty can be combined for the purpose of estimating risk. The proposed method is applied to a propylene oxide polymerisation reactor. It takes into account both stochastic and epistemic uncertainties in the risk calculation. This study explores areas where random and fuzzy logic models may be applied to improve risk assessment in industrial plants with a dynamic system (change over time). It discusses the methodology and the process involved when using random and fuzzy logic systems for risk management.     

Fuzzy Reliability Analysis of the Washing System in a Paper Plant for Components with Different Membership Function

The washing system in paper plant is a complex engineering system that needs to develop effective maintenance programs for enhancing its performance via reliability analysis. The reliability analysis of these systems require precise numerical data which may be very difficult to obtain in desired crisp form due to uncertainty. In general, triangular fuzzy number are used to quantify data uncertainty and fuzzy arithmetic operations are employed which give vide range of prediction for each computed reliability index due to accumulating phenomenon of fuzziness. To reduce the range of prediction of system reliability and fasten the computation process, this paper presents \(T_\omega \) (weakest t-norm) based generalized fuzzy lambda–tau technique in which different fuzzy membership functions are used to quantify uncertainty while \(\alpha \)-cut and \(T_\omega \) based approximate fuzzy arithmetic operations are employed for computation. The advantage of this technique is that this technique uses different fuzzy numbers as input to quantify different types of uncertainties and gives fuzzy reliability indices of the system having shape preserving characteristic, fitter decision values with compressed range of prediction under vague environment which is better for strong decision making to improve system performance. To show the effectiveness of the presented approach, computed results have been compared with results obtained from four other existing approaches. Moreover, this paper uses extended Tanaka et al. (Komal in Ocean Eng 155:278–294, 2018b) approach to rank the critical components of the system. Sensitivity, long run reliability and availability analyses have also been conducted to analyse the impact of variation of different reliability indices and time respectively on system performance.     

Part-period balancing with uncertainty: a fuzzy sets theory approach

The part-period balancing lot-sizing algorithm is modified to use fuzzy data for the single-stage lot-sizing problem. Triangular fuzzy numbers are used to represent uncertainty in the master production schedule. This paper shows that uncertain demand can be easily incorporated into the part-period balancing lot-sizing algorithm and that a fuzzy master production schedule can be used to determine production lot sizes. A detailed example is presented to illustrate the technique.     

A possibilistic programming approach for the location problem of multiple cross-docks and vehicle routing scheduling under uncertainty

This article considers the design of cross-docking systems under uncertainty in a model that consists of two phases: (1) a strategic-based decision-making process for selecting the location of cross-docks to operate, and (2) an operational-based decision-making process for vehicle routing scheduling with multiple cross-docks. This logistic system contains three echelons, namely suppliers, cross-docks and retailers, in an uncertain environment. In the first phase, a new multi-period cross-dock location model is introduced to determine the minimum number of cross-docks among a set of location sites so that each retailer demand should be met. Then, in the second phase, a new vehicle routing scheduling model with multiple cross-docks is formulated in which each vehicle is able to pickup from or deliver to more than one supplier or retailer, and the pickup and delivery routes start and end at the corresponding cross-dock. This article is the first attempt to introduce an integrated model for cross-docking systems design under a fuzzy environment. To solve the presented two-phase mixed-integer programming (MIP) model, a new fuzzy mathematical programming-based possibilistic approach is used. Furthermore, experimental tests are carried out to demonstrate the effectiveness of the presented model. The computational results reveal the applicability and suitability of the developed fuzzy possibilistic two-phase model in a variety of problems in the domain of cross-docking systems.     

Capacity and material requirement planning modelling by comparing deterministic and fuzzy models

A model for the capacity and material requirement planning problem with uncertainty in a multi-product, multi-level and multi-period manufacturing environment is proposed. An optimization model is formulated which takes into account the uncertainty that exists in both the market demand and capacity data, and the uncertain costs for backlog. This work uses the concept of possibilistic programming by comparing trapezoidal fuzzy numbers. Such an approach makes it possible to model the ambiguity in market demand, capacity data, cost information, etc. that could be present in production planning systems. The main goal is to determine the master production schedule, stock levels, backlog, and capacity usage levels over a given planning horizon in such a way as to hedge against the uncertainty. Finally, the fuzzy model and the deterministic model adopted as the basis of this work are compared using real data from an automobile seat manufacturer. The paper concludes that fuzzy numbers could improve the solution of production planning problems.     

Filter allocation and replacement strategies in fluid power system under uncertainty: a fuzzy robust nonlinear programming approach

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.     

Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters

This paper proposes a fuzzy interval perturbation method (FIPM) and a modified fuzzy interval perturbation method (MFIPM) for the hybrid uncertain temperature field prediction involving both interval and fuzzy parameters in material properties and boundary conditions. Interval variables are used to quantify the non‐probabilistic uncertainty with limited information, whereas fuzzy variables are used to represent the uncertainty associated with the expert opinions. The level‐cut method is introduced to decompose the fuzzy parameters into interval variables. FIPM approximates the interval matrix inverse by the first‐order Neumann series, while MFIPM improves the accuracy by considering higher‐order terms of the Neumann series. The membership functions of the interval temperature field are eventually derived using the fuzzy decomposition theorem. Three numerical examples are provided to demonstrate the feasibility and effectiveness of the proposed methods for solving heat conduction problems with hybrid uncertain parameters, pure interval parameters, and pure fuzzy parameters, respectively. Copyright © 2015 John Wiley & Sons, Ltd.     

Hammersley stochastic annealing: efficiency improvement for combinatorial optimization under uncertainty

This paper presents hierarchical improvements to combinatorial stochastic annealing algorithms using a new and efficient sampling technique. The Hammersley Sequence Sampling (HSS) technique is used for updating discrete combinations, reducing the Markov chain length, determining the number of samples automatically, and embedding better confidence intervals of the samples. The improved algorithm, Hammersley stochastic annealing, can significantly improve computational efficiency over traditional stochastic programming methods. This new method can be a useful tool for large-scale combinatorial stochastic programming problems. A real-world case study involving solvent selection under uncertainty illustrates the usefulness of this new algorithm.     

Fuzzy handling of measurement errors in instrumentation

This paper focuses on the use of possibility theory and of fuzzy subset theory to deal with the uncertainty of the measurements handled in instrumentation systems. Methods are described for building fuzzy subsets from numerical data coming from imprecise “physical” sensors on the one hand, and handling approximate estimations provided by “human” sensors on the other hand. The propagation of the fuzzy representation of acquired measures in further treatments, such as those involved in performance indicators aimed at controlling manufacturing production, is also considered     

Reliability analysis of multi‐state series systems with performance sharing mechanism under epistemic uncertainty

For real engineering systems, it is sometimes difficult to obtain sufficient data to estimate the precise values of some parameters in reliability analysis. This kind of uncertainty is called epistemic uncertainty. Because of the epistemic uncertainty, traditional universal generating function (UGF) technique is not appropriate to analyze the reliability of systems with performance sharing mechanism under epistemic uncertainty. This paper proposes a belief UGF (BUGF)‐based method to evaluate the reliability of multi‐state series systems with performance sharing mechanism under epistemic uncertainty. The proposed BUGF‐based reliability analysis method is validated by an illustrative example and compared with the interval UGF (IUGF)‐based methods with interval arithmetic or affine arithmetic. The illustrative example shows that the proposed BUGF‐based method is more efficient than the IUGF‐based methods in the reliability analysis of multi‐state systems (MSSs) with performance sharing mechanism under epistemic uncertainty.     

Fuzzy logic based approach to FRP retrofit of columns

Current design approaches for seismic retrofit use deterministic variables to describe the geometry, material properties and the applied loads on the bridge column. Using a mechanistic model that considers nonlinear material behavior, these deterministic input variables can be directly mapped to the design parameters. However the results often give a false sense of reliability due to neglecting uncertainties related to the input variables of the analysis (data uncertainty), unpredictable fluctuations of loads and natural variability of material properties, and/or the uncertainty in the analytical model itself (model uncertainty). While methods of reliability analysis can provide a means for designing so as not to exceed specific levels of “acceptable” risk, they do not consider the uncertainty in the assumption of distribution functions for each of the input variables and are built on the basic assumption that the models used perfectly describe reality. This, however, still results in significant unknowns and often design models that are not truly validated across their response space. This paper describes the application of a fuzzy probabilistic approach to capture the inherent uncertainty in such applications. The application of the approach is demonstrated through an example and results are compared to those obtained from conventional deterministic analytical models. It is noted that the confidence in the achieved safety of the retrofit system that is based on the use of the fuzzy probabilistic approach is much higher than that achieved using the deterministic approach. This is due to the consideration of uncertainty in the material parameters as well as the consideration of uncertainty in the assumed crack angle during the design process.     

Analysis for fractional‐order predator–prey model with uncertainty

Here, the authors analyse the fractional‐order predator–prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator–prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.Inspec keywords: ecology, fuzzy set theory, predator‐prey systems, approximation theoryOther keywords: ecological model, fractional‐order predator–prey model, ecological systems, approximate solution, higher order term, fractional Euler method, uncertainty initial conditions, fuzzy initial conditions     

Reliability importance analysis of Markovian systems at steady state using perturbation analysis

Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies.     

A fuzzy-logic-based approach to qualitative safety modelling for marine systems

Safety assessment based on conventional tools (e.g. probability risk assessment (PRA)) may not be well suited for dealing with systems having a high level of uncertainty, particularly in the feasibility and concept design stages of a maritime or offshore system. By contrast, a safety model using fuzzy logic approach employing fuzzy IF–THEN rules can model the qualitative aspects of human knowledge and reasoning processes without employing precise quantitative analyses. A fuzzy-logic-based approach may be more appropriately used to carry out risk analysis in the initial design stages. This provides a tool for working directly with the linguistic terms commonly used in carrying out safety assessment. This research focuses on the development and representation of linguistic variables to model risk levels subjectively. These variables are then quantified using fuzzy sets. In this paper, the development of a safety model using fuzzy logic approach for modelling various design variables for maritime and offshore safety based decision making in the concept design stage is presented. An example is used to illustrate the proposed approach.     

Representing imprecision in engineering design: Comparing fuzzy and probability calculus

A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [25]. An analogous approach to representing and manipulatinguncertainty in choosing among alternatives (design imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. Examples using both approaches are presented, where the examples represent a progression from simple operations to more complex design equations. Results of the fuzzy sets and probability methods for the examples are shown graphically. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty in design, and that probability is best used to represent stochastic uncertainty.     

基于Markov随机场的区域跟踪算法

由于视频序列的对象跟踪相当于把图像帧分割成跟踪与非跟踪两个不重叠区域,为此,引入图像分割算法中的Markov随机场模型,提出了一种多目标模糊规划求取Markov标记场的最优估计来实现区域跟踪的算法。此算法为了克服传统离散Markov随机场运算速度慢的缺点,利用双随机矢量,建立连续的Markov标记场,同时提取区域视觉和运动信息的模糊特征,从而改善了算法的鲁棒性和运算复杂度。最终实验结果表明,此方法不仅跟踪效果好,而且还有运算速度快、抗干扰能力强等特点。     

A fuzzy technique for supply chain network design with quantity discounts

This paper proposes a hierarchical technique for Supply Chain Network (SCN) efficiency maximisation under uncertainty composed of three steps. The first step extends a previous fuzzy cross-efficiency Data Envelopment Analysis approach, originally intended for suppliers’ selection, in order to evaluate and rank all the actors in each SCN stage under conflicting nondeterministic criteria. Afterwards, a fuzzy linear integer programming model is stated and solved for each pair of subsequent SCN stages to determine the quantities required from each stakeholder to maximise the overall SCN efficiency while satisfying the estimated demand and respecting the nodes capacity. Finally, a heuristics is applied to limit the exchange of small quantities in the SCN, in which the trade is not economically convenient according to quantity discounts. An illustrative example from the literature shows the technique effectiveness.