Fuzzy Stochastic Research Articles

Discrete-Time Finite Fuzzy Markov Chains Realized Through Supervised Learning Stochastic Fuzzy Discrete Event Systems

Discrete-Time Finite Fuzzy Markov Chains Realized Through Supervised Learning Stochastic Fuzzy Discrete Event Systems

A Novel Approach for Efficiency Evaluation in Data Envelopment Analysis Framework with Fuzzy Stochastic Variables

A Novel Approach for Efficiency Evaluation in Data Envelopment Analysis Framework with Fuzzy Stochastic Variables

Fault Tolerant Control of Fuzzy Stochastic Distribution Systems With Packet Dropout and Time Delay

The fault diagnosis (FD) and fault tolerant control (FTC) problem of the fuzzy stochastic distribution system (SDS) over packet dropout and time delay is studied. Firstly, the static model of linear fuzzy logic system that approximates the output PDF and the dynamic model with the multiplicative fault in a fuzzy system are established. The random packet dropout and time delay caused by the network are described in a unified framework, in which the lost data is compensated with the latest data received by the buffer. On this basis, an adaptive observer is devised to estimate the unknown multiplicative fault. The design of sliding mode predictive fault tolerant controller is discussed to ensure that the system still has good tracking performance after the fault occurs. Numerical simulations on a molecular weight distribution control system are supplied to prove the effectiveness of the presented scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to improve the reliability of the fuzzy stochastic distribution system with packet dropout and time delay. This kind of stochastic distribution systems is described by the relationship between the input and the output PDF rather than the normal relationship between the input and the output. When the multiplicative fault occurs in the system, the design of fault diagnosis strategy and fault-tolerant controller becomes an important challenge, especially when the system is subject to packet dropout and time delay. To address the above problems, a new fault diagnosis and fault-tolerant control scheme is proposed, which can accurately estimate the time and size of the fault and obtain the satisfactory fault-tolerant control effect.

Almost automorphic behaviours of nonlocal stochastic fuzzy Cohen–Grossberg lattice neural networks

Discrete-time Cohen–Grossberg neural networks (CGNNs) play important role in feedback neural networks. The existing literatures of CGNNs only regarded integral order discrete-time models without other variables. This paper builds the lattice model for nonlocal stochastic fuzzy CGNNs with reaction diffusions by employing the finite difference and Mittag–Leffler time Euler difference techniques. Further, the existence of a unique bounded almost automorphic sequence solution in distribution and global exponential convergence in the mean-square sense to the achieved difference model are investigated. At last, by using the tool of Matlab and time Euler difference for the Brownian motions, an illustrative example with simulations is used to show the feasible of the works of the current paper. We think that this work can contribute to achieve some effective real tasks, e.g. content-addressable memory, auto-association, dynamic reconstruction of a chaotic process, etc.

A Novel Approach to Solve Multi-objective Fuzzy Stochastic Bilevel Programming Using Genetic Algorithm

A Novel Approach to Solve Multi-objective Fuzzy Stochastic Bilevel Programming Using Genetic Algorithm

Asynchronous Parallel Fuzzy Stochastic Gradient Descent for High-Dimensional Incomplete Data Representation

Asynchronous Parallel Fuzzy Stochastic Gradient Descent for High-Dimensional Incomplete Data Representation

Stochastic Fuzzy Discrete Event Systems and Their Model Identification.

We introduce a new class of fuzzy discrete event systems (FDESs) called stochastic FDESs (SFDESs), which is significantly different from the probabilistic FDESs (PFDESs) in the literature. It offers an effective modeling framework for applications that are unsuitable for the PFDES framework. An SFDES is comprised of multiple fuzzy automata that occur randomly one at time with different occurrence probabilities. It uses either the max-product fuzzy inference or the max-min fuzzy inference. This article focuses on single-event SFDES-each of the fuzzy automata of such an SFDES has one event. Assuming nothing is known about an SFDES, we develop an innovative technique capable of determining number of fuzzy automata and their event transition matrices as well as estimating their occurrence probabilities. The technique, called prerequired-pre-event-state-based technique, creates and uses merely N particular pre-event state vectors of dimension N to identify event transition matrices of M fuzzy automata, involving a total of MN2 unknown parameters. One necessary and sufficient condition and three sufficient conditions are established for the identification of SFDES with different settings. The technique does not have any adjustable parameter or hyperparameter to set. A numerical example is provided to concretely illustrate the technique.

Identification of Multievent Stochastic Fuzzy Discrete Event Systems.

We recently introduced a novel category of fuzzy discrete event systems (FDESs) termed stochastic FDESs (SFDESs), wherein multiple fuzzy automata occur randomly with different probabilities. We also developed two techniques for identifying event transition matrices in single-event SFDES employing the max-product fuzzy inference. One of them, named the equation-systems-based technique, focuses on the single-event SFDES identification, where the fuzzy automaton of each FDES has only one event. Expanding on our research, this article delves into multievent SFDES identification, allowing each FDES to encompass a sequence of events. This is a new research direction that has not been mentioned in the literature before. Upon activation of an FDES, all its events occur sequentially. Our mathematical proof first establishes the associativity of the max-product inference operation, leading to the introduction of a pivotal and novel concept called an equivalent overall event transition matrix for a consecutive event sequence. This concept establishes a theoretical framework for utilizing the equation-systems-based technique in a novel three-step method for identifying multievent SFDESs. The technique is employed in the first two steps to: 1) determine the number of fuzzy automata in an SFDES and 2) calculate their occurrence frequencies. In the third step, multievent transition matrices of the SFDES are learned by using the stochastic-gradient-descent-based algorithms that we previously developed for multievent FDESs, provided the numbers of consecutive events for each fuzzy automaton within the SFDES are known. Theoretical analysis reveals, for the first time, the interconnections between the event transition matrices learned by the algorithms, the equivalent overall event transition matrices derived from these matrices, and the target event transition matrices. To illustrate our findings, we present an informative example.

Multi-Segments Stochastic Fuzzy Goal Programming: A Novel Paradigm for Multi-Objective Transport Optimization

Multi-Segments Stochastic Fuzzy Goal Programming: A Novel Paradigm for Multi-Objective Transport Optimization

Existence and Uniqueness Theorem of Fuzzy Stochastic Ordinary Differential Equations

A fuzzy valued diffusion term, which in a fuzzy stochastic differential equation refers to one-dimensional Brownian motion, is defined by the meaning of the stochastic integral of a fuzzy process. In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.

A New Fuzzy Stochastic Integrated Model for Evaluation and Selection of Suppliers

In light of the rapid rate of change and unforeseen occurrences seen in the realms of technology, market dynamics, and the wider business landscape, there is a growing need for the inclusion of uncertainty and risk factors in the realm of supply chain planning. Supplier evaluation and selection (SES) is a major strategic decision area where the impact of uncertainty and risk can be more proactively dealt with. A review of extant literature reveals that there is a strong need for developing practitioner-oriented and more comprehensive frameworks and models to mitigate both the capability- and performance-related risks, in the context of SES decisions. This paper presents an integrated model to support SES decisions involving quantity discounts and multiple planning periods under stochastic conditions. The proposed model employs the Fuzzy Analytical Hierarchy Process (FAHP), Fuzzy Evaluation Based on Distance from Average Solution EDAS (EDAS-F), and fuzzy stochastic goal programming (FSGP) to effectively address the above requirements. A case study from a garment manufacturing industry is used to demonstrate the efficacy of the proposed model. The findings of the study provide confirmation that the suggested FSIM has the ability to provide substantial advantages in the context of making choices related to quantity discounts in SES. The proposed FSIM model incorporates the use of FAHP and EDAS-F techniques to effectively reduce the number of suppliers to a manageable level, taking into consideration capability-based risks. Additionally, fuzzy stochastic goal programming (FSGP) is employed to mitigate performance-based risks, enabling the selection of suppliers and the allocation of orders among them. The paper contributes to the literature by proposing a comprehensive framework to solve the SES problem, considering certain practical situations faced by organizations.

Green Reverse Supply Chain Models with Fuzzy Stochastic Re-manufacturing Capacity

Green Reverse Supply Chain Models with Fuzzy Stochastic Re-manufacturing Capacity

Opportunistic maintenance optimization of continuous process manufacturing systems considering imperfect maintenance with epistemic uncertainty

Due to the production process for continuous process manufacturing system (CPMS) cannot be stopped, the “opportunities” for maintenance can only occur within the specified time intervals. To improve the completion rate of production process, the focus of opportunistic maintenance for CPMS is whether the maintenance is to be performed at known time. Meanwhile, several opportunistic maintenance optimization models assumed imperfect maintenance to develop more reasonable maintenance plan. However, the parameters of imperfect maintenance cannot be accurately assessed (namely epistemic uncertainty) due to inadequate knowledge of maintenance and degradation mechanisms. This epistemic uncertainty was ignored in previous studies. Therefore, a novel opportunistic maintenance optimization model for CPMSs is proposed. The opportunity time window (OTW) concept is introduced to constrain the production-constrained maintenance opportunity. Three types of maintenance actions, including do nothing, perfect maintenance, and imperfect maintenance with epistemic uncertainty, are considered during the OTW to improve the production efficiency and performance of the manufacturing system. In the context of random and epistemic uncertainty, a stochastic fuzzy flow manufacturing network (SFFMN) is established to describe dynamic production processes and evaluate machine reliability. Moreover, a simulated annealing-based adaptive immune algorithm (SAAIA) with multiple immune operators is developed to address the opportunity maintenance optimization model of CPMSs. Finally, a case study of the hot rolling manufacturing system is provided to better understand the proposed method and demonstrate its effectiveness.

Symmetric Fuzzy Stochastic Differential Equations Driven by Fractional Brownian Motion

We consider symmetric fuzzy stochastic differential equations where diffusion and drift terms arise in a symmetric way at both sides of the equations and diffusion parts are driven by fractional Brownian motions. Such equations can be used in real-life hybrid systems, which include properties of being both random and fuzzy and reflecting long-range dependence. By imposing on the mappings occurring in the equation the conditions of Lipschitzian continuity and additional constraints by an integrable stochastic process, we construct an approximation sequence of fuzzy stochastic processes and apply this to prove the existence of a unique solution to the studied equation. Finally, a model from population dynamics is considered to illustrate the potential application of our equations.

A data-driven model for sustainable and resilient supplier selection and order allocation problem in a responsive supply chain: A case study of healthcare system

This research attempts to study the Supplier Selection and Order Allocation Problem (SSOAP) considering three crucial concepts, namely responsiveness, sustainability, and resilience. To do so, the current research develops a Multi-Stage Decision-Making Framework (MSDMF) to select potential suppliers and determine the quantity of orders. The first stage aims at computing the scores of the suppliers based on several indicators. To do this, a novel decision-making approach named the Stochastic Fuzzy Best–Worst Method (SFBWM) is developed. Then, in the second stage, a Multi-Objective Model (MOM) is suggested to deal with supplier selection and order allocation decisions. In the next step, a data-driven Fuzzy Robust Stochastic (FRS) optimization approach, based on the fuzzy robust stochastic method and the Seasonal Autoregressive Integrated Moving Average (SARIMA) methods, is employed to efficiently treat the hybrid uncertainty of the problem. Afterwards, a novel solution method named the developed Chebyshev Multi-Choice Goal Programming with Utility Function (CMCGP-UF) is developed to obtain the optimal solution. Moreover, given the crucial role of the Medical Equipment (ME) industry in society’s health, especially during the recent Coronavirus disease, this important industry is taken into account. The outcomes of the first stage demonstrate that agility, cost, GHG emission, quality, robustness, and Waste Management (WM), respectively, are the most important criteria. The outcomes of the second stage determine the selected suppliers, utilized transportation systems, and established sites. It is also revealed that demand directly affects all the objective functions while increasing the rate of disruptions has a negative effect on the sustainability measures.

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.

Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

Type-2 Fuzzy Stochastic Transportation Problem with Gamma Distribution

A novel stochastic fuzzy decision model for agile and sustainable global manufacturing outsourcing partner selection in footwear industry

PurposeThe decision-making to outsource and select the most suitable global manufacturing outsourcing partner (MOP) is complex and uncertain due to multiple conflicting qualitative and quantitative criteria as well as multiple alternatives. Vagueness and variability exist in ratings of criteria and alternatives by group of decision-makers (DMs). The paper provides a novel Stochastic Fuzzy (SF) method for evaluation and selection of agile and sustainable global MOP in uncertain and volatile business environment.Design/methodology/approachFour main selection criteria for global MOP selection were identified such as economic, agile, environmental and social criteria. Total 16 sub-criteria were selected. To consider the vagueness and variability in ratings by group of DMs, SF method using t-distribution or z-distribution was adopted. The criteria weights were determined using the Stochastic Fuzzy-CRiteria Importance Through Intercriteria Correlation (SF-CRITIC), while MOP selection was carried out using Stochastic Fuzzy-VIseKriterijumskaOptimizacija I KompromisnoResenje (SF-VIKOR) in the case study of footwear industry. Sensitivity analysis was performed to test the robustness of the proposed model. A comparative analysis of SF-VIKOR and VIKOR was made.FindingsThe worker’s wages and welfare, product price, product quality, green manufacturing process and collaboration with partners are the most important criteria for MOP selection. The MOP3 was found to be the best agile and sustainable global MOP for the footwear company. In sensitivity analysis, significance level is found to have important role in MOP ranking. Hence, the study concluded that integrated SF-CRITIC and SF-VIKOR is an improved method for MOP selection problem.Research limitations/implicationsIn a group decision-making, ambiguity, impreciseness and variability are found in relative ratings. Fuzzy variant Multi-Criteria Decision-Making methods cover impreciseness in ratings but not the variability. On the other hand, deterministic models do not cover either. Hence, the stochastic method based on the probability theory combining fuzzy theory is proposed to deal with decision-making problems in imprecise and uncertain environments. Most notably, the proposed model has novelty as it captures and reveals both the stochastic perspective and the fuzziness perspective in rating by group of DMs.Practical implicationsThe proposed multi-criteria group decision-making model contributes to the sustainable and agile footwear supply chain management and will help the policymakers in selecting the best global MOP.Originality/valueTo the best of the authors’ knowledge, SF method has not been used to select MOP in the existing literature. For the first time, integrated SF-CRITIC and SF-VIKOR method were applied to select the best agile and sustainable MOP under uncertainty. Unlike other studies, this study considered agile criteria along with triple bottom line sustainable criteria for MOP selection. The novel method of SF assessment contributes to the literature and put forward the managerial implication for improving agility and sustainability of global manufacturing outsourcing in footwear industry.

A novel stochastic fuzzy decision model for optimizing decision-making in the manufacturing industry

In unpredictable and imprecise production environments, this research introduces a stochastic fuzzy decision model for the manufacturing industry. Decision-makers can use the stochastic and fuzzy logic model to capture uncertainties, variability, and language representations of industrial factors. The choice problem, fuzzy input variables, and crisp outcome variables are identified to start the research. Linguistic terms related with fuzzy input variables are represented by fuzzy sets and membership functions. Fuzzy rules link fuzzy input variables to crisp output variables based on expert knowledge or historical data. Objective function, restrictions, and fuzzy rules are incorporated into the stochastic fuzzy decision model's mathematical formulation. Decision-makers can maximize outcomes by considering stochastic factors and fuzzy logic with the model. The model uses an optimization technique to find the optimal choice variable values. A numerical example of manufacturing production planning illustrates the model's use. The results show that the stochastic fuzzy decision model may minimize production costs by calculating optimal production quantities depending on demand. The research concludes that the proposed approach helps manufacturing companies make decisions. Decision-makers can use the model to make educated judgments despite uncertainties and inaccurate information. Future study will explore additional aspects and integrate the model into decision support systems or industrial software. In dynamic and uncertain manufacturing contexts, the stochastic fuzzy decision model empowers manufacturing decision-makers to make optimal decisions

A Two-Stage Stochastic Fuzzy Mixed-Integer Linear Programming Approach for Water Resource Allocation under Uncertainty in Ajabshir Qaleh Chay Dam

Due to the dry climate and unsuitable distribution of rainfall in Iran, sustainable agriculture depends on the proper use of water resources. In this study, the optimal allocation of water at Ajabshir Qaleh Chay Dam in agricultural sector is investigated using an interval parameter two-stage stochastic mixed-integer linear programming approach. Indeed, interval parameters two-stage stochastic programming (ITSP) with fuzzy variables is developed based on mixed-integer programming for a water resource allocation model to retrieve the water shortage of agricultural products and to achieve the optimal allocation of Ajabshir Qaleh Chay Dam water through its river canals between different products under uncertainty conditions. In this developed method, called extended ITSP (EITSP), a number of alternatives are used to compensate for the difference between the amount of promised water allocation targets and the actual allocated water in the optimal allocation of water. Then a new solving approach based on Huang Algorithm, fuzzy chance constrained programming and Zimmermann fuzzy programming will be presented to solve the problems. Furthermore, using a case study in this dam, the results are obtained for the developed approaches to clarify the described methods and to compare these results with each other. Finally, comparing the total system profits of the models shows that in the fuzzy model, the profit and system certainty increase simultaneously. Therefore, due to the lack of water resources in the agricultural sector and the uncertainty, the agricultural authorities of Ajabshir can decrease the unsustainability of water resources using the optimal model while increasing the cost-effectiveness of the farmers.