Fuzzy Stochastic Research Articles

A New Method for Solving Dual DEA Problems with Fuzzy Stochastic Data

Data envelopment analysis (DEA) is a widely used mathematical programming technique for measuring the relative efficiency of decision-making units which consume multiple inputs to produce multiple outputs. Although precise input and output data are fundamentally used in classical DEA models, real-life problems often involve uncertainties characterized by fuzzy and/or random input and output data. We present a new input-oriented dual DEA model with fuzzy and random input and output data and propose a deterministic equivalent model with linear constraints to solve the model. The main contributions of this paper are fourfold: (1) we extend the concept of a normal distribution for fuzzy stochastic variables and propose a DEA model for problems characterized by fuzzy stochastic variables; (2) we transform the proposed DEA model with fuzzy stochastic variables into a deterministic equivalent linear form; (3) the proposed model which is linear and always feasible can overcome the nonlinearity and infeasibility in the existing fuzzy stochastic DEA models; (4) we present a case study in the banking industry to exhibit the applicability of the proposed method and feasibility of the obtained solutions.

A Reliability-Oriented Fuzzy Stochastic Framework in Automated Distribution Grids to Allocate $\mu$ -PMUs

This paper proposes a reliability-oriented stochastic aggregated integer linear framework for full observability of the automated distributed systems based on the $\mu $ -synchrophasor units. The $\mu $ -synchrophasor unit as a newly introduced high-tech device makes it possible for an accurate and high-speed measurement of the voltage and current waveforms in the distribution systems. This paper proposes a multi-stage strategy for the $\mu $ -synchrophasor unit placement together with the communication system requirements in the reconfigurable distribution systems, considering the zero-injection constraints in the model. To determine the optimal topology at the end of each phase, a reliability-based cost function is developed to optimize the customer interruption costs and power losses simultaneously. In order to model the uncertainties of forecast error in the active and reactive load demands as well as the failure rate and repair rate parameters, a stochastic framework based on the fuzzy cloud theory is employed. The proposed bi-level mixed integer linear programing approach is used to co-optimize the network switching scheme as well as the optimal $\mu $ -synchrophasor positions and communication infrastructure costs in the same framework. The simulation results on a practical test system verify the observability of the automated reconfigurable distribution system during the reconfiguration process.

A Fuzzy Stochastic Model for Carbon Price Prediction Under the Effect of Demand-related Policy in China's Carbon Market

The establishment of China's carbon market has an obvious policy-oriented feature, and the carbon price is easily affected by demand-related policies within a compliance period. As prior models cannot help with clear simulation of the volatility of carbon price in China, this paper develops a fuzzy stochastic model to predict such price under the effect of demand-related policy. First, we quantify corporate final profit obtained from carbon trading based on different free allowance policies to measure the actual allowance demand in the carbon market. Second, based on such demand, we add the fuzzy number in each parameter of a stochastic differential equation and then develop a fuzzy stochastic model that can help to analyse the effect of demand-related policy on carbon price in the immature carbon market. Third, by analysing the demand-related policy formulated in the second-developing-phase of the Shanghai Environment and Energy Exchange (from Nov. 17 in 2016) through our model, we predict the price trend after each demand-related policy publication. Experimental results reveal the accurate fitting effect of the developed model that can help to estimate the supply-and-demand in the carbon market and evaluate the effectiveness of current carbon trading policy as well. Further, our model can provide a robust theoretical implication for both corporate carbon trading strategies and governmental regulations on carbon demand-related policy.

Ant Colony Optimization and Genetic Algorithm for Fuzzy Stochastic Production-Distribution Planning

In this paper, a tactical Production-Distribution Planning (PDP) has been handled in a fuzzy and stochastic environment for supply chain systems (SCS) which has four echelons (suppliers, plants, warehouses, retailers) with multi-products, multi-transport paths, and multi-time periods. The mathematical model of fuzzy stochastic PDP is a NP-hard problem for large SCS because of the binary variables which determine the transportation paths between echelons of the SCS and cannot be solved by optimization packages. In this study, therefore, two new meta-heuristic algorithms have been developed for solving fuzzy stochastic PDP: Ant Colony Optimization (ACO) and Genetic Algorithm (GA). The proposed meta-heuristic algorithms are designed for route optimization in PDP and integrated with the GAMS optimization package in order to solve the remaining mathematical model which determines the other decisions in SCS, such as procurement decisions, production decisions, etc. The solution procedure in the literature has been extended by aggregating proposed meta-heuristic algorithms. The ACO and GA algorithms have been performed for test problems which are randomly generated. The results of the test problem showed that the both ACO and GA are capable to solve the NP-hard PDP for a big size SCS. However, GA produce better solutions than the ACO.

Mean-Square Exponential Input-to-State Stability of Stochastic Fuzzy Recurrent Neural Networks with Multiproportional Delays and Distributed Delays

We are interested in a class of stochastic fuzzy recurrent neural networks with multiproportional delays and distributed delays. By constructing suitable Lyapunov-Krasovskii functionals and applying stochastic analysis theory, Ito^’s formula and Dynkin’s formula, we derive novel sufficient conditions for mean-square exponential input-to-state stability of the suggested system. Some remarks and discussions are given to show that our results extend and improve some previous results in the literature. Finally, two examples and their simulations are provided to illustrate the effectiveness of the theoretical results.

Adaptive Event-Triggered Fault Detection for Fuzzy Stochastic Systems With Missing Measurements

This paper discusses adaptive event-triggered fault detection filter design for fuzzy stochastic models with missing measurements. First, a novel event-triggered strategy is introduced, while an adaptive law is provided to adjust communication threshold dynamically. Compared with traditional event-triggered methods with fixed threshold, the proposed strategy is more effective on saving network communication resources. Second, a Bernoulli stochastic process is proposed to describe the measurement missing phenomenon, which always appears in real network environment. Then, an integrated fault detection model for fuzzy stochastic systems is constructed by taking network-induced delays, adaptive event-triggered strategy and missing measurements into account. A new method is provided to achieve mean-square asymptotical stability of residual model with one desired fault detection objective. Finally, simulation cases are introduced to verify the validity of the designed strategy.

Fuzzy Stochastic Linear Fractional Programming based on Fuzzy Mathematical Programming

ABSTRACTIn this paper, we consider a Fuzzy Stochastic Linear Fractional Programming problem (FSLFP). In this problem, the coefficients and scalars in the objective function are the triangular fuzzy number and technological coefficients and the quantities on the right side of the constraints are fuzzy random variables with the specific distribution. Here we change an FSLFP problem to an equivalent deterministic Multi-objective Linear Fractional Programming (MOLFP) problem. Then by using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective Linear programming (LP) problem. A numerical example is presented to demonstrate the effectiveness of the proposed method.

Stochastic plans in SMEs: A novel multidimensional fuzzy logic system (mFLS) approach

Manufacturing planning in small and medium enterprises (SMEs) uses a deterministic behavior, and the execution of these plans has a stochastic behavior. The evaluation of the manufacturing planning is based on a simple criterion as job on time or job delayed, without integrating conditions of uncertainty in the cycle times for each job. The aim of this paper is to propose a novel multidimensional stochastic Fuzzy Logic System (msFLS) approach to execute a plan with stochastic behavior in knitting SMEs and their evaluation. In this paper, two main contributions are identified. On one hand, the generation of a multi-dimensional diffuse system is proposed. Normal probability density function is used to generate multi linguistic variables to transform deterministic plans to stochastic plans in knitting SMEs. The fuzzy subsets or linguistic terms are labelled and categorized in a simple and clear language as poor (P), regular (R), good (G) and excellent (E). The Gaussian function was used as a membership function. On the other hand, the second contribution is the use of the sum of frequencies in the stage of implication for the multi-Fuzzy system. This research was validated through an integration of two different intelligent techniques such as the proposed novel msFLS and artificial neural networks. Neural networks were used as a generalization mechanism to perform any stochastic planning in the knitting companies. The inputs and outputs of the fuzzy system are used as training patterns in the neural network. The stages of the proposed approach are explicitly described and applied to random data and validated with real data of SMEs of the South of Guanajuato, Mexico. The proposed system had a positive response in the textile company, which continues to be used to carry out its manufacturing planning and the evaluation of its execution.

Identifying Emotion Regulation Altering Targets as Depressive Mood Disorder Treatments Using Fuzzy Stochastic Hybrid Petri Nets

Identifying Emotion Regulation Altering Targets as Depressive Mood Disorder Treatments Using Fuzzy Stochastic Hybrid Petri Nets

A stochastic fuzzy multi-criteria decision-making model for optimal selection of clean technologies

Abstract Selection of clean technology options requires systematic evaluation based on multiple criteria which are often conflicting. The optimal choice should consider not just technical performance but also the economic, environmental and social aspects of technologies. Furthermore, the interdependencies of these aspects should also be considered. The decision-maker often needs to make explicit trade-offs while ranking the alternatives. In addition, data gaps and imprecise information that are typical when dealing with emerging technologies make conventional methods ineffective. This work thus proposes a Stochastic Fuzzy Analytic Hierarchical Network Process decision model to address the complexity and uncertainty involved in the clean technology selection process. This method first decomposes the problem into a hierarchical network structure, and then derives the probability distribution of the priority weights needed for ranking. The capabilities of the methodology are demonstrated with three case studies, involving the comparison of different carbon nanotube synthesis methods, nutrient removal treatment technology options for municipal wastewater, and low-carbon electricity sources in the Philippines.

Fuzzy Stochastic Unit Commitment Model with Wind Power and Demand Response under Conditional Value-At-Risk Assessment

With the increasing penetration of wind power and demand response integrated into the grid, the combined uncertainties from wind power and demand response have been a challenging concern for system operators. It is necessary to develop an approach to accommodate the combined uncertainties in the source side and load side. In this paper, the fuzzy stochastic conditional value-at-risk criterions are proposed as the risk measure of the combination of both wind power uncertainty and demand response uncertainty. To improve the computational tractability without sacrificing the accuracy, the fuzzy stochastic chance-constrained goal programming is proposed to transfer the fuzzy stochastic conditional value-at-risk to a deterministic equivalent. The operational risk of forecast error under fuzzy stochastic conditional value-at-risk assessment is represented by the shortage of reserve resource, which can be further divided into the load-shedding risk and the wind curtailment risk. To identify different priority levels for the different objective functions, the three-stage day-ahead unit commitment model is proposed through preemptive goal programming, in which the reliability requirement has the priority over the economic operation. Finally, a case simulation is performed on the IEEE 39-bus system to verify the effectiveness and efficiency of the proposed model.

Networked Estimation of a Class of Fuzzy Stochastic Hybrid Systems With Variable Rates of Packet Losses.

This paper focuses on the state estimator design problem for a class of Takagi-Sugeno fuzzy stochastic hybrid systems with intermittent measurements in discrete-time domain. The hybrid systems are characterized with the stochastic switching among a set of subsystems, and the switching is supposed to be governed by a semi-Markov process with finite sojourn time. The random packet dropouts are modeled by a Bernoulli distributed sequence, and the packet dropout rate, which is considered to be variable, is described by the semi-Markov stochastic process that governs the switching dynamics of the fuzzy stochastic hybrid system. A more general class of Lyapunov functions that not only depends on the system modes, but also on the time that the current mode has been in since the last mode switching, is employed to analyze the stability and H∞ performance of the estimation error system. Then, numerically testable conditions on the existence of a desired fuzzy mode-dependent state estimator are presented such that the estimation error system approaches to be mean square stable to an adjustable level and achieves a prescribed H∞ disturbance attenuation index. Finally, an illustrative example of a single-link robotic arm system is provided to demonstrate the effectiveness and the superiority of the design method of state estimator.

Proposal of the Use of a Fuzzy Stochastic Network for the Preliminary Evaluation of the Feasibility of the Process of the Adaptation of a Historical Building to a Particular Form of Use

The knowledge of a real estate developer regarding the possibilities of adapting a historical building to a particular form of use and the knowledge of the approximate costs associated with this process are some of the more important pieces of information that can influence the making of the final decision regarding commencing with such a project. The preliminary analysis of the process of adapting a historical building is a difficult task due to the specific character of this type of project. The specific character of such a project is proven by the fact that the often insufficient analysis of the structure and architecture of a building and its historical substance at the stage of carrying out the process of adaptation can generate the necessity to perform previously unforeseen additional actions. An equally important problem is the difficulty in estimating the funds required to conduct research and the analyses associated with developing design documentation, as well as carrying out construction and conservation work. This is why a real estate developer should analyse various scenarios of carrying out a project during the stage of the preliminary analysis of its feasibility, taking into account the fact that some of them can occur in a random manner. The authors of the paper propose the use of one of the planning tools known as stochastic networks, which can be used to model the undetermined structure of these types of projects. Fuzzy logic was used in order to estimate uncertain values of the parameters of a model (the probability of performing work and paying the associated costs). The approach proposed by the authors was used to perform a preliminary analysis of the adaptation of the Arsenal in Gdańsk to a particular form of use along with estimating the costs associated with it. The results that were obtained have confirmed the potential of this method for real-world application.

Fuzzy Stochastic Data Envelopment Analysis with Undesirable Outputs and its Application to Banking Industry

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision-making units (DMUs) with multiple inputs and multiple outputs. The classical DEA models were initially formulated only for desirable inputs and outputs. However, undesirable outputs may be present in the production process which needs to be minimized. In addition, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, decision makers may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. In order to deal with the above problems, this paper proposes fuzzy stochastic DEA model with undesirable outputs. Three fuzzy DEA models with respect to probability–possibility, probability–necessity and probability–credibility constraints are applied. The contribution of this paper is fourfold: (1) the proposed approach considers the impact of undesirable outputs on the performance of DMUs; (2) unlike the existing methods, the proposed solution approach provides efficiency scores in the range of zero and one for all DMUs; (3) the proposed approach analyzes the influence of the presence of both fuzzily imprecision and probabilistic uncertainty in the data over the efficiency results; and (4) a case study in the banking industry is presented to exhibit the efficacy of the procedures and demonstrate the applicability of the proposed model.

Pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented.

Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach

In this paper, a fuzzy goal programming (FGP) approach is considered for solving stochastic fuzzy multi-level multi-objective fractional programming (ML-MOFP) problem. In the developed stochastic fuzzy ML-MOFP model the fractional objective function coefficients and scalars are represented by fuzzy parameters. Moreover, in the constraints, the right-hand sides are independent random variable with known distribution function while both the left-hand side coefficients and the tolerance measures are considered to be fuzzy parameters. Therefore, the chance-constrained approach with dominance possibility criteria and the α-cut approach are utilized to transform the stochastic fuzzy ML-MOFP problem to its equivalent deterministic-crisp problem. Then, the membership functions for the defined fuzzy goals are setup. Also, in the proposed FGP model, a linearization procedures for the membership goals of the objective functions is developed. Hence, the FGP approach is used to achieve the highest degree of each of the membership goals by minimizing the sum of the negative deviational variables. Finally, an algorithm to clarify the developed FGP approach, as well as Illustrative numerical example, are presented.

Approaches to Pythagorean Fuzzy Stochastic Multi-criteria Decision Making Based on Prospect Theory and Regret Theory with New Distance Measure and Score Function

In this paper, we initiate a new axiomatic definition of Pythagorean fuzzy distance measure, which is expressed by Pythagorean fuzzy number that will reduce the information loss and remain more original information. Then, the objective weights of various criteria are determined via grey system theory. Combining objective weights with subjective weights, we present the combined weights, which can reflect both the subjective considerations of the decision maker and the objective information. Meanwhile, a novel score function is proposed. Later, we present two algorithms to solve stochastic multicriteria decision making problem, which takes prospect preference and regret aversion of decision makers into consideration in the decision process. Finally, the effectiveness and feasibility of approach is demonstrated by a numerical example.

Interval Neutrosophic Fuzzy Stochastic Multi-Criteria Decision-making Methods Based on MYCIN Certainty Factor and Prospect Theory

For the stochastic multi-criteria decision-making problem, in which the information on criteria's weights is incomplete and the indices value of alternatives are in the form of interval neutrosophic fuzzy numbers, an interval neutrosophic random decision-making approach based on WYCIN certainty factor and prospect theory is proposed. According to the score function of interval neutrosophic fuzzy numbers and prospect theory, the MYCIN certainty factors of different alternatives in different indices are obtained. And the trust degrees of different indices are determined by using the grey incidence analysis. Then, the certainty factor fusion method in different indices is deduced to get the optimal alternative. And the best alternative is got by using the method. Finally, an example shows the feasibility and validity of this method.

Two echelon supply chain model of agricultural products based on stochastic fuzzy process of cost demand

Stochastic fuzziness existed in supply chain process has important influence on inventory maintenance and decision processing of normal system operation, especially under the situation of coupling existed in two echelon supply chain, this influence will be amplified to some extent. First, for the studied two echelon supply chain objects, joint cost has been taken as target to make optimal model design; second, considering about the stochastic fuzziness existed in two echelon supply chain, the demand rate of market for products as well as supply and distribution time have been selected as main research parameters, two echelon supply stochastic demand model based on triangular fuzzy number has been constructed and then model solving process has been deduced according to the characteristics of design model; last, verification for the performance of proposed model has been made based on parameter influence experiment and horizontal contrast.

Inexact Fuzzy Stochastic Chance Constraint Programming for Emergency Evacuation in Qinshan Nuclear Power Plant under Uncertainty

Nuclear power accidents are one of the most dangerous disasters posing a lethal threat to human health and have detrimental effects lasting for decades. Therefore, emergency evacuation is important to minimize injuries and prevent lethal consequences resulting from a nuclear power accident. An inexact fuzzy stochastic chance constrained programming (IFSCCP) method is developed to address various uncertainties in evacuation management problems. It integrates the interval-parameter programming (IPP) and fuzzy stochastic chance constrained programming (FSCCP) methods into a general framework, in which the IPP method addresses the uncertainties presented as intervals defined by crisp lower and upper bounds, and the FCCP treat the dual-uncertainties expressed as fuzzy random variables. The measures of possibility and necessity were employed to convert the fuzzy random variables into crisp values to reflect the decision maker’s pessimistic and optimistic preferences. The IFSCCP model is applied to support nuclear emergency evacuation management in the Qinshan Nuclear Power Site, which is one of the largest nuclear plants in China. The results pro-vide stable intervals for the objective function and decision variables with different fuzzy and probability confidence levels regarding the local residents’ distribution. Nine scenarios are analyzed to reflect the impacts of the imprecision (fuzziness and randomness) associated with the size of the population in a plume emergency planning zone. The results are valuable for supporting local decision makers to generate effective emergency evacuation strategies.