Fuzzy Uncertainty Research Articles

Power battery third-party reverse logistics provider selection: Fuzzy evidential reasoning

Massive power batteries (PBs) are crucial to new energy vehicle enterprises. Due to Extended Producer Responsibility (EPR), the third-party reverse logistics provider selection(3PRLPs) process has become an important decision to save cost. This paper uses an innovative combination of qualitative analysis and quantitative data integration to address the PB 3PRLPs problem by using Failure Modes and Effects Analysis (FMEA) and fuzzy evidential reasoning (FER). Firstly, the possible failures and potential effects in the PB 3PRLPs are identified by the FMEA to determine criteria and importance grades. Subsequently, AHP is utilized to calculate the criteria weight based on the importance of grades. FER is creatively applied to address the intersection of assessment grades and allocate the belief degree (BD) of the interaction to fuse heterogeneous data. Additionally, sensitivity analysis is done to look into the stability of the sequencing. Compared with other methods, the proposed method not only solves the subjectivity of AHP weighting but also manipulates probabilistic and fuzzy uncertainties for multi-criteria decision-making (MCDM). This method is useful in quantitatively analyzing the 3PRLPs problem and in providing auxiliary decision support for enterprises.

Non-Probabilistic Reliability Analysis of Slopes Based on Fuzzy Set Theory

Aimed at the problem of fuzzy uncertainty of geotechnical parameters in slope stability analysis, a non-probabilistic reliability analysis method for slopes based on fuzzy set theory is proposed. Geotechnical parameters are described as fuzzy numbers, which are transformed into interval numbers at different cut set levels by taking fuzzy sets. The corresponding non-probabilistic reliability indexes and failure degrees of the slope are calculated by the non-probabilistic reliability analysis method based on the ellipsoidal model, and then the overall failure degree of the slope is obtained by weighted average to judge the stability state of the slope. The feasibility of the method was verified by a case analysis. The results show that the type and shape parameters of the fuzzy affiliation function of geotechnical parameters have a great influence on the non-probabilistic reliability of the slope. The slope failure degrees obtained from trapezoidal fuzzy numbers were larger, the slope failure degrees obtained from triangular fuzzy numbers and normal fuzzy numbers were medium, and the slope failure degrees obtained from lognormal fuzzy numbers were smaller. When considering soil parameters as triangular fuzzy numbers, normal fuzzy numbers, or lognormal fuzzy numbers, with the reduction of the shape parameters, the non-probabilistic reliability indexes of the slope increased while the failure degrees decreased. Additionally, adopting the overall failure degree to evaluate the stability of the slope can effectively solve the problem where the calculation results are too conservative (if the non-probabilistic reliability index is greater than 1) to judge the stability state of the slope in the traditional non-probabilistic reliability method.

Propagation algorithm for hybrid uncertainty parameters based on polynomial chaos expansion

AbstractThis article presents an uncertainty analysis method for systems with hybrid stochastic and fuzzy uncertainty parameters based on polynomial chaos expansion (PCE). Parameters in the system are described by probability boxes, interval numbers, and fuzzy sets, respectively, based on the differences in their limited stochastic knowledge. First, this method transforms the uncertain parameters into standard normal distribution and interval variables through equal probability transformation or ‐cut operations. Second, the Legendre and Hermite polynomials are used as the PCE model's primary functions, and the expansion coefficients are calculated by the Galerkin projection method based on sparse grid numerical integration. Then, the system response bounds under the pre‐defined confidence level can be obtained using a genetic algorithm to solve the optimization problem constructed based on PCE models. Finally, the feasibility and effectiveness of the method are illustrated by taking the tank bi‐directional stabilized system and the double‐pendulum‐controlled system as examples. The numerical results show that the system response bounds obtained by the PCE model optimization algorithm are consistent with the Monte Carlo simulation. Still, the computational efficiency is much higher. The proposed method effectively combines fuzzy sets and probability boxes and dramatically simplifies the analysis process of uncertain systems. The method exhibits fine precision even in high‐dimensional uncertainty analysis problems.

New Computational Technique for Solving Linear Programming Problem Subjected to Fuzzy Uncertainty

This paper proposes two new computational methods for solving linear programming problem under trapezoidal and triangular fuzzy uncertainties with equality constraints. The coefficients of the constraints and the objective functions are assumed to be crisp. However, the decision variables and the right-hand side vector of the constraints are considered as uncertain in nature. The concepts of fuzzy addition and subtraction have been used to develop the proposed methods. In the first method, the coefficients are considered as non-negative, whereas mixed coefficients (i.e. both negative and non-negative) are considered in the second method. The obtained results are compared with Behera et al. [D. Behera, K. Peters and S. A. Edalatpanah, Alternative methods for linear programming problem under triangular fuzzy uncertainty, Journal of Statistics and Management Systems, 25 (2022) 521–539; D. Behera, K. Peters, S. A. Edalatpanah and D. Qiu, New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty, Journal of Information and Optimization Sciences, 42 (2021) 603–629], and Saati et al. [S. Saati, M. Tavana, A. Hatami-Marbini and E. Hajiakhondi, A fuzzy linear programming model with fuzzy parameters and decision variables, International Journal of Information and Decision Sciences, 7 (2015) 312–333.] for the validation.

High-order interaction feature selection for classification learning: A robust knowledge metric perspective

Feature selection is an important learning task in data mining and knowledge discovery. Nevertheless, the fuzziness, uncertainty, and noise presented by the data greatly complicate the construction of learning models. Moreover, most works focus on exploring low-order correlations between variables using low-dimensional mutual information, without paying attention to high-order interaction for multiple variables, resulting in the loss of some potentially important dependency information. Driven by these two issues, a robust knowledge metric approach is invented to perceive and excavate the latent information hidden in interaction. In this study, firstly, a robust fuzzy granularity space is constructed from different granular structures induced by different features, and the robust fuzzy uncertainty measures (RFUMs) are successively devised. Then, RFUMs are used to measure pair-wise, three-order, and even higher-order interaction dependencies among features. Further, a constrained high-order interaction evaluation function inspired by the N-gram language model is formulated, and a corresponding high-order interaction feature selection algorithm with RFUMs (HIFS-RFUMs) is designed. Next, comparative experiments with seven representative algorithms on twenty datasets illustrate its effectiveness. In addition, ablation experiments are conducted on the high-order interaction feature selection algorithm with fuzzy uncertainty measures (HIFS-FUMs) and the relative reduction algorithm with RFUMs (R2-RFUMs), which demonstrate the robustness of the metric and the effectiveness for mining high-order interactive features, respectively.

A novel learning function of adaptively updating Kriging model for reliability analysis under fuzzy uncertainty

A novel learning function of adaptively updating Kriging model for reliability analysis under fuzzy uncertainty

Fuzzy Random Option Pricing in Continuous Time: A Systematic Review and an Extension of Vasicek’s Equilibrium Model of the Term Structure

Fuzzy random option pricing in continuous time (FROPCT) has emerged as an active research field over the past two decades; thus, there is a need for a comprehensive review that provides a broad perspective on the literature and identifies research gaps. In this regard, we conducted a structure review of the literature by using the WoS and SCOPUS databases while following the PRISMA criteria. With this review, we outline the primary research streams, publication outlets, and notable authors in this domain. Furthermore, the literature review revealed a lack of advancements for the equilibrium models of the yield curve. This finding serves as a primary motivation for the second contribution of this paper, which involves an extension of Vasicek’s yield curve equilibrium model. Specifically, we introduce the existence of fuzzy uncertainty in the parameters governing interest rate movements, including the speed of reversion, equilibrium short-term interest rate, and volatility. By incorporating fuzzy uncertainty, we enhance the model’s ability to capture the complexities of real-world interest rate dynamics. Moreover, this paper presents an empirical application of the proposed extension to the term structure of fixed-income public bonds in European Union. The empirical analysis suggests the suitability of the proposed extension of Vasicek’s model for practical applications.

Solving the time capacitated arc routing problem under fuzzy and stochastic travel and service times

AbstractStochastic, as well as fuzzy uncertainty, can be found in most real‐world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper we propose a fuzzy simheuristic to solve the Time Capacitated Arc Routing Problem (TCARP) when the nature of the travel time can either be deterministic, stochastic or fuzzy. The main goal is to find a solution (vehicle routes) that minimizes the total time spent in servicing the required arcs. However, due to uncertainty, other characteristics of the solution are also considered. In particular, we illustrate how reliability concepts can enrich the probabilistic information given to decision‐makers. In order to solve the aforementioned optimization problem, we extend the concept of simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated into the CARP. In order to test our approach, classical CARP instances have been adapted and extended so that customers' demands become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones. In particular, our fuzzy simheuristic is capable of generating new best‐known solutions for the stochastic versions of some instances belonging to the tegl, tcarp, val, and rural benchmarks.

Hybrid reliability-based sequential optimization for PID vibratory controller design considering interval and fuzzy mixed uncertainties

Vibration control is an important problem in practical engineering. Optimal control is widely used, but the uncertainties in practical engineering may lead to the failure of the system. To reach a balance of safety and energy-consuming, taking the widely-used proportional-integral-differential control as an example, a framework for hybrid reliability-based sequential optimization for vibratory controller design considering interval and fuzzy mixed uncertainties is proposed in this paper. Firstly, the fuzzy uncertainties are transformed into interval uncertainties according to the cut-level strategy. Then the response interval under a certain membership can be calculated by the subinterval collocation method, which can guarantee the accuracy of the calculated response interval. In this process, to choose proper memberships as cut-levels and improve efficiency, the adaptive fitting method based on the differences of areas is adopted. Next, taking interval and fuzzy uncertainties into consideration, a novel non-probabilistic reliability evaluation is performed based on the area ratio, which is composed of upper and lower boundaries of the minimum value of the extreme state function. Finally, the sequential optimization is adopted to improve the efficiency of optimization, in which the constraint is changed according to the proposed non-probabilistic area-ratio reliability. Two engineering examples are presented to demonstrate the accuracy and practicability of this framework.

Research on uncertain multiple attribute decision making based on improved possibility degree relation model and its application

In this paper, we mainly focus on the triangular fuzzy number-based uncertain multiple attribute decision making problem, which not only attribute weights are unknown but also preference for decision-making objects do not exist, and give a new decision-making approach and consistency test method based on the improved possibility relation model. This method fully considers the influence of the comparison possibility degree measurement information between the measured values of the indicator attribute itself in the course of processing uncertain reasoning such as fuzziness and randomness, reconstructs a new and more optimized triangular fuzzy number-based decision making object improved possibility degree relation model (TFN-DMOIPDRM) to determine the attribute weight vector, and creatively designs a general formula to test the consistency of the improved possibility degree relation matrix. Next the criterion of consistency test is given to solve the remaining problem of the lack of consistency test in the construction of fuzzy number possibility degree relation model and fuzzy complementary judgment matrix. Moreover, another major contribution of this paper is to present the improved possibility degree relation theory of triangular fuzzy numbers on the basis of defining the comparative possibility degree of triangular fuzzy numbers, and fully study a series of its relevant properties and conclusions, as well as its application in constructing model to determine the attribute weight. By aggregating the improved possibility degree information measured by pairwise comparing decision objects, the overall improved possibility degree value of each decision object is obtained, and a new algorithm of the improved possibility relation model for triangular fuzzy number multi-attribute decision object is given, which improves and expands the application of fuzzy number possibility theory in the field of fuzzy uncertainty reasoning and intelligent computing of artificial intelligence.

Performance evaluation of possibilistic fuzzy portfolios with different investor risk attitudes based on DEA approach

By considering the stock market’s fuzzy uncertainty and investors’ psychological factors, this paper studies the portfolio performance evaluation problems with different risk attitudes (optimistic, pessimistic, and neutral) by the Data Envelopment Analysis (DEA) approach. In this work, the return rates of assets are characterized as trapezoidal fuzzy numbers, whose membership functions with risk attitude parameters are described by exponential expression. Firstly, these characteristics with risk attitude are strictly derived including the possibilistic mean, variance, semi-variance, and semi-absolute deviation based on possibility theory. Secondly, three portfolio models (mean-variance, mean-semi-variance, and mean-semi-absolute-deviation) with different risk attitudes are proposed. Thirdly, we prove the real frontiers determined by our models are concave functions through mathematical theoretical derivation. In addition, two novel indicators are defined by difference and ratio formulas to characterize the correlation between DEA efficiency and portfolio efficiency. Finally, numerical examples are given to verify the feasibility and effectiveness of our model. No matter what risk attitude an investor holds, the DEA can generate approximate real frontiers. Correlation analysis indicates that our proposed approach outperforms in evaluating portfolios with risk attitudes. At the same time, our model is an improvement of Tsaur’s work (2013) which did not study the different risk measures, and an extension of Chen et al.’s work (2018) which only considered risk-neutral attitude.

A hybrid group decision-making approach involving Pythagorean fuzzy uncertainty for green supplier selection

Green supplier selection is a significant issue in green supply chain management field and has drawn worldwide attention from academia, industry, and governments. Numerous methodological models have emerged for correctly choosing an appropriate green supplier, but some inadequate aspects of these models, such as the use of high-order fuzzy uncertainty, incompatible designed criteria, the weight methods used by decision experts, and consensus on distinct ranks, should be improved. This research propounds a hybrid approach that combines the analytic hierarchy process (AHP), technique for order preference by similarity to ideal solutions (TOPSIS), and linear assignment method (LAM) under Pythagorean fuzzy (PF) uncertainty to assess candidate suppliers. A new hierarchical evaluative criteria system with green factors that run throughout procurement, production, and transaction is built. The ordered weighted averaging operation predicated on a normal distribution is adopted to figure out the significance of the relevant decision experts, and the PF-AHP technique is exploited to recognize relevant criteria significance. To find the best green supplier, the PF-TOPSIS technique employs the most recent generalized distance measure and magnitudes. The LAM is exploited to arrive at a consensus on distinct ranks depending on differentiated distance parameter values in the distance formula for the PF sets, and then the optimal green supplier can be obtained. Additionally, the presented PF-AHP-TOPSIS-LAM approach was applied to an illustrative case, and the outcomes were shown to be more beneficial and efficacious than the solutions by other existing techniques. Hence, our presented hybrid approach provides a better methodological framework, establishes a critical foundation for artificial intelligence applications within a decision support field, and contributes to such competitiveness of microenterprises and the long-term development of society.

Fuzzy Evaluation of Inland Ship Lock Service Condition Based on Combination Weighting and Matter-Element Extension Cloud Model

Ship lock as a typical hydraulic structure has become an important node in waterway transportation. Due to the long operating life and high demand of throughput, many locks are under the overloaded operation situation. However, the service condition assessment of ship locks has rarely been directly studied, and there is a lack of an efficient and standardized method owing to the complex structure of the ship lock system. In this paper, a multi-level hierarchical system including 36 indexes was constructed based on the engineering breakdown structure theory. The synthetic weights of indexes were determined by the order relation method and entropy weight method combining subjectivity and objectivity. The extension cloud model combining the extension theory and cloud model was put forward, aiming to deal with the uncertainty of fuzziness and randomness in the evaluation process. Then, two typical locks were investigated, and the numerical scores indicated that their states belong to Level III and Level IV, respectively. The proposed method reveals the structural condition and provides theoretical reference for the maintenance of ship locks, which can be applied with generalizability and operability.

Fixed-Time Sliding Mode Synchronization of Uncertain Fractional-Order Hyperchaotic Systems by Using a Novel Non-Singleton-Interval Type-2 Probabilistic Fuzzy Neural Network

In this study, we proposed a sliding mode control method based on fixed-time sliding mode surface for the synchronization of uncertain fractional-order hyperchaotic systems. In addition, we proposed a novel self-evolving non-singleton-interval type-2 probabilistic fuzzy neural network (SENSIT2PFNN) to estimate the uncertain dynamics of the system. Moreover, an adaptive compensator was designed to eliminate the influences of random uncertainty and fuzzy uncertainty, thereby yielding an asymptotically stable controlled system. Furthermore, an adaptive law was introduced to optimize the consequence parameters of SENSIT2PFNN. The membership layer and rule base of SENSIT2PFNN were optimized using the self-evolving algorithm and whale optimization algorithm, respectively. The simulation results verified the effectiveness of the proposed methods for the synchronization of uncertain fractional-order hyperchaotic systems.

Booster Optimization for Water Distribution System Based on Trapezoidal Fuzzy Distribution

In this work, an optimization model to deal with uncertainty of boosters in water distribution systems (WDSs) was proposed. The model proposed can cope with the nonlinearities and intervals of the objective function, the intervals of the left-hand sides of the constraints, and trapezoidal fuzzy uncertainty of the right-hand sides of the constraints. The proposed model was applied to two case studies to obtain the optimal intervals of booster costs. The results indicated that the lower bounds and the upper bounds increased with confidence levels, preference parameter λ values, and the booster numbers. In addition, the boosters located at the end far from the source is beneficial for reducing booster costs. Moreover, the operation costs decreased with increase of booster numbers, and increased with λ values and the confidence levels. The results obtained can help managers making economical decisions for booster numbers and injection rates under uncertainty.

Multi-Objective Reliability-Based Partial Topology Optimization of a Composite Aircraft Wing

Reliability-based partial topology optimization (RBPTO) is a new approach for aircraft structural design; however, it brings computational complexity and makes aeroelasticity analysis quite challenging. Therefore, the present study proposed the multi-objective reliability-based partial topology optimization of a composite aircraft wing using a fuzzy-based metaheuristic (MRBPTOFBMH) approach. The objective is to obtain an optimal layout including partial topology and sizing of the aircraft wing structure. Here, an optimal aeroelastic structure is designed by taking into account the uncertain nature of material properties and the permitted transverse displacement. To increase computational efficiency in the design process, a non-probabilistic approach called a possibilistic safety index-based design optimization (PSIBDO) with fuzzy uncertainties is proposed to quantify the uncertainties due to aeroelastic and structural constraints. Various optimum partial topological shapes and sizing of aircraft wing structures with various PSI values in the range of [0.001, 1.0] have been obtained in a single optimization run. These outcomes, including deterministic and reliable optimal aircraft wing structures, demonstrate the high effectiveness of the proposed MRBPTOFBMH technique to alleviate the complexity of unconventional aircraft wing structure design. The findings also reveal the ease in cooperation of the suggested technique with a high-performance multi-objective evolutionary algorithm (MOEA) and its application in real-world multi-objective design optimization (MODO) problems with the least computational requirements against the traditional method’s multiple runs. Furthermore, the proposed methodology can generate potential aircraft wing structures in a range of m = [89.38–127.84] kg, and flutter speed = [285.61–632.78] m/s, that adhere to all the constraints requirements.

Selection of cloud service providers using MCDM methodology under intuitionistic fuzzy uncertainty

Selection of cloud service providers using MCDM methodology under intuitionistic fuzzy uncertainty

Economic ordering quantity inventory model with verhulst’s demand under fuzzy uncertainty for geographical market

Inventory plays an important role in the production process. One of the primary reasons why inventory management modeling is essential for the industry is because it will suffer immensely if there are insufficient food products to stock during the shutdown period. By determining the combined optimal cost of the retailers and wholesalers, this research significantly improves the service of the supply chain from wholesaler to retailer. The stochastic number for the imperfect perishable items is provided in this inventory study. By altering the parameter values, the uniform distribution is used to calculate these damaged items. This approach identifies the backordering quantity for both regular and uncertain fish band circumstances. The cost of maintaining the inventory will rise significantly of increased wastage due to a rise in deteriorating, which will result in the loss of perishable food items. The primary goal of this research paper is to transport them without being destroyed until they reach their desired consumers. By determining the back ordering quantity during a shutdown, one can decrease the overall expenses incurred by the retailers. These computational complexity measures are proven in a fuzzy uncertain environment. The main goal of this paper is to analyze the variation of demand during the unanticipated period and find the optimum total cost of the perishable products. The growth of production in a particular area at a particular time, interconnect with another large number of products in the same area and is calculated by Verhulst’s demand with time depended on proficiency rate. Concerning the existing Verhulst’s demand pattern for the production process, this paper introduced that for perishable items in a fuzzy unanticipated situation. A bountiful system analysis is performed to find the cost function under fuzzy environment and the sensitivity analysis is carried out to perform the key representation constant.

Transportation Mode Selection for Organ Transplant Networks by a New Multi-Criteria Group Decision Model Under Interval-Valued Intuitionistic Fuzzy Uncertainty

This study introduces a new multi-criteria group decision-making model in organ transplant transportation networks under uncertain situations. A new combined weighting approach is presented to obtain expert weights with various kinds of opinions by integrating similarity measure and subjective judgments of experts. Also, the CRITIC approach is given to obtain transportation criteria weights. Finally, a novel integrated ranking approach is proposed to calculate the rank of each alternative based on ideal point solution and relative preference relation (RPR) methods. This study regards an interval-valued intuitionistic fuzzy set to cope with the vagueness of uncertain conditions in a real case study.

Behavioral Decision-Making of Key Stakeholders in Public-Private Partnerships: A Hybrid Method and Benefit Distribution Study

Public-private partnerships (PPPs) have been used by governments around the world to procure and construct infrastructural amenities. It relies on private sector expertise and funding to achieve this lofty objective. However, given the uncertainties of project management, transparency, accountability, and expropriation, this phenomenon has gained tremendous attention in recent years due to the important role it plays in curbing infrastructural deficits globally. Interestingly, the reasonable benefit distribution scheme in a PPP project is related to the behavior decision-making of the government and social capital, as well as the performance of the project. In this paper, the government and social capital which are the key stakeholders of PPP projects were selected as the research objects. Based on the fuzzy expected value model and game theory, a hybrid method was adopted in this research taking into account the different risk preferences of both public entities and private parties under the fuzzy demand environment. To alleviate the problem of insufficient utilization of social capital in a PPP project, this paper seeks to grasp the relationship that exists between the benefit distribution of stakeholders, their behavioral decision-making, and project performance, given that they impact the performance of both public entities and private parties, as well as assist in maximizing the overall utility of the project. Furthermore, four game models were constructed in this study, while the expected value and opportunity-constrained programming model for optimal decision-making were derived using alternate perspectives of both centralized decision-making and decentralized decision-making. Afterward, the optimal behavioral decision-making of public entities and private parties in four scenarios was discussed and thereafter compared, which led to an ensuing discussion on the benefit distribution system under centralized decision-making. Lastly, based on an example case, the influence of different confidence levels, price, and fuzzy uncertainties of PPP projects on the equilibrium strategy results of both parties were discussed, giving credence to the effectiveness of the hybrid method. The results indicate that adjusting different confidence levels yields different equilibrium points, and therefore signposts that social capital has a fair perception of opportunities, as well as identifies reciprocal preferences. Nevertheless, we find that an increase in the cost coefficient of the government and social capital does not inhibit the effort of both parties. Our results also indicate that a reasonable benefit distribution of PPP projects can assist them in realizing optimum Pareto improvements over time. The results provide us with very useful strategies and recommendations to improve the overall performance of PPP projects in China.