Membership Grades Research Articles

Relaxed static output stabilization of polynomial fuzzy control systems by Lagrange membership functions

AbstractThis article is concerned with the stability analysis of the static output‐feedback polynomial fuzzy‐model‐based (SOF PFMB) control systems through designing a novel membership grade integration (MGI) approach. The nonconvex problems of the SOF PFMB control systems are convexificated into the convex conditions by introducing block diagonal positive‐definite Lyapunov matrix and nonsingular transformation matrix. We proposed new approximate membership functions, that is, Lagrange membership functions (LMFs), which can be introduced into the stabilization process to relieve the conservativeness of stability results. The LMFs are general representations of piecewise‐linear membership functions, which makes the number of stability conditions not limited by the number of sample points. In a fixed subdomain, arbitrary sample points can be employed by the LMFs method and achieve higher approximation capability by increasing more sample points so that membership grades can be incorporated into the system analysis. Furthermore, a novel MGI approach, including the information of premise variables and LMFs, is proposed making the stability conditions more relaxed. Finally, two simulation examples show the merits of the developed techniques.

A design of fuzzy rule-based classifier optimized through softmax function and information entropy

Takagi–Sugeno–Kang (TSK) classifiers have achieved great success in many applications due to their interpretability and transparent model reliability for users. At present, however, how to evaluate classification results is still an unsolved issue for TSK classifiers. This study designs a fuzzy rule-based classifier based on TSK classifiers, the outputs of which for an instance can be considered as the membership grades that the instance belongs to all classes. Then, an information entropy-based method is proposed to estimate the certainty of the outputs, which facilitates the further evaluation of the classification results of the instance for users. If the confidence level is not high, users can reject the classification results, and use other more advanced classifiers or collect more information about the instance. Moreover, the developed mechanism is suitable for handling large data since the adaptive moment estimation algorithm is used to identify the parameters of it. Experimental results demonstrate that the developed mechanism outperforms several rule-based classifiers.

An enhanced decision making model for industrial robotic selection using three factors: Positive, abstained, and negative grades of membership

Traditional packaging industries that lack automation often grapple with a spectrum of challenges that impede operational efficiency, productivity and overall competitiveness. To maintain quality and safety, the food industry must transition from manual to robotic packaging processes. The most suitable robot for executing such task is identified via a new hybrid fuzzy Stratified Multi-Attribute Decision-Making (S-MADM). This model comprises Fuzzy-PIvot Pairwise RElative Criteria Importance Assessment (F-PIPRECIA) and Stratified Network Mapping (SNM). The Hesitant T-Spherical Fuzzy (HT-SF) set effectively tackles the uncertainty associated with the selection process by introducing three factors, namely, positive, abstained, and negative grades of membership. A case study is presented to demonstrate the novel fusion model and determine the optimal food packaging robot. A total of twelve criteria are selected from the literature based on the decision-maker’s judgment. Among the seven industrial robots, the ”Delta robot” gained the highest ranking (71%), followed by the ”Scara robot” (56%), and the ”Multi-Axis Gantry” (49%). Delta robots, with spider-like limbs, can move gently and accurately at fast speeds, with heavy motors fixed on the frame, allowing for lightweight moving parts. The proposed SNM technique helps to enhance the effectiveness of these alternatives by analyzing the possible, inefficient, and highly influential states of the system. The sensitivity study confirms this analysis and the system’s durability while the comparative study verifies the effectiveness and feasibility of the proposed technique than existing MADM models. This paradigm enables company stakeholders to invest in an industrial robot that not only delivers better results but also efficiently overcome barriers associated with manual packaging procedures.

Legendre wavelet method based solution of fractional order prey–predator model in type-2 fuzzy environment

Researchers have recently examined several fractional-order prey–predator population models in a crisp or type-1 fuzzy environment. But incompleteness in the membership may also be present. In this regard, type-2 fuzzy numbers are employed in this inquiry to address the system’s imprecision since they are more realistic than type-1 fuzzy numbers in light of the uncertain membership grades. To numerically estimate the solution, the Legendre wavelet method (LWM) is used in conjunction with the r2-cut of the r1-plane form of the type-2 fuzzy parameters. To test the applicability of the present method, three cases are examined. The present solutions are quantitatively compared with the RK4 solutions in the crisp case. Approximations of the type-2 fuzzy prey and predator populations are also included. In addition, two- and three-dimensional plots are depicted to examine the behaviour of prey and predator populations in crisp and type-2 fuzzy cases. To assess the LWM’s efficacy, comparison graphs of the acquired solutions and the results of the RK4 approach are also provided. Numerical validation against the RK4 method in crisp cases demonstrates strong agreement, while revealing contrasting population behaviours in first two scenarios, whereas in the third case, both populations reduce with time. Further, the behaviour of the fuzzy solution has also been shown graphically using the footprint of uncertainty (FOU).

A Spectral Method for Identifiable Grade of Membership Analysis with Binary Responses.

Grade of membership (GoM) models are popular individual-level mixture models for multivariate categorical data. GoM allows each subject to have mixed memberships in multiple extreme latent profiles. Therefore, GoM models have a richer modeling capacity than latent class models that restrict each subject to belong to a single profile. The flexibility of GoM comes at the cost of more challenging identifiability and estimation problems. In this work, we propose a singular value decomposition (SVD)-based spectral approach to GoM analysis with multivariate binary responses. Our approach hinges on the observation that the expectation of the data matrix has a low-rank decomposition under a GoM model. For identifiability, we develop sufficient and almost necessary conditions for a notion of expectation identifiability. For estimation, we extract only a few leading singular vectors of the observed data matrix and exploit the simplex geometry of these vectors to estimate the mixed membership scores and other parameters. We also establish the consistency of our estimator in the double-asymptotic regime where both the number of subjects and the number of items grow to infinity. Our spectral method has a huge computational advantage over Bayesian or likelihood-based methods and is scalable to large-scale and high-dimensional data. Extensive simulation studies demonstrate the superior efficiency and accuracy of our method. We also illustrate our method by applying it to a personality test dataset.

An integrated description of election information using domination and dual domination in picture fuzzy graph

The concept of the fuzzy graph (FG) and the simplification of its type have been designed with many real-world concerns, decision-making, network problems, and other types of impression in mind. This article is essentially a generalization of fuzzy graph theory with their association in settings where four organizations of membership grade are characterized by imprecision. The contemporary idea of domination in picture fuzzy graph (PFG) is given the generalization of fuzzy graph domination and intuitionistic fuzzy graph (IFG) domination is unit on the innovative idea of picture fuzzy graph. This article is the main focus on the graph of the picture fuzzy set. Additionally, this research paper concludes with the concept of domination theory (DT) and double domination theory (DDT) in the concept of environment. Obviously, the framework of picture fuzzy graph is purposed and their connected theory is obtained together with presented examples. Supplementary the domination theory (DT) in the picture fuzzy graph. A few order, strength, cardinality, and domination of completeness, neighbors in a picture fuzzy graph, and the DDS and given some examples are likewise studied in the concept of picture fuzzy graph in the environment. The application of the politician campaign is novel exploiting the projected study and curious how to double dominate would relationship with the politician campaign. Finally, a comparison between the current effort and the prior effort is made, and the advantages of the work done in the context of a picture fuzzy graph are discussed.

A novel approach to fuzzy N-soft sets and its application for identifying and sanctioning cyber harassment on social media platforms

This study proposes a novel approach to fuzzy N-soft sets for handling cases where membership degree and grade are not related. In the standard model of fuzzy N-soft sets, membership degree and grade are assumed to be directly proportional. This assumption may not hold true in real-world situations, so a more flexible and nuanced approach is necessary. The proposed approach includes two novel algorithms for decision-making problems involving fuzzy N-soft sets. As a result, it is able to be adaptable and sensitive when addressing uncertainties in real-world scenarios, with a particular focus on identifying and sanctioning cyber harassment on social media platforms. Additionally, an innovative perspective and approach to decision-making problems involving fuzzy N-soft sets is introduced by extending an established selection process that prioritizes the dominant parameter, resulting in more precise and dependable outcomes. Our study offers an effective tool for decision-making in various fields, including e-commerce, social media, and product reviews.

TOPSIS method based on q-rung orthopair picture fuzzy soft environment and its application in the context of green supply chain management

<abstract> <p>Green supplier selection has been an important technique for environmental sustainability and reducing the harm of ecosystems. In the current climate, green supply chain management (GSCM) is imperative for maintaining environmental compliance and commercial growth. To handle the change related to environmental concern and how the company manages and operates, they are integrated the GSCM into traditional supplier selection process. The main aims of this study were to outline both traditional and environmental criteria for selecting suppliers, providing a comprehensive framework to assist decision-maker in prioritizing green supplier effectively. In order to address issue to simulate decision-making problems and manage inaccurate data. A useful technique of fuzzy set was proposed to handle uncertainty in various real-life problems, but all types of data could not be handled such as incomplete and indeterminate. However, several extensions of fuzzy set were considered, such as intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and q-rung orthopair fuzzy soft set considering membership and nonmember ship grade to handle the uncertainty problem. However, there was a lack of information about the neutral degree and parameterization axioms lifted by existing approaches, so to fill this gap and overcome the difficulties Ali et al. proposed a generalized structure by combining the structure of picture fuzzy set and q-rung orthopair fuzzy soft set, known as q-rung orthopair picture fuzzy soft sets, characterized by positive, neutral and negative membership degree with parameterization tools and aggregation operator to solve the multi criteria group decision-making problem. Additionally, the TOPSIS method is a widely utilized to assist individuals and organizations in selecting the most appropriate option from a range of choices, taking into account various criteria. Finally, we demonstrate an illustrative example related to GSCM to enhance competitiveness, based on criteria both in general and with a focus on environmental consideration, accompanied by an algorithm and flow chart.</p> </abstract>

Enhanced Academic Stress-Coping Skills Assessment in College Students: A Comparative Study of Neutrosophic Distance Measure and Proposed Cubic Pythagorean Fuzzy Hypersoft TOPSIS Method

In multi-criteria decision-making scenarios involving real numbers, interval numbers, and a combination of membership and non-membership grades, accurate decision-making is crucial yet challenging. The integration of diverse grade values into a single value poses a significant challenge for decision-makers. To address this issue, this study introduces the concept of a cubic Pythagorean fuzzy hypersoft set, facilitating information aggregation without ambiguity. The characteristics of correlation coefficients and aggregation operators are emphasized, underscoring their importance in decision-making processes. An algorithm based on correlation coefficients (CC) is proposed for the TOPSIS method, which ranks preferences based on their similarity to the ideal solution, applied here to examine how college students cope with academic stress. Furthermore, the efficiency of the proposed method is demonstrated through a comparative study, wherein the correlation coefficient in the TOPSIS method is contrasted with existing distance measures (DMs). Results indicate the superiority of CC in the TOPSIS method over DMs. In addition to comparing the proposed method with existing distance measures, the efficacy of the proposed approach is further demonstrated through a comparative analysis with established neutrosophic distance measures. This comprehensive evaluation highlights the robustness and versatility of the proposed method in addressing the complexities of multi-criteria decision-making scenarios, particularly in assessing stress management strategies among college students, thus providing valuable contributions to decision-making contexts. This study contributes to enhancing decision-making processes, particularly in evaluating stress management strategies among college students, thereby offering valuable insights for academic contexts.

A multi-attribute decision making context for supply chain management using possibility single-valued neutrosophic soft settings

Argued decisions, risk estimation, empirical study, forecasts, apprehension supervision, and productive exposition depend on the degree of possibility. It enables us to assess the degree to which specific results are acceptable and to make more informed decisions by drawing on the information at our disposal and logic. Although some scholars have previously examined hybrid structures resembling fuzzy soft sets with possibility degree settings serving as fuzzy membership grades, the current study introduces an innovative structure that permits more adaptable and comprehensive settings: single-valued neutrosophic grades, to serve as possibility degrees. Thus, this study aims to introduce a new mathematical structure, i.e., possibility single-valued neutrosophic soft set (psv-NSOS), which combines three important theories (i.e., possibility theory, single-valued neutrosophic theory, and soft set theory). The basic notions, and set-theoretic operations, i.e., union and intersection, of psv-NSOS are investigated and manipulated with matrix representations. Considering evaluating suppliers for a real estate construction project as a multi-attribute decision-making issue, an algorithm that utilizes the matrix manipulations of proposed set-theoretic operations is presented. The suggested algorithm?s robustness is confirmed by comparison to evaluate its dependability and adaptability for modeling uncertainties related to the supplier selection problem.

Linear Diophantine Fuzzy Sets: Image Edge Detection Techniques based on Similarity Measures

In the digital imaging process, fuzzy logic provides many advantages, including uncertainty management, adaptability to variations, noise tolerance, and adaptive classification. One of the techniques of digital image processing is the edge detection. The edge detection process is an essential tool to segment the foreground objects from the image background. So, it facilitates subsequent analysis and comprehension of the image’s underlying structural properties. This process can be moved on with the notion of fuzzy sets and their generalizations. The concept of Linear Diophantine fuzzy sets is a generalization of fuzzy sets where reference parameters correspond to membership and non-membership grades. This study aims to apply linear Diophantine fuzzy sets (LDFSs) to edge detection of images. The novelty of this paper is twofold. The first one is that we conduct a comprehensive evaluation to ascertain the similarity values using the linear Diophantine fuzzy similarity measure by leveraging the gray normalized membership values associated with fundamental edge detection techniques. The other is to modify the image pixels into the LDFSs and then filter the images by using the presented similarity measure operators given in the LDFS environment.

Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles

This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables. The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets. For this purpose, a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities. Then, an asynchronous fuzzy sampled-data controller, featuring distinct premise variables from the active suspension system, is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership. Furthermore, novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous H2 and H∞ performance requirements. Finally, the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles.

Accelerated Fuzzy C-Means Clustering Based on New Affinity Filtering and Membership Scaling

Fuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its many accelerated variants have low efficiency in the mid-to-late stage of the clustering process. In this stage, all samples are involved in updating their non-affinity centers, and the fuzzy membership grades of most samples, whose assignments remain unchanged, are still updated by calculating the sample-center distances. All these factors lead to the algorithms converging slowly. In this paper, a new affinity filtering technique is developed to recognize a complete set of non-affinity centers for each sample with low computations. Then, a new membership scaling technique is suggested to set the membership grades between each sample and its non-affinity centers to 0 and maintain the fuzzy membership grades for others. By integrating these two techniques, FCM based on new affinity filtering and membership scaling (AMFCM) is proposed to accelerate the whole convergence process of FCM. Numerous experimental results performed on synthetic and real-world data sets have shown the feasibility and efficiency of the proposed algorithm. Compared with state-of-the-art algorithms, AMFCM is significantly faster and more effective. For example, AMFCM reduces the number of FCM iterations by 80 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> on average.

Interval-Valued p,q-Rung Orthopair Fuzzy Exponential TODIM Approach and Its Application to Green Supplier Selection

An interval-valued q-rung orthopair fuzzy set (IVqrOFS) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q≥1. Expanding its applicability, we propose a refinement to it, termed the interval-valued p,q-rung orthopair fuzzy set, denoted IVp,qrOFS. This advancement enables the handling of scenarios where varied assessment levels for membership and non-membership grades are necessary, a challenge unaddressed by existing extensions of interval-valued intuitionistic fuzzy sets. We establish the fundamental mathematical operations for the IVp,qrOFS and explore their key properties. To compare interval-valued p,q-rung orthopair fuzzy (IVp,qrOF) numbers, a novel score function is put forward and compared to the known IVqrOFS-based score functions to determine its viability. Moreover, we present IVp,qrOF aggregation operators (AOs), accompanied by rigorous proof of their essential characteristics, including boundedness, monotonicity, and symmetry. This study introduces the interaction of IVp,qrOF criteria through the inter-criteria correlation (CRITIC) approach. This method determines criteria weights based on the proposed distance measurements and the score function. The CRITIC method is integrated with the exponential TODIM approach (exp-TODIM), resulting in an innovative decision-making framework that is less susceptible to parameter fluctuations and showcases a high stability. An illustrative example of selecting a suitable supplier is provided to demonstrate the practical application of the developed exp-TODIM approach. Finally, a sensitivity analysis is conducted to exhibit the method’s stability, and a comparative analysis is performed to elucidate its strengths and advantages.

On a value of a matrix game with fuzzy sets of player strategies

The present paper investigates a fuzzy matrix game with fuzzy sets of player strategies. We construct a game value with the help of Zadeh's extension principle in combination with an approach to fuzzy matrix games worked out by Liu and Kao. We prove that the FSs of players strategies in a fuzzy matrix game generate a game value in the form of a type-2 fuzzy set (T2FS) on the real line. Furthermore, the corresponding type-2 membership function is given. It is shown that the T2FS of the game value can be decomposed according to the secondary membership grades into a finite collection of fuzzy numbers. Each of them is the value of the corresponding fuzzy matrix game for crisp sets of player strategies. These sets are the corresponding cuts of the original fuzzy sets of player strategies. Illustrative examples are given.

On Kemeny Optimization Scheme for Fuzzy Set of Relations

The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation (T2FR). The decomposition approach was used to analyze the group T2FR. It is shown that the group T2FR can be decomposed according to secondary membership grades into a finite collection of Type-1 fuzzy relations. Each of them is a group fuzzy relation for a crisp set of DMs, which is the corresponding α-cut of the original fuzzy set of DMs. Illustrative examples are given.

A new ELECTRE-based decision-making framework with spherical fuzzy information for the implementation of autonomous vehicles project in Istanbul

This research study keenly employs the ground-breaking theory of ELECTRE method in order to advance the literature with a more competent technique for the frequently implemented and incredibly practical model of spherical fuzzy sets. The eminent characteristics, broader approach and adaptable model of spherical fuzzy set empowers the proposed strategy to captivate each type of the imprecise human judgement (whether in favor, against, neutral or hesitant) using a dependent and three independent membership grades. The remarkable novelty of the proposed approach is its successful application even with no criteria weights knowledge. Furthermore, the proposed technique processes the spherical fuzzy data and examines different types of preferences among alternatives using three threshold values. These preferences contribute to classify the outranking relations among the alternatives within five different levels of dominance. Later on, the iterative approach of distillation is deployed to figure out the final ranking. The proposed strategy is applied to meet the challenges in the implementation of autonomous vehicles in Turkey. After a through evaluation of five corridors via proposed technique in reference to fifteen criteria, metrobus corridor appears as the most appropriate for the autonomous vehicle operation. In the last, the consistency of the proposed approach is delineated via comparative analysis with existing spherical fuzzy CODAS and spherical fuzzy PROMETHEE approaches and other convincing evidences.

Changes to routes to Institution membership: a summary for members

IStructE Head of Membership, Rebecca Carey, explains the changes to the Institution's membership grades and qualifying requirements that have come into force in 2023.

On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies

The present paper investigates a finite game with fuzzy sets of player strategies. It is proven that Nash equilibria constitute a type-2 fuzzy set defined on the universal set of strategy profiles. Furthermore, the corresponding type-2 membership function is provided. This paper demonstrates that the Nash equilibria type-2 fuzzy set of the game can be decomposed based on the secondary membership grades into a finite collection of crisp sets. Each of these crisp sets represents the Nash equilibria set of the corresponding game with crisp sets of player strategies. A characteristic feature of the proposed decomposition approach is its independence from the chosen method for calculating the Nash equilibria in crisp subgames. Some properties of game equilibria T2FSs are studied. These sets correspond to specific partitions or cuts of the original fuzzy sets of player strategies. An illustrative example is also included for clarity.

On basic arithmetic operations for interval-valued intuitionistic fuzzy sets using the Hamming distance with their application in decision making

Atanassov’s intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂[0,1]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers.