Membership Grades Research Articles

Type-1 fuzzy forecasting functions with elastic net regularization

Fuzzy functions have recently been used for forecasting problems. The main concepts behind a fuzzy functions are to cluster the inputs using a fuzzy clustering method and to include the obtained membership grades and their non-linear transformations as new variables in the input matrix. Then, multiple linear regression models are solved for different clusters. However, adding related variables to the input matrix leads to the multicollinearity problem. Thus, the main contribution of the proposed method is to employ an elastic net in fuzzy functions to overcome the aforementioned problem. Two regularization terms occur in an elastic net that come from the ridge and the lasso regression. These regularization terms are optimized using the nested cross-validation approach to overcome the multicollinearity problem in the fuzzy functions method. Twelve practical time-series datasets are analyzed to evaluate the performance of the proposed fuzzy functions. The outstanding performance of the proposed method has been verified in terms of root mean squared errors and mean absolute percentage errors for the selected datasets.

Complex Spherical Fuzzy Decision Support System Based on Entropy Measure and Power Operator

The objectives of this paper are to define novel aggregation operators (AOs) for aggregating different complex spherical fuzzy numbers (CSFNs) under the influence of their membership grades. The uncertainties included in the information are dealt with in contemporary studies of the fuzzy set and its extensions by membership grades, which are a subset of real numbers that lose some relevant information and hence alter the decision results. The conversion to these complex spherical fuzzy sets addresses the classes’ uncertainty, whose ranges differ from the specific subset of the complex subset of the unit disk. For this purpose, we defined new CSF power AOs. Some of the desirable properties of these operators have also been investigated. A multiattribute group decision-making (MAGDM) approach is implemented in the structure developed by the CSFNs on the basis of these operators. A numerical example concerning the selection of the best alternatives is given to demonstrate the effectiveness of the defined method and is tested by comparing its results with the various methods.

Development and application of an analytical framework for mapping probable illegal dumping sites using nighttime light imagery and various remote sensing indices

Illegal dump sites (IDS) pose significant risks to human and the environment and are a pressing issue worldwide. Due to their secretive nature, the detection of IDS is costly and ineffective. In this study, an analytical framework was developed to detect probable IDSs in rural and remote areas using nighttime light (NTL) as a proxy for populated areas. An IDS probability map is produced by aggregation of Landsat-8 and Suomi NPP satellite imagery, multiple-criteria decision-making analysis, and classification tools. Six variables are considered, including modified soil adjusted index, land surface temperature, NTL, highway length, railway length, and the number of landfills. Vulnerability of the inhabitants on reserve lands was assessed using three sample regions. The method appears effective in reducing potential IDSs. Only about 7% of the 31,285 km2 study area are identified as probable IDS, being classified as “very high” and “high”. Landfills without permit are found more effective in lowering IDS occurrence. Spatial distributions of reserve lands and the maturity of highways network nearby may be more important than the length of railways when assessing the inhabitant vulnerability due to IDS. Highway length is the most decisive factor on IDS probability among all classes, with membership grades ranging from 0.99 to 0.55. Land surface temperature appears less effective for the identification of smaller scale IDS. NTL is more prominent on IDS probability in the “very high” class, with a membership grade of 0.80. The finding suggests that populated areas represented by NTL is a priori of IDS.

Mixed H∞ and passivity guaranteed cost proportional‐integral control for interval‐valued type‐2 fuzzy systems with input delay

AbstractThe paper focuses on the problem of mixed and passivity guaranteed cost control of an interval‐valued type‐2 (IT‐2) fuzzy system with time‐varying input delay and exogenous disturbance. For this, an IT‐2 fuzzy‐model‐based system with a mismatched membership grade function is formulated. The main objective is to design a proportional‐integral controller that stimulates our system to attain its equilibrium state even with the occupancy of exogenous disturbance and input delay in the system. In addition, a quadratic cost function is constructed such that the cost function of the closed‐loop IT‐2 fuzzy system is lower than the upper‐bound cost index. Mixed and passivity performance indices are then calculated to address the exogenous disturbance in the system. A set of new criteria ensuring the asymptotic stability of the closed‐loop IT‐2 fuzzy system with input delay are derived in terms of linear matrix inequalities with the aid of Lyapunov stability theory and the employment of a Wirtinger‐based inequality. Finally, two example simulations are conducted to validate our theoretical results.

Fuzzy C means Based Evaluation Algorithms For Cancer Gene Expression Data Clustering

The influx of data in bioinformatics is primarily in the form of DNA, RNA, and protein sequences. This condition places a significant burden on scientists and computers. Some genomics studies depend on clustering techniques to group similarly expressed genes into one cluster. Clustering is a type of unsupervised learning that can be used to divide unknown cluster data into clusters. The k-means and fuzzy c-means (FCM) algorithms are examples of algorithms that can be used for clustering. Consequently, clustering is a common approach that divides an input space into several homogeneous zones; it can be achieved using a variety of algorithms. This study used three models to cluster a brain tumor dataset. The first model uses FCM, which is used to cluster genes. FCM allows an object to belong to two or more clusters with a membership grade between zero and one and the sum of belonging to all clusters of each gene is equal to one. This paradigm is useful when dealing with microarray data. The total time required to implement the first model is 22.2589 s. The second model combines FCM and particle swarm optimization (PSO) to obtain better results. The hybrid algorithm, i.e., FCM–PSO, uses the DB index as objective function. The experimental results show that the proposed hybrid FCM–PSO method is effective. The total time of implementation of this model is 89.6087 s. The third model combines FCM with a genetic algorithm (GA) to obtain better results. This hybrid algorithm also uses the DB index as objective function. The experimental results show that the proposed hybrid FCM–GA method is effective. Its total time of implementation is 50.8021 s. In addition, this study uses cluster validity indexes to determine the best partitioning for the underlying data. Internal validity indexes include the Jaccard, Davies Bouldin, Dunn, Xie–Beni, and silhouette. Meanwhile, external validity indexes include Minkowski, adjusted Rand, and percentage of correctly categorized pairings. Experiments conducted on brain tumor gene expression data demonstrate that the techniques used in this study outperform traditional models in terms of stability and biological significance.

Possibilistic classification by support vector networks

In many real-world classification problems, the available information is often uncertain. In order to effectively describe the inherent vagueness and improve the classification performance, this paper proposes a novel possibilistic classification algorithm using support vector machines (SVMs). Based on possibility theory, the proposed algorithm aims at finding a maximal-margin fuzzy hyperplane by solving a fuzzy mathematical optimization problem Moreover, the decision function of the proposed approach is generalized such that the values assigned to the data vectors fall within a specified range and indicate the membership grade of these data vectors in the positive class. The proposed algorithm retains the advantages of fuzzy set theory and SVM theory. The proposed approach is more robust for handling data corrupted by outliers. Moreover, the structural risk minimization principle of SVMs enables the proposed approach to effectively classify the unseen data. Furthermore, the proposed algorithm has additional advantage of using vagueness parameter v for controlling the bounds on fractions of support vectors and errors. The extensive experiments performed on benchmark datasets and real applications demonstrate that the proposed algorithm has satisfactory generalization accuracy and better describes the inherent vagueness in the given dataset.

A study on weighted aggregation operators for q‐ rung orthopair m‐ polar fuzzy set with utility to multistage decision analysis

Modeling uncertainties with multipolar information is an important tool in computational intelligence to address complexities in real-world circumstances. An m-polar fuzzy set (mPFS) is the strong model to express multipolarity with m $m$ membership grades (MGs) in the unit closed interval [ 0 , 1 ] $[0,1]$ . A q-rung orthopair fuzzy set (qROFS) is the strong model to express vague and uncertain information with MGs and nonmembership grades (NMGs). The notion of q-rung orthopair m-polar fuzzy set is a new hybrid extension of both mPFS and qROFS. An ROmPFS is a generalized concept that has the ability to deal with multipolarity with m $m$ ordered pairs of MGs and NMGs. Motivated by these robust concepts, in this article, various aggregation operators (AOs) for the aggregation of q-rung orthopair m-polar fuzzy numbers are proposed, including q-rung orthopair m-polar fuzzy weighted averaging operator, symmetric q-rung orthopair m-polar fuzzy weighted averaging operator, q-rung orthopair m-polar fuzzy weighted geometric operator, symmetric q-rung orthopair m-polar fuzzy weighted geometric operator, and q $q$ -rung orthopair m-polar fuzzy Maclaurin symmetric mean operator. On the basis of proposed AOs, a robust multicriteria decision-making approach is proposed. An application of proposed AOs is presented to address economic crises during COVID-19. Furthermore, the comparison analysis is designed to discuss the validity and rationality of proposed AOs.

The exploitation of “Grade of Membership (GoM) model” and “Combined Analysis method” in analysing of urban dynamics and urban hierarchy in Khorasan region (1956-2016)

The exploitation of “Grade of Membership (GoM) model” and “Combined Analysis method” in analysing of urban dynamics and urban hierarchy in Khorasan region (1956-2016)

Refined Pythagorean Fuzzy Sets: Properties, Set-Theoretic Operations and Axiomatic Results

Refined Pythagorean fuzzy set is the generalization of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, refined fuzzy set, and refined intuitionistic fuzzy set as it not only bears the characteristics of these models but also addresses their limitations for real-life scenarios with sub-grades corresponding to membership and non-memberships grades. In order to equip the existing literature with conceptual framework of refined Pythagorean fuzzy sets, essential properties, set-theoretic operations, and axiomatic results are characterized with the help of numerical examples.

An approach to robust condition monitoring in industrial processes using pythagorean membership grades

In this paper, a robust approach to improve the performance of a condition monitoring process in industrial plants by using Pythagorean membership grades is presented. The FCM algorithm is modified by using Pythagorean fuzzy sets, to obtain a new variant of it called Pythagorean Fuzzy C-Means (PyFCM). In addition, a kernel version of PyFCM (KPyFCM) is obtained in order to achieve greater separability among classes, and reduce classification errors. The approach proposed is validated using experimental datasets and the Tennessee Eastman (TE) process benchmark. The results are compared with the results obtained with other algorithms that use standard and non-standard membership grades. The highest performance obtained by the approach proposed indicate its feasibility.

Data-Driven Anomaly Detection and Event Log Profiling of SCADA Alarms

Network human operators’ decision-making during grid outages requires significant attention and the ability to perceive real-time feedback from multiple information sources to minimize the number of control actions required to restore service, while maintaining the system and people safety. Data-driven event and alarm management have the potential to reduce human operator cognitive burden. However, the high complexity of events, the data semantics, and the large variety of equipment and technologies are key barriers for the application of artificial intelligence (ai) to raw scada data. In this context, this paper proposes a methodology to convert a large volume of alarm events into data mining terminology, creating the conditions for the application of modern ai techniques to alarm data. Moreover, this work also proposes two novel data-driven applications based on scada data: (i) identification of anomalous behaviors regarding the performance of the protection relays of primary substations, during circuit breaker tripping alarms in hv and mv lines; (ii) unsupervised learning to cluster similar events in hv line panels, classify new event logs based on the obtained clusters and membership grade with a control parameter that helps to identify rare events. Important aspects associated with data handling and pre-processing are also covered. The results for real data from a dso showed: (i) that the proposed method can detect unexpected relay pickup events, e.g., one substation with nearly 41% of the circuit breaker alarms had a ’atypical’ event in their context (revealed an overlooked problem on the electrification of a protection relay); (ii) capability to automatically detect and group issues into specific clusters, e.g., SF6 low-pressure alarms and blocks with abnormal profiles caused by event time-delay problems.

The Prognosis of Allergy-Based Diseases Using Pythagorean Fuzzy Hypersoft Mapping Structures and Recommending Medication

The Pythagorean fuzzy set (PFS), which Yager extended, is a novel tool for dealing with ambiguity when considering membership(MS) grade p and non-membership (NMS) q that fulfil the criteria <inline-formula> <tex-math notation="LaTeX">$p^{2} + q^{2} \leq 1$ </tex-math></inline-formula> allowing the structure to characterise fuzziness more thoroughly and precisely than intuitionistic fuzzy sets. The Pythagorean Fuzzy Hypersoft (PFHS) set theory is a useful method for dealing with abnormalities and uncomfortable information in real-life situations. The Pythagorean fuzzy set and the Hypersoft set, which comprise the truthfulness grade (TG) and falsehood grade (FG) in the Pythagorean environment, are combined in the PFHS principle. This study tries to define the arguments around allergy diagnosis and the effects that arise with it. After considering the dire outcomes of Allergies, it becomes challenging to distinguish between the various types of Allergies and their complexity. Because the false portions of practical assessments are usually ignored, precision in the person&#x2019;s developmental history is difficult to recognize, and number of sessions cannot be projected. This work presents the PFHS set and PFHS mapping with its inverse mapping (INM) to alleviate these constraints. These notions are capable and necessary for correctly analyzing the problem by combining it with scientific modelling. This study establishes a link between symptoms and medications, lowering the narrative&#x2019;s complexity. For the various types of allergies, a table based on a fuzzy interval between &#x005B;0, 1&#x005D; is created. The techniques that are based on PFHS-mapping, which is used to effectively identify a problem then choose the right treatment for each patient&#x2019;s condition.

On neutrosophic αψ -supra open sets

Neutrosophic topological space is an extension of fuzzy topology. Neutrosophic topological space addresses each element’s membership, indeterminacy and non-membership grades. Dropping an axiom in the neutrosophic topological space produces a new topological space called neutrosophic supra topological space. Elements in this neutrosophic supra topology are neutrosophic sets. We established the neutrosophic αψ-supra open set in neutrosophic supra topological spaces in this paper. Also, we investigate the properties of the newly defined set. Neutrosophic αψ -supra continuity is introduced and studied subsequently.

N,m-Rung Orthopair Fuzzy Sets With Applications to Multicriteria Decision Making

A q-rung orthopair fuzzy set is one of the effective generalizations of fuzzy set for dealing with uncertainties in information. Under this environment, in this study, we define a new type of extensions of fuzzy sets called n,m-rung orthopair fuzzy sets and investigate their relationship with Fermatean fuzzy sets, Pythagorean fuzzy sets and intuitionistic fuzzy sets. The n,m-rung orthopair fuzzy sets can supply with more doubtful circumstances than Fermatean fuzzy sets, Pythagorean fuzzy sets and intuitionistic fuzzy sets because of their larger range of depicting the membership grades. There is a symmetry between the values of this membership function and non-membership function. Here, any power function scales are utilized to widen the scope of the decision-making problems. In addition, the novel notion of an n,m-rung orthopair fuzzy set through double universes is more flexible when debating the symmetry between two or more objects that are better than the diffusing concept of an n-rung orthopair fuzzy set, as well as m-rung orthopair fuzzy set. The main advantage of n,m-rung orthopair fuzzy sets is that it can describe more uncertainties than Fermatean fuzzy sets, which can be applie in many decision-making problems. Then, we discover the essential set of operations for the n,m-rung orthopair fuzzy sets along with their several properties. Finally, we introduce a new operator, namely, n,m-rung orthopair fuzzy weighted power average (n,m-ROFWPA) over n,m-rung orthopair fuzzy sets and apply this operator to the MADM problems for evaluation of alternatives with n,m-rung orthopair fuzzy information.

Cubic m-polar fuzzy topology with multi-criteria group decision-making

&lt;abstract&gt;&lt;p&gt;The concept of cubic m-polar fuzzy set (CmPFS) is a new approach to fuzzy modeling with multiple membership grades in terms of fuzzy intervals as well as multiple fuzzy numbers. We define some fundamental properties and operations of CmPFSs. We define the topological structure of CmPFSs and the idea of cubic m-polar fuzzy topology (CmPF topology) with P-order (R-order). We extend several concepts of crisp topology to CmPF topology, such as open sets, closed sets, subspaces and dense sets, as well as the interior, exterior, frontier, neighborhood, and basis of CmPF topology with P-order (R-order). A CmPF topology is a robust approach for modeling big data, data analysis, diagnosis, etc. An extension of the VIKOR method for multi-criteria group decision making with CmPF topology is designed. An application of the proposed method is presented for chronic kidney disease diagnosis and a comparative analysis of the proposed approach and existing approaches is also given.&lt;/p&gt;&lt;/abstract&gt;

Synthesizing fuzzy tree automata

Fuzzy tree automata are mathematical devices for modeling and analyzing vaguely defined tree structures. The behavior of a fuzzy tree automaton generates a fuzzy tree language by mapping a set of regular trees on a ranked alphabet to fuzzy membership values. It calculates the membership grade of trees using a set of rules that process their structural characteristics. This paper deals with constructing fuzzy tree automata models that their behavior satisfies a set of given logical propositions (called properties) on the structure of trees. Our goal is uncertainty modeling by synthesizing fuzzy tree automata whose behavior is described by fuzzy linguistic variables. In this regard, we first provide several patterns and heuristic tricks and techniques for constructing fuzzy tree automata that satisfy simple properties. Then, we develop a method for modeling complex propositional formulas based on the conversion of a logical formula into a computation tree, as well as a step-by-step combination of models.

Aircraft total turnaround time estimation using fuzzy critical path method

Airport Collaborative Decision Making (ACDM) flight scheduling plans rely on accurate predictions of both optimal and reliable aircraft turnaround times, which is one of the most difficult things to complete. In order to account for the effects of randomness and fuzziness on the turnaround process duration, this paper deals with transforming the probability distribution of well-fitted sub-processes into a cumulative density function, which is equivalent to the fuzzy membership function (FMF), and then using goodness-of-fit to determine the fuzzy membership grade of each turnaround sub-process. The turnaround time is calculated using the fuzzy critical path method (FCPM), which is a combination of the Critical Path Method (CPM) and fuzzy set theory. In order to verify this estimate, we created the FMF using historical data and compared it to turnaround times based on FCPM. A linear regression model is used to examine the relationship between arrival delays and the FCPM-based turnaround process. We also use historical data to generate fuzzy sets of different arrival delays using Frankfurt airport data from the summer of 2017 and conclude that delays are positively correlated with the FCPM-based turnaround process.

Group Generalized q-Rung Orthopair Fuzzy Soft Sets: New Aggregation Operators and Their Applications

In recent years, q-rung orthopair fuzzy sets have been appeared to deal with an increase in the value of q &gt; 1 , which allows obtaining membership and nonmembership grades from a larger area. Practically, it covers those membership and nonmembership grades, which are not in the range of intuitionistic fuzzy sets. The hybrid form of q-rung orthopair fuzzy sets with soft sets have emerged as a useful framework in fuzzy mathematics and decision-makings. In this paper, we presented group generalized q-rung orthopair fuzzy soft sets (GGq-ROFSSs) by using the combination of q-rung orthopair fuzzy soft sets and q-rung orthopair fuzzy sets. We investigated some basic operations on GGq-ROFSSs. Notably, we initiated new averaging and geometric aggregation operators on GGq-ROFSSs and investigated their underlying properties. A multicriteria decision-making (MCDM) framework is presented and validated through a numerical example. Finally, we showed the interconnection of our methodology with other existing methods.

Novel fuzzy matrix swap algorithm for fuzzy directed graph on image processing

This paper discusses a fuzzy-directed graph-based theoretical technique for image analysis. Due to the property that, in a fuzzy graph, the membership grade of the edges must be less than or equal to the minimum of the membership grades of the end vertices, they do not straightaway represent an image. First, a novel method to overcome this barrier is proposed by directly transforming an image as a collection of fuzzy directed graphs using a fuzzy graph-based matrix swap algorithm. Second, the fuzzy graph terminologies for representing images are described through main definitions and theorems. Finally, the application of the algorithm is demonstrated with the help of a fuzzy inference system under two different scenarios of image classification.

Fuzzy-soft set approach for ranking the functional requirements of software

Software requirements are the need of the stakeholders which are determined by the requirements elicitation techniques. Different fuzzy based methods have been developed to select the software requirements based on the ranking order so that high priority requirements can be implemented during the development process. Based on our review, we found that in these methods’ prior information about the data such as grades of membership during the computation is required and these methods are also incompatible with the parameterization tools. To address this issue, we proposed an approach for ranking the functional requirements of software using fuzzy-soft set theory. The relative deviation between counts of non-functional requirements has been used to construct the fuzzy-soft sets. The weights of the non-functional requirements and the ranking order of the functional requirements are computed from fuzzy soft-set derived from raw data in which no prior information about data is required. An example is presented to illustrate the application of the proposed approach.