Fuzzy Set Membership Research Articles

Intuitionistic fuzzy least squares MLTSVM for noisy label data using label-specific features and local label correlation

The multilabel twin support vector machine (MLTSVM) has been widely applied to multilabel classification fields because of its excellent classification performance, but it has the following three disadvantages. (a) In practical classification tasks, due to human negligence or some objective factors, there are many data with noise labels. Noisy label data have a negative effect on generating classification hyperplanes. However, MLTSVM cannot effectively reduce the negative effects on noisy label data. (b) Each label has its own specific features. However, for each label, MLTSVM can only use the same feature representation for classification. Therefore, it cannot obtain the optimal classification results. (c) In multilabel classification problems, there is a general correlation among the labels. However, when MLTSVM constructs a classification hyperplane for each label, it ignores the label correlation information. To address the above disadvantages, in this paper, a novel algorithm is proposed the called intuitionistic fuzzy least squares MLTSVM for noisy label data using label-specific features and local label correlation (SFLLC-IFLSMLTSVM). First, SFLLC-IFLSMLTSVM constructs an intuitionistic fuzzy set for each label; second, SFLLC-IFLSMLTSVM exploits the membership and nonmembership degrees in the intuitionistic fuzzy set to filter out the samples with noise labels and then performs clustering analysis to extract the label-specific features and the structure information of samples; finally, SFLLC-IFLSMLTSVM mines the local label correlation information in the process of constructing classification hyperplanes and exploits the membership and nonmembership degrees to suppress the negative effects of noise labels. Extensive comparative experiments on multilabel datasets show that SFLLC-IFLSMLTSVM can efficiently handle the multilabel classification problems with noise labels.

Shadowed set approximations of L-fuzzy sets

Pedrycz shadowed sets are three-way approximations of fuzzy sets by transforming the infinite levels of fuzzy set membership grades in the unit interval [0,1] into three levels. The three levels represent qualitatively the sets of the white, grey, and black members of a shadowed set. In this paper, we generalize the notion of shadowed sets to the case of L-fuzzy sets by making three new contributions. First, we consider two representations of a shadowed set. One is a three-valued L-fuzzy set and the other is three pairwise disjoint sets. Second, we introduce two methods for constructing a shadowed set. One divides a finite lattice based on the notion of a pair of a set of designated core membership grades and a set of designated null membership grades. The other uses a pair of threshold sets, which generalizes the method that uses a pair of thresholds. We study formal properties of the two methods and show that they are equivalent. Finally, based on a distance function on a lattice, we present a simple method to build the sets of designated core and null membership grades.

METHOD OF HIGH-PRECISION NEURO-FUZZY SYSTEMS DEFUZZIFIERS’ AUTOMATIC CONSTRUCTION

Increasing the precision of neuro-fuzzy approximation systems is considered. Modification of defuzzifier, which allows producing multiple types of approximating functions is presented. RMSE (Root Mean Square Error), maximal error, training time and models’s size are used to evaluate the efficiency of proposed method. Post-processing functions were also considered as a tool to increase approximation precision. Common solution to this problem is a modification of model’s fuzzy sets (membership functions and their number), which significantly increases model’s size and complexity. Given approach uses search algorithms to find the configuration of defuzzification layer, which produces the best approximation precision for a given function and fuzzy sets configuration, since all possible configurations are checked. It is possible to model classic approximation methods and combine them. Possible modifications of presented search algorithms application are described. Search depth can be limited in order to reduce the size of produced model. The computing experiment, aimed at finding best approximation precision was carried out. Presented method provided lowering of RMSE without significant increasing of model’s size. Using Fourier series components in resulting expression can be used for precise periodic functions approximation or for general precision improvement. Using post-processing functions provided significant improvement in precision for multiplication approximation, which proves, that it can be used as another tool to be used to reduce errors in some specific cases.

An integrated complex T-spherical fuzzy set and soft set model for quantum computing and energy resource planning

This study introduces the Complex T-Spherical Fuzzy Soft Set (CTSFSS), a novel and practical model for representing two-dimensional ambiguous information. This is achieved by integrating the Complex T-Spherical Fuzzy Set (CTSFS) with the Soft Set (SS). The development of the CTSFSS theory is motivated by the absence of neutral membership in complex q-rung orthopair fuzzy soft sets and the limitations of Traditional Spherical Fuzzy Soft Sets (TSFSS) in capturing two-dimensional data. Data storage and processing in the modern technological landscape necessitate sophisticated algorithmic computations and robust representation of information. To this end, computational systems predominantly rely on a binary system structured on two fundamental states: 0 (off) and 1 (on). Moreover, the significance of energy resources and computer-aided tools is underscored in this domain, especially considering the potential impact of quantum computing and advances in energy resources on the evolution of digital technology. In addressing these complexities, we propose Complex T-Spherical Fuzzy Soft Relations (CTSFSRs), formulated through the Cartesian product of two CTSFSSs. These relations are adept at handling complex and uncertain data in real-world scenarios. We define and categorize various types of CTSFSRs, followed by an in-depth analysis of their outcomes. Additionally, this paper introduces innovative visualization techniques based on CTSFSRs, tailored for decision-making processes involving energy resources and quantum computing applications. The efficacy and applicability of these proposed methodologies are substantiated through comparative analysis with existing models.

Исследование методов модификации функций принадлежности нечетких множеств на основе эталонов

Fuzzy set membership functions are widely used to reflect expert preferences in situations of uncertainty. Procedures for modifying membership functions provide the opportunity to obtain new functions based on existing ones without the additional involvement of experts. The work examines existing and proposes new approaches to the construction of modification procedures, methods for their implementation and compensation for the difficulties arising in this case.

Condition Rating of Bridge Decks with Fuzzy Sets Modeling for SF-GPR Surveys

Highway agencies monitor the condition of thousands of bridge decks every year. Even though Ground Penetrating Radar (GPR) has been used in bridge-deck evaluation, Step-Frequency GPR (SF-GPR) provides advanced condition assessment yet requires extensive and complex post-processing analysis. An SF-GPR analysis system was recently developed and used for monitoring the condition of all the bridge decks in the state of Maryland. The objective of this study was to develop a bridge deck condition rating approach using fuzzy sets modeling on the SF-GPR data and analysis. The fuzzy sets membership functions needed to reflect rating score categories similar to those considered in the National Bridge Inventory (NBI) database for uniformity. Thus, the fuzzy sets modeling was built considering nine condition membership functions. The overall bridge deck condition score leading to each of the nine condition states was based on both physical and condition-related bridge deck parameters as obtained from the SF-GPR analysis. The modeling approach is presented herein, along with two bridge deck examples. The proposed novel fuzzy sets modeling can be considered for possible adoption elsewhere where similar GPR systems are used.

Автоматизація підбору кадрового складу за принципами нечіткої логіки

This article discusses the development of an expert system for personnel selection using fuzzy logic. The system uses a fuzzy set structure and membership functions for each criterion to calculate how well a candidate matches the criteria. The algorithm was implemented in Python and the results show that the system can improve automated recruitment for vacant positions and be developed further as a software product.

Comparative analysis of Fuzzy Tsukamoto's membership functions for determining irrigated rice field feasibility status

The representation of the fuzzy set membership curve consisting of trapezoidal, triangular, and linear shapes, has an important role in the fuzzy logic system. The selection of the curve's shapes determines the useable membership function and affects the fuzzy output value. Previous studies generally used curves that had been employed in predecessors or other studies that did not explain the reason for choosing a fuzzy member curve. This condition became problem because there was not a guide in selecting the appropriate membership function model for the parameters used in the fuzzy process so that most researchers only use membership functions that are commonly used in previous studies or in the same case as their research. The purpose of this study was to determine the effect of selecting trapezoidal and triangular curves on the performance of Tsukamoto's fuzzy logic for determining the rice-fields suitability status. The research methodology comprised 3 main stages. The first stage was data collecting, to collect soil pH values, soil moisture, and air temperature in rice fields. The second stage was the implementation of the Tsukamoto fuzzy. At this stage, two membership function curves were used. The third stage was a comparative analysis of Tsukamoto's fuzzy's output of trapezoidal and triangular curves. The results obtained indicate that there is no significant performance difference between the two different membership functions. The results of the research with the trapezoidal membership function have a better accuracy rate of 93% while the triangular membership function has an accuracy rate of 90%.

MODEL OF THE PROCESS OF GEOSPATIAL MULTI-CRITERIA DECISION ANALYSIS FOR TERRITORIAL PLANNING

Context. The process of multi-criteria decision analysis for territorial planning and rational placement of spatial objects, based on modeling the properties of the territory, is considered. Objective. Development of technology for multi-criteria decision analysis for territorial planning based on the apparatus of the theory of fuzzy sets and functions of geoinformation analysis. Method. An object-spatial approach to the formation of a set of alternatives and criteria is proposed, according to which the process of multicriteria decision analysis is divided into two stages: macro- and microanalysis.The macroanalysis stage involves the assessment of the ecological and socio-economic properties of the territory using geomodeling functions. The paper provides a formalized description of the macroanalysis stage, including methods for assessing the qualitative and quantitative impact of spatial objects on the properties of the territory and decomposing objects into thematic layers of criteria. At the stage of microanalysis, the ranking of alternatives is performed taking into account the chosen decision-making strategy. The method of standardization of criteria attributes using fuzzy set membership functions and the modification of the method for calculating the coefficients of relative importance (weights) of criteria, taking into account the spatial heterogeneity of the preferences of the decision maker, are considered. A comparative analysis of the methods for aggregating the estimates of alternatives according to different criteria has been carried out. A feature of the presented technology of geospatial multi-criteria decision analysis of decisions for territorial planning is the possibility of its integration into modern geographic information systems. Results. The procedure of geospatial multi-criteria decision analysis was implemented in the environment of the geographic information system ESRI ArcGIS 10.5 and was studied in solving the spatial problem of rational location of an enterprise. Conclusions. The proposed object-spatial approach to multi-criteria decision analysis makes it possible to explicitly take into account the spatial heterogeneity of geographic data, which is the result of the influence of geographic objects on the properties of the territory. The developed technology can be used to solve a wide range of problems related to determining the most rational placement of various capital construction and infrastructure facilities.

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

In this article, the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering. First, an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule. Then, compared to traditional prediction-based ones, two types of fuzzy set-membership filters are proposed to effectively improve filtering performance, where the structure of both filters consists of two parts: prediction and filtering. Under the locally Lipschitz continuous condition of membership functions, unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error. Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state. Finally, the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.

Soft-sensing of effluent total phosphorus using adaptive recurrent fuzzy neural network with Gustafson-Kessel clustering

To address the issue of soft-sensing of effluent total phosphorus in wastewater treatment processes (WWTPs), a soft-sensing system based on an adaptive recursive fuzzy neural network with Gustafson-Kessel (GK) clustering and hierarchical adaptive second-order optimization algorithm (HAS) is proposed in this paper. In GK-ARFNN, first, the GK clustering algorithm was utilized to cluster the input–output dataset. Thus, the establishment of the initial fuzzy rule base and the determination of the parameter value of the fuzzy set membership function was realized. Then, the recursive layer was added into FNN to improve the dynamic mapping ability of the system. Finally, the HAS algorithm was developed based on the improved Levenberg-Marquardt (LM) optimization algorithm, and all the free parameters of the GK-ARFNN were adjusted online using HAS to improve the generalization capability and prediction accuracy of the soft-sensing system. In addition, the convergence of the proposed GK-ARFNN algorithm was also analyzed in this paper, which can ensure the effectiveness of the solutions to modelling issues for practical industrial processes. The simulation results demonstrate that the GK-ARFNN-based soft-sensing system introduced in this paper achieved satisfactory accuracy in the prediction of effluent total phosphorus in WWTPs. The source codes of GK-ARFNN and some competitors can be downloaded from https://github.com/hyitzhb/GK-ARFNN.

Real-time deep learning-based market demand forecasting and monitoring

• Develop a CNN algorithm consists of two parts of feature extraction and classification in one model which makes it a unique and practical model in the area. • Develop a model to find the highest effective features for the market demand prediction • Training the CNN hyper parameters using a heuristic model based on PSO . • Considering the very complexity of the market demand in the new competitive environment using a novel fuzzy-based PSO • Use the fuzzy membership concept with aid of PSO to change its parameters dynamically rather than considering constant values. Abstract The concept of market demand forecasting is a very precious and significant problem in the industry without which the generator companies would not be able to give a suitable offer and may experience big losses. This research introduces a novel deep learning based on convolutional neural networks (CNN) to learn the market behavior in details. The model comprises a weight update mechanism in the backpropagation process of CNN to enhance its performance. Moreover, a fuzzy particle swarm optimization (FPSO) based algorithm is used to enhance the CNN performance and find the most accurate predictions. The proposed FPSO would utilize the fuzzy set theory and membership function to update the weighting coefficients . To validate this proposal, real market demand data are used as the benchmark and the results are discussed in the paper. The simulation results prove the suitable performance of the proposed CNN-FPSO model.

A Critique of the Capital Market Content in Nigerian Real Estate Education

The Nigerian Stock Exchange (NSE) is taking on an increasing relevance for the Nigerian estate surveyor and valuer as it grows in capitalization and sophistication. This can be seen in the NSE’s second-largest status in sub-Saharan Africa, the introduction of property securitization and the listing of property companies. Since these changes have implications for the valuer’s professional practice, they necessitate an evaluation of the real estate training curriculum. The capital market content of real estate education in Nigeria is examined in this paper by assessing the knowledge held by recent graduates of estate management. A questionnaire founded on a checklist of pertinent issues which realistically depict a working knowledge of Nigeria’s much improved stock market was used to collect data. This was analyzed by simple descriptive tools to provide a basis for evaluation. The results point to a scanty curriculum. In addition, there is a low awareness of the administrative and economic functions of the NSE. Furthermore, respondents have a poor understanding of core issues in equity investment analysis. Again, there is an inadequate grasp of the relationship between the two investment alternatives, although a majority rightly credit property as a better option. Lastly, respondents mainly do not consider an understanding of the market as relevant to their professional function in a modern economy. The study concludes that the demonstrated knowledge of respondents suggests that the curriculum does not have adequate content on the capital market. It is, therefore, recommended that the capital market content of the estate management course be enriched with more depth and detail which adequately reflect the increasing significance of the market to the valuer’s practice and his true role as an investment adviser in an increasingly financially interconnected world.

Sensitivity Analysis of Suspected External Driving Factors Contributing to Land Use Land Cover Dynamics in Jos Plateau State, Nigeria

Land use land cover change (LULCC) processes are directly or indirectly product of underlying causative factors playing out on the landscape. This study examines the contributing factors responsible for LULCC in Jos Plateau state using two different methods. The Analytical hierarchical process (AHP) and Binary models were used to prepare sixteen (16) suspected external driving factors (EDFs). Euclidean distance analysis was carried out on the proximity EDFs as well as reclassification based on AHP scale 1 – 9 and binary mode as 1 & 0. Saaty’s pairwise comparison matrix was employed to generate the weights for all the EDFs with a consistency index (CI) of 0.17was achieved. Suitability images were generated by multiplying each EDF with the corresponding weight. The fuzzy set membership standardization was carried out on the AHP image through sigmoidal function type with monotonically increasing membership function.The multiple regression technique was used to measure the sensitivity of each driver against the change period (1986 – 2019). The result shows that five (5) EDFs where consistent in both approaches (AHP & Binary). They are: distance to conflict areas, distance to major roads, LULC, distance to settlements and distance to river/ channels. It is therefore, appropriate to examine EDFs to know how each driver is contributing to the changing landscape in the study area. The findings has revealed the main factors driving LULC changes in the study area and has provided a reference frame for assisting in the development of sustainable land management and ecological protection policy making and decisions.

Evaluation of Wind Turbine Failure Modes Using the Developed SWARA-CoCoSo Methods Based on the Spherical Fuzzy Environment

Accurately recognizing potential failures in the early stages of providing products or services can prevent the loss of investment and time and reduce the risk of safety hazards. Failure mode and effects analysis (FMEA) is a conventional approach for detecting and prioritizing the probable failures of a product’s design or production process. Nevertheless, the traditional risk priority number (RPN) method has come under criticism for its deficiencies. This paper proposes a modified FMEA method based on fuzzy Multi-Criteria Decision Making (MCDM) techniques to cope with the weaknesses of the previous methodologies and improve the primary method. The concept of spherical fuzzy sets (SFS) is utilized to address the vagueness and impreciseness of the information that allows the experts to have more freedom in making decisions by including membership, non-membership, and hesitation of fuzzy sets. Initially, the procedure of assigning weights to the RPN criteria is implemented with SFS step-wise weight assessment ratio analysis (SWARA). Then, the failure modes are ranked by the SFS combined compromise solution (CoCoSo) method. The effectiveness and practicality of the suggested approach are illustrated through a case study on the Manjil wind farm in Iran. Results show that the suggested model is more reliable and realistic to be utilized in the prioritization of failures than the common FMEA method or other integrated MCDM approaches.

The Statistical Methods of Membership Function in Structural Serviceability Failure Criterion

The failure criterion of structural serviceability is often fuzzy, which has a direct impact on the results of structural reliability analysis. Membership function is a basic mathematical tool to describe the fuzziness of failure criteria. At present, the fuzzy statistical method for generating the fuzzy set membership function is to take the numerical interval of the fuzzy set as a sample, and directly generate the membership function through statistics. However, this kind of sample will cover the uncertainty of the individual's understanding of fuzzy boundaries to a certain extent, and its statistical results are difficult to truly reflect the characteristics of fuzzy sets. The fuzzy boundary is described by the membership density function, and the numerical interval covering the fuzzy boundary is taken as the sample. The fuzzy statistical method for generating the membership density function is proposed, and the indirect statistical method for generating the membership function is established. The comparative analysis results show that the membership functions generated by the two statistical methods are different. The membership function generated by indirect statistical method can fully reflect the uncertainty of the individual's understanding of the fuzzy boundary, more truly reflect the characteristics of the fuzzy set, and provide a more solid foundation for the fuzzy probability analysis of structural serviceability.

The New Fuzzy Analytical Hierarchy Process with Interval Type-2 Trapezoidal Fuzzy Sets and Its Application

The degree of type-1 fuzzy sets membership function cannot express the linguistic variable of a complex problem. The type-2 fuzzy sets as a problem solver such that more fuzziness for constructing membership functions can be handled. Recently, many multi-criteria decision making (MCDM) methods have been expanded using type-2 fuzzy sets. Analytical Hierarchy Process (AHP) is one of the well-known MCDM that can take into account multiple and conflicting criteria at the same time. Our goal is to develop an interval type-2 trapezoidal fuzzy AHP through the new proposed ranking i.e. the modified total integral value. Based on the illustrative examples for trapezoidal type-2 fuzzy sets, the new proposed ranking has a well-performance in ranking. Furthermore, we apply the new trapezoidal type-2 fuzzy AHP to a supplier selection problem. Based on the results of the application, the new fuzzy AHP has the same ranking results as the existing fuzzy AHP.

Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear Functions

Summary. IF-THEN rules in fuzzy inference is composed of multiple fuzzy sets (membership functions). IF-THEN rules can therefore be considered as a pair of membership functions [7]. The evaluation function of fuzzy control is composite function with fuzzy approximate reasoning and is functional on the set of membership functions. We obtained continuity of the evaluation function and compactness of the set of membership functions [12]. Therefore, we proved the existence of pair of membership functions, which maximizes (minimizes) evaluation function and is considered IF-THEN rules, in the set of membership functions by using extreme value theorem. The set of membership functions (fuzzy sets) is defined in this article to verifier our proofs before by Mizar [9], [10], [4]. Membership functions composed of triangle function, piecewise linear function and Gaussian function used in practice are formalized using existing functions. On the other hand, not only curve membership functions mentioned above but also membership functions composed of straight lines (piecewise linear function) like triangular and trapezoidal functions are formalized. Moreover, different from the definition in [3] formalizations of triangular and trapezoidal function composed of two straight lines, minimum function and maximum functions are proposed. We prove, using the Mizar [2], [1] formalism, some properties of membership functions such as continuity and periodicity [13], [8].

Novel Approach for Third-Party Reverse Logistic Provider Selection Process under Linear Diophantine Fuzzy Prioritized Aggregation Operators

Aggregation operators are fundamental concept for information fusion in real-life problems. Many researchers developed aggregation operators for multi-criteria decision-making (MCDM) under uncertainty. Unfortunately, the existing operators can be utilized under strict limitations and constraints. In this manuscript, we focused on new prioritized aggregation operators which remove the strict limitations of the existing operators. The addition of reference parameters associated with membership and non-membership grades in the linear Diophantine Fuzzy sets provide a robust modeling for MCDM problems. The primary objective of this manuscript is to introduce new aggregation operators for modeling uncertainty by using linear Diophantine Fuzzy information. For this objective we develop aggregation operators (AO) namely, "linear Diophantine Fuzzy prioritized weighted average" (LDFPWA) operator and "linear Diophantine Fuzzy prioritized weighted geometric" (LDFPWG) operator. Certain essential properties of new prioritized AOs are also proposed. A secondary objective is to discuss a practical application of third party reverse logistic provider (3PRLP) optimization problem. The efficiency, superiority, and rationality of the proposed approach is analyzed by a numerical example to discuss 3PRLP. The symmetry of optimal decision and ranking of feasible alternatives is followed by a comparative analysis.

Implementation of Minkowski-Chebyshev Distance in Fuzzy Subtractive Clustering

Clustering is a method of the grouping which is done by looking at the similarities between data in a data set. Fuzzy clustering is a clustering method that uses fuzzy set membership values as the basis for grouping data. Fuzzy Subtractive Clutering (FSC) is a fuzzy clustering method where the number of clusters to be formed is unknown. The concept of FSC is to determine the highest data density and the data with the most number of neighbors will be selected as the center of the cluster. Thus, the size of the proximity or distance between points is needed to determine the members of each cluster. The distance used in this study is a combination of the Minkowski and Chebyshev distances. The number of clusters formed will be evaluated using the Partition Coefficient (PC) value where the highest PC value indicates the best number of clusters. The results obtained indicate that the best clusters are three clusters with a PC value of 0.7422