Novel construction methods for picture fuzzy divergence measures with applications in pattern recognition, MADM, and clustering analysis

In this paper, we first give an example to show that Theorem 1 in Hung and Yang (Inf Sci 178(6):1641–1650, 2008) does not hold, implying that the J-divergence introduced by Hung and Yang does not satisfy the axiomatic definition of intuitionistic fuzzy divergence measure. Inspired by this, a new Jensen–Shannon divergence measure for intuitionistic fuzzy sets (IFSs) is introduced and some basic properties for this new divergence measure are obtained. In particular, this divergence measure, and its induced similarity measure, and induced entropy measure satisfy the axiomatic definitions of divergence, similarity, and entropy for IFSs. Based on our proposed divergence measure, entropy measure, and entropy-weight method, a new TOPSIS method is introduced to deal with multi-attribute decision making (MADM) problems under the intuitionistic fuzzy framework. Finally, a practical example on the credit evaluation of potential strategic partners and a comparative analysis with other TOPSIS methods is developed to illustrate the efficiency of the proposed TOPSIS method.

The Hunza-Nagar districts in northern Pakistan, nestled in the central Karakoram range, are known for their distinct climate and geology. However, the area is geologically unstable due to steep mountains, active faults, seismic zones, and sheared rock masses, leading to frequent landslides. This research aims to assess the comparative efficacy of three cutting-edge deep machine learning techniques (DMLTs), namely, the Universal Network U-Net, InceptionV3+, and DeeplabV3+, alongside three bivariate statistical models: Weight of Evidence (WofE), Intuitionistic Fuzzy Divergence (IF-D), and Frequency Ratio (FR), for Landslide Susceptibility Mapping (LSM) in Hunza-Nagar, North Pakistan. Initially, 148 landslide locations were marked, and 10 conditional factors were chosen to create a Landslide Inventory Map (LIM). The validation of landslide susceptibility models was assessed using several metrics: Area under the Curve (AUC), Density of Landslide Distribution (DLA), and the Seed Cell Area Index (SCAI). The evaluation of landslide susceptibility maps, produced through statistical models and DMLTs, revealed notable Prediction Rate Curves (PRC). Specifically, the WofE model achieved an 85 % PRC, the FR model reached 82 %, and the IF-D model also achieved an 85 % PRC. Furthermore, when estimating the performance of DMLTs using PRC, DeeplabV3+ established an 82 % success rate, InceptionV3+ reached 79 %, and U-Net achieved 80 %. In conclusion, the analysis designates that the WofE model, with an 85 % PRC and a D-value of 3.6, and the IF-D model, boasting an 85 % PRC and a D-value of 2.4, exhibited the highest prediction accuracy and classification ability.

The mountainous region of the Hunza River watershed basin, especially along the Karakorum highway, and also known as a third pole for the high accumulation of glaciers, which leads to huge devastating landslides occurring every year. Landslide susceptibility mapping was carried out using two deep machine learning techniques (DeeplabV3+ & universal network U-Net) and two statistical models (Intuitionistic Fuzzy divergence IF-D & Frequency ratio FR). The landslide susceptibility mapping is conducted using landslide inventory data and twelve conditional factors. The landslide susceptibility maps obtained from the two statistical models were compared with those generated by two deep machine learning models based on prediction accuracy measures, such as the Area Under the Curve (AUC) and Seed Cell Area Index (SCAI). The Success Rate Curve (SRC) was obtained using the training dataset, and the AUC values for the four models were as follows: 76.9% for IF-D, 76.9% for FR, 80.4% for DeeplabV3+, and 76.3% for U-Net. In terms of the Prediction Rate Curve (PRC) obtained from the validation dataset, the AUC values were found to be 80.8% for IF-D, 80.8% for FR, 81% for DeeplabV3+, and 77.8% for U-Net. To assess the classification ability of the models, the Seed Cell Area Index (SCAI) test was conducted. The results indicated that the SCAI (D-value) was 7.3 for U-Net, 10 for DeeplabV3+, 7.6 for IF-D, and 9.1 for FR. Overall, the findings revealed that DeeplabV3+ exhibited the highest prediction accuracy and classification ability, making it the most suitable choice for landslide susceptibility mapping in the relevant study area.

The implementation of multi-attribute decision-making (MADM) and the different approaches that facilitate it are addressed in this article. We focus on a recently developed fuzzy divergence measure, which is critical in improving decision accuracy when faced with several conflicting criteria. To highlight its real-world relevance, we present a detailed case study focusing on picking the best market for investment. In this case study, the previously studied Fuzzy divergence measure that is used to evaluate and prioritize various market possibilities based on important characteristics such as risk, return, and market potential. In this example, we demonstrate how this unique measure improves decision-making processes by providing a more precise and comprehensive method to selecting the greatest investment possibilities in uncertain and complicated contexts. The findings highlight the measure's usefulness in guiding investment decisions and enhancing the overall efficacy of MADM applications. JEL Codes: C44, D80, D81, D11 Received: 19/07/2024. Accepted: 06/10/2024. Published: 20/10/2024.

The uncertainty that characterizes the external mechanical loads to which any connection plate in steel structures is subjected determines the non-uniqueness of the isochoric deformation distributions. Since the eddy currents induced on the plates produce magnetic field maps with a high fuzziness content, similar to those of the isochoric deformations, their use can be exploited to evaluate the extent of the external load that determines a specific induced current map. Starting from an approach known in the literature, according to which the map-external load association is operated through fuzzy similarity computations, in this paper, we generalize this method by reformulating it in terms of intuitionistic fuzzy logic by proposing a classification based on divergence computations. Our approach, acting adaptively on the fuzzification of the maps, results in a better classification percentage, besides significantly reducing the presence of doubtful cases due to the uncertainty of each applied load. Furthermore, a FEM software tool was developed, which turned out to be, to a certain extent, a substitute for the experimental procedure, notoriously more expensive. Even if the procedure was applied on plates subjected to bi-axial loads, it could be used for other types of loads since the classification operator processes the eddy current maps exclusively, regardless of their cause.

Attribute reduction with fuzzy divergence-based weighted neighborhood rough sets

Decision making using novel Fermatean fuzzy divergence measure and weighted aggregation operators

Fuzzy set theory has extensively employed various divergence measure methods to quantify distinctions between two elements. The primary objective of this study is to introduce a generalized divergence measure integrated into the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. Given the inherent uncertainty and ambiguity in multi-criteria decision-making (MCDM) scenarios, the concept of the fuzzy α-cut is leveraged. This allows experts to establish a broader spectrum of rankings, accommodating fluctuations in their confidence levels. To produce consistent criteria weights with the existence of outliers, the fuzzy Method based on the Removal Effects of Criteria (MEREC) is employed. To showcase the viability and effectiveness of the proposed approach, a quantitative illustration is provided through a staff performance review. In this context, the findings are compared with other MCDM methodologies, considering correlation coefficients and CPU time. The results demonstrate that the proposed technique aligns with current distance measure approaches, with all correlation coefficient values exceeding 0.9. Notably, the proposed method also boasts the shortest CPU time when compared to alternative divergence measure methodologies. As a result, it becomes evident that the proposed technique yields more sensible and practical results compared to its counterparts in this category.

In many real-world applications, data are described by high-dimensional feature spaces, posing new challenges for current ensemble clustering methods. The goal is to combine sets of base clusters to enhance clustering accuracy, but this makes them susceptible to low quality. However, the reliability of present ensemble clustering in high-dimensional data still needs improvement. In this context, we propose a new fuzzy divergence-weighted ensemble clustering based on random projection and spectral learning. Firstly, random projection (RP) is used to create various dimensional data and find membership matrices via fuzzy c-means (FCM). Secondly, fuzzy partitions of random projections are ranked using entropy-based local weighting along with Kullback-Leibler (KL) divergence to detect any uncertainty. Then it used to evaluate the weight of each cluster. Finally, we create regularized graphs from these membership matrices and use spectral matrices to estimate the affinity matrices of these graphs using fuzzy KL divergence anchor graphs. Subsequently, obtaining the final clustering results is considered as an optimization problem, and the ensemble clustering results are obtained. The experimental results on high-dimensional data demonstrate the efficiency of our method compared to state-of-the-art methods.

Segmentation is one of the inferential applications for detecting patterns indigital images, which has been widely used in the health area. Thresholding, a type of segmentation, consists of separating the gray groups of an image, through one or more thresholds applied to the histogram. Thus, we used the gray tone with the lowest Fuzzy Divergence found to apply the enhancement method, through membership values. This paper presents a method to assist physicians in interpreting lung radiography images, especially in the pandemic caused by COVID-19, when enhancing lung images. In addition, we consulted with a group of medical experts who saw an improvement in image quality, providing the perception of detail in the enhanced image compared to the original image.

In the literature on fuzzy information theory, there are numerous divergence metrics and fuzzy information. Disparities are crucial for determining relationships. Here, we'll discuss some fresh information inequalities related to fuzzy measures and how they apply to the detection of patterns. With the aid of the fuzzy f-divergence measure and Jensen's inequality, links between new and well-known fuzzy divergence measures were also created.

This paper is devoted to develop the theory of temporal intuitionistic fuzzy sets. The matrix representation of a TIFS is also introduced for easy symbolization. In addition to a few basic operations, length of a TIFS and its properties are discussed. Morphological operations on temporal intuitionistic fuzzy sets are defined using (i) mathematical operations, (ii) structuring element, (iii) inclusion indicators, and (iv) temporal intuitionistic fuzzy divergence and verified with suitable examples.

Student-t kernelized fuzzy rough set model with fuzzy divergence for feature selection

Experts are using picture fuzzy sets (PFSs) in their probes to resolve the uncertain and vague information during the process of decision making because PFSs describe human attitudes naturally. Divergence measure (DM) plays a dominant role in discriminating between two distributions of probability and extracting consequences from that discrimination. In the present work, a novel picture fuzzy divergence measure (PF-DM) is developed between two PFSs. Some of the suggested measure’s important qualities are also discussed with particular situations to validate it. Based on the suggested PF-DM, a multiple-criteria decision-making (MCDM) model is established to grab the fuzzy information. The suggested measure’s performance is compared to that of various existing measures in the literature. An MCDM model has been proven for the usefulness of the suggested technique in dealing with real-life scenarios in the context of dengue sickness and pattern identification. Validation of the suggested MCDM model has been further investigated using validity testing. To improve the generated model, a thorough comparison with several current methodologies has been carried out while taking the time complexity (TC) factor into account.

A novel hyperbolic intuitionistic fuzzy divergence measure based mammogram enhancement for visual elucidation of breast lesions

<p style='text-indent:20px;'>Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for image despeckling. The intuitionistic fuzzy divergence function has been used to distinguish between edges and noise. To the best of the authors' knowledge, most of the studies on the multiplicative speckle noise removal process focus only on diffusion-based filters, and little attention has been paid to the study of fuzzy set theory. The proposed approach enjoys the benefits of both telegraph total variation equation and fuzzy edge detector, which is robust to noise and preserves image structural details. Moreover, we establish the existence and uniqueness of weak solutions of a regularized version of the present system using the Schauder fixed point theorem. With the proposed technique, despeckling is carried out on natural, real synthetic aperture radar, and real ultrasound images. The experimental results computed by the suggested method are reported, which are found better in terms of noise elimination and detail/edge preservation, concerning the existing approaches.</p>

Low-dose computed tomography (LDCT) can effectively reduce radiation exposure in patients. However, with such dose reductions, large increases in speckled noise and streak artifacts occur, resulting in seriously degraded reconstructed images. The non-local means (NLM) method has shown potential for improving the quality of LDCT images. In the NLM method, similar blocks are obtained using fixed directions over a fixed range. However, the denoising performance of this method is limited. In this paper, a region-adaptive NLM method is proposed for LDCT image denoising. In the proposed method, pixels are classified into different regions according to the edge information of the image. Based on the classification results, the adaptive searching window, block size and filter smoothing parameter could be modified in different regions. Furthermore, the candidate pixels in the searching window could be filtered based on the classification results. In addition, the filter parameter could be adjusted adaptively based on intuitionistic fuzzy divergence (IFD). The experimental results showed that the proposed method performed better in LDCT image denoising than several of the related denoising methods in terms of numerical results and visual quality.

Many fuzzy information and divergence measures developed by various researchers and authors. Here, authors proposed new fuzzy divergence measure using the properties of convex function and fuzzy concept. The applications of novel fuzzy divergence measures in pattern recognition with case study, are discussed. Obtained various novel fuzzy information inequalities on fuzzy divergence measures. The new relations among new and existing fuzzy divergence measure by new f-divergence, Jensen inequalities, properties of convex functions and inequalities have studied. Finally, verified these results and proposed fuzzy divergence measures by numerical example.

Background: The notion of fuzzy set was introduced by Zadeh. After that, many researchers extended the concept of fuzzy sets in different ways. Atanassov introduced the concept of intuitionistic fuzzy sets as an extension of fuzzy sets. This concept is applied in many fields such as bio-informatics, image processing, decision making, feature selection, pattern recognition, etc. Objectives: The prime objective of this paper is to introduce a new generalized intuitionistic fuzzy divergence measure with proof of its validity and discussions on its elegant properties. Applications of the proposed divergence measure in multi-attribute decision making and pattern recognition are also discussed with some numerical illustrations. Further, the proposed divergence measure is compared with other methods for solving MADM and pattern recognition problems which exist in the literature. Methods: The divergence measure method is used to measure the divergence between two given sets. In addition, the results of the other existing measures are also given to compare with the proposed measure. Results: It was observed that the proposed divergence measure found much better results in comparison with the other existing methods. Conclusion: A new divergence measure for intuitionistic fuzzy sets is introduced with some of its properties. Applications of the proposed divergence measure to pattern recognition and MADM are illustrated through examples. The comparison of the proposed method with the existing methods shows the legacy of the results of the proposed method. It is concluded that the proposed divergence measure is effective for solving real-world problems related to MADM and pattern recognition.