Sugeno Fuzzy Integral Research Articles

Morphological classification of neurons based on Sugeno fuzzy integration and multi-classifier fusion

In order to extract more important morphological features of neuron images and achieve accurate classification of the neuron type, a method is proposed that uses Sugeno fuzzy integral integration of three optimized deep learning models, namely AlexNet, VGG11_bn, and ResNet-50. Firstly, using the pre-trained model of AlexNet and the output layer is fine-tuned to improve the model’s performance. Secondly, in the VGG11_bn network, Global Average Pooling (GAP) is adopted to replace the traditional fully connected layer to reduce the number of parameters. Additionally, the generalization ability of the model is improved by transfer learning. Thirdly, the SE(squeeze and excitation) module is added to the ResNet-50 variant ResNeXt-50 to adjust the channel weight and capture the key information of the input data. The GELU activation function is used to better fit the data distribution. Finally, Sugeno fuzzy integral is used to fuse the output of each model to get the final classification result. The experimental results showed that on the Img_raw, Img_resample and Img_XYalign dataset, the accuracy of 4-category classification reached 98.04%, 91.75% and 93.13%, respectively, and the accuracy of 12-category classification reached 97.82%, 85.68% and 87.60%, respectively. The proposed method has good classification performance in the morphological classification of neurons.

Algoritmi za procenu kvalitativnih i kvantitativnih rizika kreditiranja malih i srednjih preduzeća zasnovani na fazi računu

Today, crisis conditions in the economy and finance require high-quality risk assessment. In the article, the authors propose two algorithms for assessing the projects lending risks (PLRs) to small and medium-sized businesses. To assess qualitative PLRs, we proposed to use a hierarchical system of criteria, in which the importance of the criteria is described using the Sugeno fuzzy measure, and the generalized estimate of the qualitative risk is calculated using the Sugeno fuzzy integral. To evaluate quantitative PLRs, we proposed to use the characteristics of fuzzy numbers that describe the project effectiveness criteria and have an arbitrary-form membership function. In addition, to describe quantitative risks, we proposed to use the risk-function of a fuzzy number, which reflects not only the size of possible losses, but also the possibility of their occurrence. This allows you to comprehensively and objectively assess the level of risks. We have demonstrated and discussed this algorithms on the example of preparing data for making a decision on lending to a project for the production of corn syrup in Ukraine.

Using the fuzzy integrals for the ensemble-based segmentation of asphalt cracks

Detection and measurement of cracks in asphalt pavement is one of the important tasks in transport industry to determine the quality of the pavement and submit repair requirements. In recent years, computer vision algorithms have been increasingly used to automate the solution of this problem. Therefore, researchers are faced with the acute issue of improving the accuracy of segmentation algorithms, since the safety of people depends on the timely detection of defects on the road. In this paper, ensemble methods based on Choquet and Sugeno fuzzy integrals are proposed to combine the scores of three pre-trained deep learning models: ResNet50, DenseNet169, and InceptionV3. We tested the proposed methods on a public dataset and compared the results with already-used popular ensemble methods.

CovidConvLSTM: A fuzzy ensemble model for COVID-19 detection from chest X-rays

The rapid outbreak of COVID-19 has affected the lives and livelihoods of a large part of the society. Hence, to confine the rapid spread of this virus, early detection of COVID-19 is extremely important. One of the most common ways of detecting COVID-19 is by using chest X-ray images. In the literature, it is found that most of the research activities applied convolutional neural network (CNN) models where the features generated by the last convolutional layer were directly passed to the classification models. In this paper, convolutional long short-term memory (ConvLSTM) layer is used in order to encode the spatial dependency among the feature maps obtained from the last convolutional layer of the CNN and to improve the image representational capability of the model. Additionally, the squeeze-and-excitation (SE) block, a spatial attention mechanism, is used to allocate weights to important local features. These two mechanisms are employed on three popular CNN models – VGG19, InceptionV3, and MobileNet to improve their classification strength. Finally, the Sugeno fuzzy integral based ensemble method is used on these classifiers’ outputs to enhance the detection accuracy further. For experiments, three chest X-ray datasets, which are very prevalent for COVID-19 detection, are considered. For all the three datasets, it is found that the results obtained by the proposed method are comparable to state-of-the-art methods. The code, along with the pre-trained models, can be found at https://github.com/colabpro123/CovidConvLSTM.

Intelligent pore type characterization: Improved theory for rock physics modelling

ABSTRACTThanks to the recent developments in both hardware and software capabilities of computers, intelligent rock physics modelling has emerged as an alternative to the conventional approach to the rock physics. Respecting the crucial contribution of the pore geometry into the rock physics modelling, I propose an accurate yet cost‐ and time‐efficient intelligent framework to measure pore space based on digital rock physics. In this method, total pore space was calculated after estimating the pore geometry through pattern recognition on thin section images captured through polarized‐light microscopy. Next, applying three different multi‐class classifiers (radial basis function, support vector machine and k‐nearest neighbours) for estimating pore type and aspect ratio, the best results were obtained using the fuzzy Sugeno integral, and the pore types were classified according to the most widely used pore type classification scheme. Next, an artificial neural network was applied to interpolate discrete data points (thin sections) into continuous profiles of pore type and aspect ratio. Subsequently, as a case study, the proposed approaches were applied to a real‐world carbonate reservoir for modelling the P‐ and S‐wave velocities through a rock physics model. Verifying the modelling results against ultrasonic and measured well‐logging data, the methodology showed promising performance at acceptable levels of uncertainty. The most significant advantage of the intelligent pore type quantification over the conventional methods was found to be its ability to estimate elastic properties with good accuracy. The key findings of this research include automatic detection of the pore types and aspect ratio, provision of a database of pore geometry, attenuation of uncertainty in pore type characterization and improvement of rock physics modelling in the absence of reliable S‐wave velocity data.

A unified deep neuro-fuzzy approach for COVID-19 twitter sentiment classification

Covid-19 braces serious mental health crisis across the world. Since a vast majority of the population exploit social media platforms such as twitter to exchange information, rapid collecting and analyzing social media data to understand personal well-being and subsequently adopting adequate measures could avoid severe socio-economic damage. Sentiment analysis on twitter data is very useful to understand and identify the mental health issues. In this research, we proposed a unified deep neuro-fuzzy approach for Covid-19 twitter sentiment classification. Fuzzy logic has been a very powerful tool for twitter data analysis where approximate semantic and syntactic analysis is more relevant because correcting spelling and grammar in tweets are merely obnoxious. We conducted the experiment on three challenging COVID-19 twitter sentiment datasets. Experimental results demonstrate that fuzzy Sugeno integral based ensembled classifiers succeed over individual base classifiers.

Estimating the potential willingness of the state to use military force based on the Sugeno fuzzy integral

Estimation of the potential willingness of the state to use military force is an integral part of the analysis of international relations and the preparation of key decisions in in security sphere. Our problem was to develop a method for numerically estimating the potential willingness of any state to use military force. This method should take into account a large number of quantitative and qualitative criteria, the uncertainty of their relationships, as well as the uncertainty of the initial data, some of which can only be obtained with the help of experts. Our analysis has shown that the known methods have a number of serious shortcomings. We proposed to solve this problem based on the representation of partial estimations of states in the form of fuzzy sets, and the importance of criteria in the form of a fuzzy measure. We also proposed to aggregate the partial estimations using the Sugeno fuzzy integral. We developed a hierarchical structure of estimation criteria, determined the importance of the criteria, built an observation channel based on the Harrington curve to obtain input estimations, and also developed an aggregation algorithm. As a result, we calculated estimations for 137 states and examined their potential willingness to use military force. The results disclose new aspects of using fuzzy-integral calculus to construct hierarchical models of multi-criteria estimating, and also demonstrate the possibility of using artificial intelligence methods to obtain numerical estimations in the sphere of international relations.

An optimized fuzzy ensemble of convolutional neural networks for detecting tuberculosis from Chest X-ray images

Early detection of Tuberculosis or TB can help in mitigating the chances of affecting the other body parts like the kidney, spine and brain, thereby reducing the death rate due to this disease. However, manual diagnosis by radiologists using Chest X-rays may include human error. Therefore, researchers have been trying hard to develop a computerized decision support system for efficient detection of TB from Chest X-ray images. In this work, we have proposed a model for screening TB using Chest X-ray images where the decisions from three base learners are combined using the type-1 Sugeno fuzzy integral based ensemble technique. Fuzzy measures required in this fuzzy integral based ensemble method are set experimentally in many state-of-the-art works. To overcome such manual tuning, we have used meta-heuristic optimization algorithms to set the fuzzy measures optimally during the training process of the model. The performance of the ensemble technique on the validation set is considered as the decider of the optimal fuzzy measures. Before applying the ensemble method we have extracted features from images using three state-of-the-art deep learning models, namely DenseNet121, VGG19 and ResNet50 pre-trained on imageNet dataset. With the above pre-trained models, the base learners are built using additional fully connected and softmax layers. We have evaluated the present work on a new and publicly available TB dataset consisting of Chest X-ray images. The obtained results (irrespective of the optimizer used) confirm that our method has outperformed state-of-the-art methods used for TB classification.

Aggregation with dependencies: Capacities and fuzzy integrals

We outline recent trends in capacity-based aggregation in large universes. Capacities (fuzzy measures) model dependencies among the inputs, and aggregation by the discrete Choquet, Sugeno and other fuzzy integrals accounts for synergies and redundancies. For large number of inputs the exponential complexity of all interactions is a major obstacle. We exemplify the need for aggregation of a large number of dependent inputs on several applications and discuss the challenges and approaches to reducing the complexity of capacity-based aggregation. We also state which mathematical and computational tools are required for large scale capacity modelling.

Estimating the outcome of an active phase in the military conflict on Eastern Ukraine based on the Sugeno fuzzy integral

A military conflict (especially its active phase) is a time of maximum exertion of all the powers of the state and society, a time that requires quick and correct decisions from state bodies. The quality of these decisions is largely determined by the estimation adequacy of the current situation. As the analysis shows, modern military conflicts start suddenly and develop rapidly. The official informing system turns out to be ineffective, what leads to numerous mistakes in decision-making. In addition, modern military conflicts are of a hybrid nature. The outcome of such military conflicts depends on many factors of a non-military nature, for example, the quality of governance, support from the population, international assistance. These factors are often formulated qualitatively (linguistically), and the conditions of the active phase of a military conflict do not give time to check the adequacy of quantitative data. Therefore, it is necessary that the method for estimating the outcome of the active phase takes into account the data uncertainty and ensures a generalization of the partial characteristics of the current situation. Based on the analysis of known approaches to the description and processing of uncertainty, the authors proposed using the methods of fuzzy integral calculus to describe partial characteristics and calculate a generalized characteristic, which is an estimation of the success of the outcome of an active phase. The authors have solved the following subproblems: identification of structure and parameters of standard for estimating; choice of the observation channel of the characteristics of the current situation; constructing the algorithm for estimations generalization. The authors demonstrated the work of the proposed algorithm by the example of estimating the results of hostilities in eastern Ukraine in July 2014.

On Random Generation of Supermodular Capacities

Discrete fuzzy measures (capacities) are a powerful tool to model interacting inputs and aggregate them using Choquet, Sugeno, and other fuzzy integrals. Simulation studies and probabilistic optimization algorithms require efficient random sampling from the set of fuzzy measures. It is a challenging problem due to an extremely high complexity of the polytope of capacities. This article addresses random sampling from two special classes: supermodular and submodular fuzzy measures. A suitable marginal contributions representation converts the problem to sampling from an order polytope, which is dealt efficiently using the Markov chain random walk.

Sugeno integral generalization applied to improve adaptive image binarization

Classic adaptive binarization methodologies threshold pixels intensity with respect to adjacent pixels exploiting integral images. In turn, integral images are generally computed optimally by using the summed-area-table algorithm (SAT). This document presents a new adaptive binarization technique based on fuzzy integral images. Which, in turn, this technique is supported by an efficient design of a modified SAT for generalized Sugeno fuzzy integrals. We define this methodology as FLAT (Fuzzy Local Adaptive Thresholding). Experimental results show that the proposed methodology produced a better image quality thresholding than well-known global and local thresholding algorithms. We proposed new generalizations of different fuzzy integrals to improve existing results and reaching an accuracy ≈0.94 on a wide dataset. Moreover, due to high performances, these new generalized Sugeno fuzzy integrals created ad hoc for adaptive binarization, can be used as tools for grayscale processing and more complex real-time thresholding applications.

SOFTWARE SELECTION ON BASE OF SUGENO INTEGRAL

The article is devoted to the problem of software selection. As a rule, this tasks are formalized as models of multi-criteria decision making (MCDM). The peculiarity of this problem is in the fact that the evaluation criteria , is generally defined by linguistic expert. This requires the use of special methods, in particularly, the theory of fuzzy sets. To solve the problem, an approach based on the a fuzzy measure was used . In general, a fuzzy measure allows one to take into account the effect of the mutual influence of criteria. The main difficulty lies in identifying this measure. The fuzzy Sugeno measure and Sugeno integral were used. An example of solving the indicated problem is given.

Fubini theorem and generalized Minkowski inequality for the pseudo-integral

This paper is devoted to generalizations of Fubini theorem, Transformation theorem, and generalized Minkowski inequality for the so called pseudo-integral. The approach is based on the relation of double pseudo-integrals and iterated pseudo-integrals. Since the pseudo-integral covers Lebesgue integral, Sugeno's fuzzy integral, and Zhao's (N)fuzzy integral (with a respect to special nonadditive measure: ∨-measure), the obtained results generalize the corresponding previously known results.

Ostrowski-Sugeno fuzzy inequalities

We present Ostrowski-Sugeno fuzzy type inequalities. These are Ostrowski-like inequalities in the context of Sugeno fuzzy integral and its special properties are investigated. Tight upper bounds to the deviation of a function from its Sugeno-fuzzy averages are given. This work is greatly inspired by [3] and [1].

Hermite-Hadamard and Fejer type integral inequalities for Harmonic Convex (Concave) fuzzy mappings

In this paper the Hermite Hadamard and Fejer type integral inequalities for harmonic convex (H-convex) and harmonic concave (H-concave) fuzzy mappings have been studied by using ranking value function. Furthermore, Hermite Hadamard inequality via Sugeno fuzzy integral has been given for H-concave fuzzy mappings. Moreover, the upper bound of the Sugeno fuzzy integral has been obtained for the H-concave fuzzy mapping by using ranking value function and the results have been justified with suitable examples.

Fractional Ostrowski-Sugeno Fuzzy univariate inequalities

Here we present fractional univariate Ostrowski-Sugeno Fuzzy type inequalities. These are of Ostrowski-like inequalities in the setting of Sugeno fuzzy integral and its special-particular properties. In a fractional environment, they give tight upper bounds to the deviation of a function from its Sugeno-fuzzy averages. The fractional derivatives we use are of Canavati and Caputo types. This work is greatly inspired by [ 8 ], [ 1 ] and [ 2 ].

General form of Chebyshev type inequality for generalized Sugeno integral

We prove a general form of Chebyshev type inequality for generalized upper Sugeno integral in the form of necessary and sufficient condition. A key role in our considerations is played by the class of m-positively dependent functions which includes comonotone functions as a proper subclass. As a consequence, we state an equivalent condition for Chebyshev type inequality to be true for all comonotone functions and any monotone measure. Our results generalize many others obtained in the framework of q-integral, seminormed fuzzy integral and Sugeno integral on the real half-line. Some further consequences of these results are obtained, among others Chebyshev type inequality for any functions. We also point out some flaws in existing results and provide their improvements.

General Type-2 Fuzzy Sugeno Integral for Edge Detection.

A type-2 fuzzy edge detection method is presented in this paper. The general process consists of first obtaining the image gradients in the four directions—horizontal, vertical, and the two diagonals—and this technique is known as the morphological gradient. After that, the general type-2 fuzzy Sugeno integral (GT2 FSI) is used to integrate the four image gradients. In this second step, the GT2 FSI establishes criteria to determine at which level the obtained image gradient belongs to an edge during the process; this is calculated assigning different general type-2 fuzzy densities, and these fuzzy gradients are aggregated using the meet and join operators. The gradient integration using the GT2 FSI provides a methodology for achieving more robust edge detection, even more if we are working with blurry images. The experimental evaluations are performed on synthetic and real images, and the accuracy is quantified using Pratt’s Figure of Merit. The results values demonstrate that the proposed edge detection method outperforms other existing algorithms.

A new approach for an intuitionistic fuzzy Sugeno integral for decision making

A new approach for an intuitionistic fuzzy Sugeno integral for decision making