Fuzzy Entropy Function Research Articles

On fuzzy entropy functions based on human attitude

A fuzzy entropy function is useful to quantify the underlying vagueness. However, unlike probability, uncertainty due to vagueness is essentially perceived by a human agent in his/her cognition. This paper presents new fuzzy entropy functions that yields fuzzy entropy specific to the agent’s attitudinal tendency. Besides, the proposed functions correspond to the conventional entropy functions in the probabilistic domain, making them amenable to represent probabilistic-fuzzy (prob-fuzzy) uncertainty easily. To demonstrate this ability, the proposed functions are also extended to the prob-fuzzy domain. A case-study is included to show the usefulness of the proposed fuzzy and prob-fuzzy entropy functions.

An improved entropy function for the intuitionistic fuzzy sets with application to cloud vendor selection

This study proposes a novel entropy function for the intuitionistic fuzzy sets to improve the existing fuzzy entropy measure. We introduce an attitude-based entropy measure by methodically calculating the experts’ attitude values through variance approach. We discuss several important properties and present an example to demonstrate the applicability and efficacy of the proposed method. An illustrative example exhibits the effectiveness of the proposed intuitionistic fuzzy entropy functions and measures. We further show the superiority of the proposed intuitionistic fuzzy entropy measures over the existing measures.

Fuzzy entropy functions based on perceived uncertainty

Fuzzy entropy functions based on perceived uncertainty

On modeling ambiguity through entropy

AbstractFirst, a concept of ambiguity function is devised as an analogue of membership function, which directly and intuitively represents the ambiguity as perceived by the agent corresponding to a membership function. The ambiguity function is then deployed to develop an adaptive fuzzy entropy function that gives the overall fuzzy entropy of a fuzzy system as perceived by the agent. The proposed function considers also the agent's specific attitude as well as the given context (e.g., collection of the membership grades with respect to an attribute/criterion or property), both of which inevitably shape our perception of uncertainty. The usefulness of the proposed fuzzy entropy function is shown in multicriteria decision aiding in identifying those criteria that are most effective in distinguishing among the alternatives.

Developing an Enterprise Diagnostic Index System Based on Interval-Valued Hesitant Fuzzy Clustering

Global economic integration drives the development of dynamic competition. In a dynamic competitive environment, the ever-changing customer demands and technology directly affect the leadership of the core competence of enterprises. Therefore, assessing the performance of enterprises in a timely manner is necessary to adjust business activities and completely adapt to new changes. Enterprise diagnosis is a scientific tool for judging the development status of enterprises, and building a scientific and rational index system is the key to enterprise diagnosis. Considering the large number of enterprise diagnostic indicators and the high similarity among indicators, this study proposes a selection method for enterprise diagnostic indicators based on interval-valued hesitant fuzzy clustering by comparing the existing indicator systems. First, enterprise organizations are considered as the starting point. Through the key analysis of relevant indicators of domestic and foreign enterprise diagnosis, enterprise diagnosis candidate indicators are constructed from three aspects, namely enterprise performance, employee health, and social benefit. In view of the ambiguity and inconsistency of expert judgment, this study proposes an interval-valued hesitant fuzzy set based on the characteristics of hesitant fuzzy sets and interval-valued evaluation. For improving the interval-valued hesitant fuzzy entropy function, an interval-valued hesitant fuzzy similarity measurement formula considering information features is designed to avoid the problem of data length and improve the degree of identification among indicators. Then, the similarity, equivalence, and truncation matrices are constructed, and the interval-valued hesitant fuzzy clustering method is used to eliminate redundant indicators with repeated information. The availability of the proposed method is illustrated via an example, and the key indicators in the enterprise diagnostic index system are found. Finally, the advantages of the proposed method are discussed using comparative analysis with existing methods. A rational and comprehensive enterprise diagnostic index system was constructed. The system can be used as a scientific basis for diagnosing the development of enterprises and providing an objective and effective reference.

AG600 Amphibious Aircraft Selection Model Based on Improved Fuzzy Evaluation Algorithm

Aiming at the selection research gap of AG600 amphibious aircraft for salvage of life at sea, the selection index system of AG600 has been established, and an interval intuitionistic fuzzy selection decision model based on fuzzy entropy and score function is constructed. An evaluation index system with 8 indexes was determined based on the rules of the applicability, safety, and accessibility by questionnaire and statistical analysis. Different from the traditional method of determining the fuzzy number of each index solely by experts' scoring, this paper establishes a 5-grade fuzzy evaluation grade and index membership function, and the interval intuitionistic fuzzy number of the index is determined by combining subjective and objective methods. Fuzzy entropy and score function are used to calculate the weights of each index and AG600 selection score for different accidents, so as to obtain the matching degree of AG600 selection in marine life accidents more scientifically and reasonably. Finally, the effectiveness of the proposed model is demonstrated by a practical case.

Research on hesitant fuzzy matroid based on satisfaction function

In this paper, we mainly extended the study of fuzzy matroid related problems to research the fuzzy decision method. Considering the ambiguity of actual event information and evaluation, we chose hesitant fuzzy set as the extended data set. To construct the hesitant fuzzy matroid, we defined the satisfaction function of hesitant fuzzy set combining hesitant fuzzy index entropy and score function, and defined the mapping function of fuzzy matroid through this function. We also defined the algorithm of hesitant fuzzy matroid and proved the theory of rank, basis of hesitant fuzzy matroid.

A novel quantum inspired genetic algorithm to initialize cluster centers in fuzzy C-means

We propose a new quantum-inspired genetic algorithm (QGA) aimed to find the optimal initial cluster centers of the Fuzzy C-Means (FCM). The quantum chromosomes of the quantum population are collapsed to conventional chromosomes formed by binary strings encoding the cluster centers. We set as fitness function to minimize a fuzzy entropy function used to measure the fuzziness of clustering. A quantum rotation gate operator is applied in any generation to evolve the quantum population. The best conventional chromosome is used to set the initial cluster centers running FCM. We execute comparative tests of our QGA with other quantum-inspired method proposed in literature in order to find the best initial cluster centers: the results show that our method provides the best trade-off between the accuracy and precision of results and execution times.

Formulation of probability-based pervasive information set features and Hanman transform classifier for the categorization of mammograms

With aim of detecting breast cancer at the early stages using mammograms, this study presents the formulation of five feature types by extending the information set to encompass the concept of an intuitionist fuzzy set. The resulting pervasive information set gives not only the certainty of the pixel intensities of mammograms to a class but also the deficiency in the fuzzy modeling referred to as the hesitancy. The generalized adaptive Hanman Anirban fuzzy entropy function is shown to be equivalent to the hesitancy entropy function. The probability-based fuzzy Hanman transform and the pervasive Information with probability taking the role of hesitancy degree help derive the above five feature types termed as probability-based pervasive Information set features. The effectiveness of each feature type is demonstrated on the mini-MIAS and DDSM databases for the multi-class categorization of mammograms using the Hanman transform classifier. The statistical analysis by ANOVA test proves that the features are statistically significant and the experimental results are shown to be clinically relevant by the expert radiologists. The performance of the five feature types is either superior to or equal to that of some deep learning architectures on comparison but they outperform the state-of-the-art literature methods in the classification of breast cancer using mammograms.

Redefining fuzzy entropy with a general framework

A general entropy framework is proposed, which could lead to intuitive, interpretable and comparable entropy functions in both probabilistic or fuzzy domain, alike. Based on the proposed general entropy framework, the existing fuzzy entropy functions are redefined. The proposed entropy functions are also extended to the probabilistic-fuzzy domain. The usefulness of the work is shown in a real world case-study.

A Novel Fuzzy Entropy-Based Method to Improve the Performance of the Fuzzy C-Means Algorithm

One of the main drawbacks of the well-known Fuzzy C-means clustering algorithm (FCM) is the random initialization of the centers of the clusters as it can significantly affect the performance of the algorithm, thus not guaranteeing an optimal solution and increasing execution times. In this paper we propose a variation of FCM in which the initial optimal cluster centers are obtained by implementing a weighted FCM algorithm in which the weights are assigned by calculating a Shannon Fuzzy Entropy function. The results of the comparison tests applied on various classification datasets of the UCI Machine Learning Repository show that our algorithm improved in all cases relating to the performances of FCM.

2lpiRNApred: a two-layered integrated algorithm for identifying piRNAs and their functions based on LFE-GM feature selection

ABSTRACT Piwi–interacting RNAs (piRNAs) are indispensable in the transposon silencing, including in germ cell formation, germline stem cell maintenance, spermatogenesis, and oogenesis. piRNA pathways are amongst the major genome defence mechanisms, which maintain genome integrity. They also have important functions in tumorigenesis, as indicated by aberrantly expressed piRNAs being recently shown to play roles in the process of cancer development. A number of computational methods for this have recently been proposed, but they still have not yielded satisfactory predictive performance. Moreover, only one computational method that identifies whether piRNAs function in inducting target mRNA deadenylation been reported in the literature. In this study, we developed a two-layered integrated classifier algorithm, 2lpiRNApred. It identifies piRNAs in the first layer and determines whether they function in inducting target mRNA deadenylation in the second layer. A new feature selection algorithm, which was based on Luca fuzzy entropy and Gaussian membership function (LFE-GM), was proposed to reduce the dimensionality of the features. Five feature extraction strategies, namely, Kmer, General parallel correlation pseudo-dinucleotide composition, General series correlation pseudo-dinucleotide composition, Normalized Moreau–Broto autocorrelation, and Geary autocorrelation, and two types of classifier, Sparse Representation Classifier (SRC) and support vector machine with Mahalanobis distance-based radial basis function (SVMMDRBF), were used to construct a two-layered integrated classifier algorithm, 2lpiRNApred. The results indicate that 2lpiRNApred performs significantly better than six other existing prediction tools.

Logarithmic Fuzzy Entropy Function for Similarity Measurement in Multimodal Medical Images Registration.

Multimodal medical images are useful for observing tissue structure clearly in clinical practice. To integrate multimodal information, multimodal registration is significant. The entropy-based registration applies a structure descriptor set to replace the original multimodal image and compute similarity to express the correlation of images. The accuracy and converging rate of the registration depend on this set. We propose a new method, logarithmic fuzzy entropy function, to compute the descriptor set. It is obvious that the proposed method can increase the upper bound value from log(r) to log(r) + ∆(r) so that a more representative structural descriptor set is formed. The experiment results show that our method has faster converging rate and wider quantified range in multimodal medical images registration.

Bridging the Gap Between Probabilistic and Fuzzy Entropy

The real-world decision making often involves a comparison of uncertain systems or alternatives based on fuzzy evaluations. The concept of fuzzy entropy is quite useful in such situations. However, fuzzy entropy and the conventional probabilistic entropy differ in their semantics. This article critically examines the existing fuzzy entropy functions and redefine them to bring them closer to the probabilistic entropy. More specifically, new variants of the extant Luca and Termini, and Pal and Pal fuzzy entropy functions are proposed. The proposed fuzzy entropy functions are extended for the probabilistic-fuzzy uncertainty, commonly observed in the real world. A real application is included to demonstrate the usefulness of the proposed entropy functions in decision making applications.

Comparison of assembly-jam learning algorithms with fuzzy entropy measure for intelligent robot’s part micro-assembly

Two assembly-jam learning algorithms are introduced for reducing the task performance time as well as getting out of an assembly-jam in a robot’s part micro-assembly. The two algorithms are then compared from the viewpoint of five factors. A comprehensive comparison of the results with other recent methods and discussions are also described. The two algorithms split or unify to simplify regions situated near a similar assembly-jam state on the assembly-jam location map. This allows the part micro-assembly task to be continuously reiterated such that the speed of task performance will be faster. The task for getting out of the assembly-jam is achieved by the fewest number of robot joint control motions. This is generated by a technique to minimize the number of control motions of the 1st algorithm, without wasting time and energy. Meanwhile, the number of the last formed regions is minimized by the region unifying process of the 2nd algorithm. The two assembly-jam learning algorithms significantly reduce the task performance time in micro-assembly processes. The degree of uncertainty (measured by a fuzzy entropy function) associated with the task for getting out of the assembly-jam is used as a criterion to determine the most valid plan for a present input. The results show that the task for getting out of the assembly-jam can be successfully achieved by the control plans generated by the two assembly-jam learning algorithms.

Study on Hesitant Fuzzy Information Measures and Their Clustering Application.

At present, research on hesitant fuzzy operations and measures is based on equal length processing, and an equal length processing method will inevitably destroy the original data structure and change the data information. This is an urgent problem to be solved in the development of hesitant fuzzy sets. Aiming at solving this problem, this paper firstly defines a hesitant fuzzy entropy function as the measure of the degree of uncertainty of hesitant fuzzy information and then proposes the concept of hesitant fuzzy information feature vector. The hesitant fuzzy distance measure and similarity measure are studied based on the information feature vector. Finally, the hesitant fuzzy network clustering method based on similarity measure is given, and the effectiveness of our algorithm through a numerical example is illustrated.

FLNL: Fuzzy entropy and lion neural learner for EDoS attack mitigation in cloud computing

Cloud computing is a technology that allows the end-users to access the network through a shared area of resources. As the demand for the cloud computing increases, vulnerabilities in the service provision also increase. EDoS is one of the attacks that take over the provider, financially affecting the various organizations which use the cloud data. This paper utilizes fuzzy entropy and lion neural learner (FLNL) for the classification of cloud users to mitigate EDoS attacks in the cloud. This technique includes a training phase, which creates a log file using various parameters and then transforms the features into database considering certain key features. There are two important stages in this classification approach: feature selection and classification. Here, the fuzzy entropy function is utilized for feature selection which effectively selects useful features without information loss. The classification is performed using lion neural learner (LNL) which incorporates Lion algorithm (LA) into the neural network and uses Levenberg–Marquardt (LM) algorithm. The experimental results finalize that the proposed FLNL is effective with 89% precision, 78% recall, and 83.13% of f-measure compared with the existing Naïve Bayes (NB), Neural [Formula: see text] Propagation [Formula: see text], and Neural [Formula: see text]–Marquardt [Formula: see text].

A new technique for multilevel color image thresholding based on modified fuzzy entropy and Lévy flight firefly algorithm

In this paper, a modified fuzzy entropy (MFE) function is proposed to perform the multilevel thresholding of color images at different segmentation levels using Lévy flight guided firefly algorithm (LFA). Modified fuzzy entropy function is the difference of adjacent entropies. Therefore, minimizing the fitness function will provide thresholding levels such that all the regions have almost equal entropies. LFA algorithm improves the search performance and gains optimal threshold values for an efficient segmentation of colored images and satellite images. A comparative study of different nature inspired algorithms using MFE as an objective function presented. The study proves that the proposed MFE-LFA algorithm exhibits better performance in terms of different fidelity parameters and computation time. In addition, the proposed method is also compared with the most widely used Kapur's entropy based segmentation approaches, where the simulation results show the proposed methodology as the most efficient and effective algorithm.

Backtracking search algorithm for color image multilevel thresholding

Multilevel thresholding of the color images such as natural and satellite images becomes a challenging task due to the inherent fuzziness and ambiguity in such images. To address this issue, a modified fuzzy entropy (MFE) function is proposed in this paper. MFE function is the difference of adjacent entropies, which is optimized to provide thresholding levels such that all regions have almost equal entropies. To improve the performance of MFE, backtracking search algorithm is used. The numerical and statistical results indicate that MFE-BSA has higher peak signal-to-noise ratio, lower mean square error for all the images at different thresholding levels. Moreover, structural and feature similarity indices for MFE-BSA are closer to unity and the average fitness value obtained using MFE-BSA is minimum (lesser than 0.5). Overall, MFE-BSA shows very good segmentation results in terms of preciseness, robustness, and stability.

Constructing Fuzzy Membership Function Subjected to GA based Constrained Optimization of Fuzzy Entropy Function

This paper presents a Genetic Algorithm based optimization algorithm for fuzzy logic system. The proposed algorithm employs fuzzy entropy function as optimization bound(s) parameter. Membership function formation plays a key role in performance of a fuzzy system, as an improperly designed MF may lead to an inefficient system. Majority of literature focuses on optimization of shape of a MF and not the support. Proposed optimization method focuses on optimizing support of MF and not on its shape. For this optimization process predefined membership functions are used, the support of these membership functions these predefined sets are varied using standard deviation of the system data obtained by simulation or real-time analysis of the system. The support of these membership functions these predefined sets are varied using standard deviation of the system data obtained by simulation or real-time analysis of the system. Entropy for each displaced Fuzzy Set is maximized subjective to constraint optimization and thus optimized value of support is obtained. The proposed algorithm optimizes the support of Fuzzy Sets and hence can be combined with any other optimization tool for obtaining even better results.