Measures of uncertainty based on Gaussian kernel for a fully fuzzy information system

Attribute reduction for multiset-valued data based on FRIC-model

A heart attack is a common cause of death globally. It can be treated successfully through a simple and accurate diagnosis. Getting the right diagnosis at the right time is very important for the treatment of heart failure. Currently, the conventional method of diagnosing heart disease is not reliable. Machine learning is a type of artificial intelligence that can be used to analyze the data collected by sensors. Data mining is another type of technology that can be utilized in the healthcare industry. These techniques help predict heart disease based on various factors. We developed a prediction and recommendation model aimed at predicting heart disease using the Optimized Deep Belief Network. It does so by taking into account the various features of the heart disease UCI and Stalog database. Finally, the proposed method classifies healthy people and people with heart illness with an accuracy of 97.91% .

Uncertainty measurement for probabilistic set-valued data: Gaussian kernel method

The uncertainty of information plays an important role in practical applications. Uncertainty measurement (UM) can help us in disclosing the substantive characteristics of information. Probabilistic set-valued data is an important class of data in machine learning. UM for probabilistic set-valued data is worth studying. This paper measures the uncertainty of a probability set-valued information system (PSVIS) by means of its information structures based on Gaussian kernel method. According to Bhattacharyya distance, the distance between objects in each subsystem of a PSVIS is first built. Then, the fuzzy Tcos-equivalence relations in a PSVIS by using Gaussian kernel method are obtained. Next, information structures in a PSVIS are defined. Moreover, dependence between information structures is investigated by using the inclusion degree. As an application for the information structures, UM in a PSVIS is investigated. Finally, to evaluate the performance of the investigated measures, effectiveness analysis is performed from dispersion analysis, correlation analysis, and analysis of variance and post-hoc test.

Information entropy based attribute reduction for incomplete heterogeneous data

Attribute reduction in an information system (IS) is an important research topic in rough set theory (RST). This paper investigates attribute reduction for incomplete heterogeneous data based on information entropy. Information entropy in an incomplete IS with heterogeneous data (IISH) is first defined. Then, some derived notions of information entropy, such as joint information entropy, conditional information entropy, mutual information entropy, gain and gain ratio in an incomplete decision IS with heterogeneous data (IDISH), are presented. Next, information entropy is applied to perform attribute reduction in an IDISH. Two attribute reduction algorithms, based on gain and gain ratio, respectively, are proposed. Finally, in order to illustrate the feasibility and efficiency of the proposed algorithms, experimental analysis is carried out and comparisons are done. It is worth mentioning that the incomplete rate is used to deal with incomplete heterogeneous data.

Some results on fuzzy relations

Fuzzy relation is one of the main research contents of fuzzy set theory. This paper obtains some results on fuzzy relations by studying relationships between fuzzy relations and their uncertainty measurement. The concepts of equality, dependence, partial dependence and independence between fuzzy relations are first introduced. Then, uncertainty measurement for a fuzzy relation is investigated by using dependence between fuzzy relations. Moreover, the basic properties of uncertainty measurement are obtained. Next, effectiveness analysis is carried out. Finally, an application of the proposed measures in attribute reduction for heterogeneous data is given. These results will be helpful for understanding the essence of a fuzzy relation.

Measures of uncertainty for a fuzzy probabilistic approximation space

 An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space. In this way, it combines three types of uncertainty (i.e., fuzziness, probability and roughness). This article is devoted to measuring the uncertainty for an FPA-space. A fuzzy relation matrix is first proposed by introducing the probability into a given fuzzy relation matrix, and on this basis, it is expanded to an FA-space. Then, granularity measurement for an FPA-space is investigated. Next, information entropy measurement and rough entropy measurement for an FPA-space are proposed. Moreover, information amount in an FPA-space is considered. Finally, a numerical example is given to verify the feasibility of the proposed measures, and the effectiveness analysis is carried out from the point of view of statistics. Since three types of important theories (i.e., fuzzy set theory, probability theory and rough set theory) are clustered in an FPA-space, the obtained results may be useful for dealing with practice problems with a sort of uncertainty.

Information structures and entropy measurement for a fuzzy probabilistic information system

An information system (IS), an important model in the field of artificial intelligence, takes information structure as the basic structure. A fuzzy probabilistic information system (FPIS) is the combination of some fuzzy relations in the same universe that satisfy probability distribution. A FPIS as an IS with fuzzy relations includes three types of uncertainties (i.e., roughness, fuzziness and probability). This paper studies information structures in a FPIS from the perspective of granular computing (GrC). Firstly, two types of information structures in a FPIS are defined by set vectors. Then, equality, dependence and independence between information structures in a FPIS are proposed, and they are depicted by means of the inclusion degree. Next, information distance between information structures in a FPIS is presented. Finally, entropy measurement for a FPIS is investigated based on the proposed information structures. These results may be helpful for understanding the nature of structures and uncertainty in a FPIS.

A dynamic knowledge base and its data compression with homomorphism

In reality there are always a large number of complex massive databases. The notion of homomorphism may be a mathematical tool for studying data compression in knowledge bases. This paper investigates a knowledge base in dynamic environments and its data compression with homomorphism, where “dynamic” refers to the fact that the involved information systems need to be updated with time due to the inflow of new information. First, the relationships among knowledge bases, information systems and relation information systems are illustrated. Next, the idea of non-incremental algorithm for data compression with homomorphism and the concept of dynamic knowledge base are introduced. Two incremental algorithms for data compression with homomorphism in dynamic knowledge bases are presented. Finally, an experimental analysis is employed to demonstrate the applications of the non-incremental algorithm and the incremental algorithms for data compression when calculating the knowledge reduction of dynamic knowledge bases.

Analysis of Sports Injury Estimation Model Based on Mutation Fuzzy Neural Network

In recent years, with the gradual development of sports, the competition between athletes is becoming more and more fierce. The long training time and heavy body load of athletes lead to the increase of the incidence of sports injury, and the evaluation and analysis of athletes' sports injury need a lot of manpower and material resources. In order to improve the calculation efficiency of sports injury estimation results and save the cost of estimation and analysis, we propose a sports injury estimation model based on the algorithm model of mutation fuzzy neural network. The sports injury model constructed in this paper can not only systematically evaluate and analyze the degree of sports injury of athletes, but also improve the accuracy and efficiency; at the same time, it has universality for the evaluation and analysis of the degree of sports injury. The construction of this model provides the theoretical basis of big data algorithm for the prevention of sports injury and the application of mutation fuzzy neural network in the field of sports.

Multivariate data-based optimization of membrane adsorption process for wastewater treatment: Multi-layer perceptron adaptive neural network versus adaptive neural fuzzy inference system

Application of machine-learning methods to assess the batch adsorption of malachite green (MG) dye on chitosan/polyvinyl alcohol/zeolite imidazolate frameworks membrane adsorbents (CPZ) was investigated in this study. Our previous research results proved the suitability of the CPZ membranes for wastewater decoloring. In the current work, the residence time was combined with the other operational variables i.e., pH, initial dye concentration, and adsorbent dose (AD), to obtain the possible interactions involved in nonequilibrium adsorption. Two well-known soft-computing approaches, multi-layer perceptron adaptive neural network (MLP-ANN) and adaptive neural fuzzy inference system (ANFIS), were selected among different machine learning alternatives and then, comprehensively compared with each other considering reliability and accuracy for a 60 number of runs. The ANFIS structure with nine centers of clusters could predict the adsorption performance better than the ANN approach. Root mean square error (RMSE) and R-square were obtained 0.01822 and 0.9958 for the test data, respectively. The interpretability test resulted a linear trend predicted by the model and disclosed that the maximum value of the removal efficiency (99.5%) could be obtained when the amount of the inputs set to the upper limit. Lastly, the sensitivity analysis uncovered that the residence time has a decisive effect (relevancy factor > 80%) on the removal efficiency. According to the results, ANFIS is an effective and reliable tool to optimize and intensify the membrane adsorption process.