Research on Fault Diagnosis of Hydraulic System of Fast Erecting Device Based on Fuzzy Neural Network

In order to improve the fault diagnosis effectiveness of hydraulic system in erecting devices, the fuzzy neural neural network is applied to carry out fault diagnosis of hydraulic system. Firstly, the main faults of hydraulic system of erecting mechanism are summarized. The main faults of hydraulic system of erecting devices concludes abnormal noise, high temperature of hydraulic oil of hydraulic system, leakage of hydraulic system, low operating speed of hydraulic system, and the characteristics of different faults are analyzed. Secondly, basic theory of fuzzy neural network is studied, and the framework of fuzzy neural network is designed. The inputting layer, fuzzy layer, fuzzy relation layer, relationship layer after fuzzy operation and outputting layer of fuzzy neural network are designed, and the corresponding mathematical models are confirmed. The analysis procedure of fuzzy neural network is established. Thirdly, simulation analysis is carried out for a hydraulic system in erecting device, the BP neural network reaches convergence after 600 times iterations, and the fuzzy neural network reaches convergence after 400 times iterations, fuzzy neural network can obtain higher accuracy than BP neural network, and running time of fuzzy neural network is less than that of BP neural network, therefore, simulation results show that the fuzzy neural network can effectively improve the fault diagnosis efficiency and precision. Therefore, the fuzzy neural network is reliable for fault diagnosis of hydraulic system in erecting devices, which has higher fault diagnosis effect, which can provide the theory basis for healthy detection of hydraulic system in erecting devices.

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.

(3, 2)-Fuzzy Sets and Their Applications to Topology and Optimal Choices

The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

A Hybrid Technique Based on a Genetic Algorithm for Fuzzy Multiobjective Problems in 5G, Internet of Things, and Mobile Edge Computing

Emerging commucation technologies, such as mobile edge computing (MEC), Internet of Things (IoT), and fifth-generation (5G) broadband cellular networks, have recently drawn a great deal of interest. Therefore, numerous multiobjective optimization problems (MOOP) associated with the aforementioned technologies have arisen, for example, energy consumption, cost-effective edge user allocation (EUA), and efficient scheduling. Accordingly, the formularization of these problems through fuzzy relation equations (FRE) should be taken into consideration as a capable approach to achieving an optimized solution. In this paper, a modified technique based on a genetic algorithm (GA) to solve MOOPs, which are formulated by fuzzy relation constraints with s -norm, is proposed. In this method, firstly, some techniques are utilized to reduce the size of the problem, so that the reduced problem can be solved easily. The proposed GA-based technique is then applied to solve the reduced problem locally. The most important advantage of this method is to solve a wide variety of MOOPs in the field of IoT, EC, and 5G. Furthermore, some numerical experiments are conducted to show the capability of the proposed technique. Not only does this method overcome the weaknesses of conventional methods owing to its potentials in the nonconvex feasible domain, but it also is useful to model complex systems.

Minimal solutions of fuzzy relation inequalities with addition-min composition1

This paper investigates minimal solutions of fuzzy relation inequalities with addition-min composition. It first shows the conditions that an element is a minimal solution of the inequalities, and presents the conditions that the inequalities have a unique minimal solution. It then proves that every solution of the inequalities has a minimal one and proposes an algorithm to searching for a minimal solution with computational complexity O (n 2) where n is the number of unknown variables of the inequalities. This paper finally describes all minimal solutions of the inequalities.