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.

Complexity Analysis in Maintenance Systems

Complexity is a very broad subject that applies to project management, engineering design and manufacturing, arithmetic, software, statistics, etc. In maintenance systems, complexity can be defined based on technical and managerial aspects of a maintenance project. Because relative complexity between two projects can be used as a yardstick for resource allocation between them, quantifying the complexity becomes important. To quantify the complexity of maintenance projects, this thesis reports two models. In uncertain situations, a fuzzy graph-based model is developed that determines relative complexities of maintenance projects based on experts‟ opinions with respect to technical and managerial aspects. These aspects may not be measured precisely due to uncertain situations. The model uses an aggregation operator to mitigate conflict of experts‟ opinions on complexity relations. Using a fuzzy relation matrix representing the degrees of membership of relative complexities, the model maps the fuzzy graph into a scaled Cartesian diagram. Also, complexity of a maintenance project can be investigated through time to repair (TTR). Performing statistical analysis shows that human cognition and project complexity have significant influence on TTR. These influential factors can be studied by a learning curve. Due to the nature of maintenance calls for repairs, a learning curve model made up of two segments is proposed. A project complexity can be derived from the learning curve at the breakpoint time. Taking into account human cognitive abilities, the breakpoint indicates the required number of trials in order to reach mastery level for performing certain tasks unsupervised.

Complexity Analysis in Maintenance Systems

Complexity is a very broad subject that applies to project management, engineering design and manufacturing, arithmetic, software, statistics, etc. In maintenance systems, complexity can be defined based on technical and managerial aspects of a maintenance project. Because relative complexity between two projects can be used as a yardstick for resource allocation between them, quantifying the complexity becomes important. To quantify the complexity of maintenance projects, this thesis reports two models. In uncertain situations, a fuzzy graph-based model is developed that determines relative complexities of maintenance projects based on experts‟ opinions with respect to technical and managerial aspects. These aspects may not be measured precisely due to uncertain situations. The model uses an aggregation operator to mitigate conflict of experts‟ opinions on complexity relations. Using a fuzzy relation matrix representing the degrees of membership of relative complexities, the model maps the fuzzy graph into a scaled Cartesian diagram. Also, complexity of a maintenance project can be investigated through time to repair (TTR). Performing statistical analysis shows that human cognition and project complexity have significant influence on TTR. These influential factors can be studied by a learning curve. Due to the nature of maintenance calls for repairs, a learning curve model made up of two segments is proposed. A project complexity can be derived from the learning curve at the breakpoint time. Taking into account human cognitive abilities, the breakpoint indicates the required number of trials in order to reach mastery level for performing certain tasks unsupervised.

Research and Practice of Quantitative Models on The Freedom of Trade Based on AHP-FCE Method: Taking Major Countries in WTO as Examples

In recent years, protectionism and unilateralism in the field of international trade are increasing. The WTO-centric multilateral trade regime has been hit. By researching the index of trade freedom among countries in international trade, this paper takes five important countries in WTO as an example, and constructs the trade freedom index and the national trade freedom model. The study reviewed and analysed global and regional developments in cross-border trade and investigated five varialbes that impacted the index of trade freedom. Then the fuzzy comprehensive analysis method (FCE) is used to obtain the comprehensive evaluation matrix by fuzzy arithmetic processing through the evaluation index weight and fuzzy relation matrix. Therefore, the changing data of the index of trade freedom in five countries from 2017 to 2018 are obtained. It is discovered that there is a significant difference in the index of trade freedom among countries. What’s worse, the average of the global index has declined year by year. This phenomenon is caused by the decline of global trade volume and the prevalence of new trade barriers. In the end, this paper proposes the implementation of multilateral negotiations and the establishment of long-term penalties as possible solutions.

Research on Unconstrained Handwritten Numeral Recognition by BP Feature Screening Based on Fuzzy Clustering

In this paper, the recognition system of fuzzy clustering based on BP feature screening was put out. The figure specimens of experiment were filtered through BP network, and the result of screening was fit into the clustering source. At last fuzzy clustering was carried out by constituting the fuzzy relation matrix. The result of experiment demonstrates that this method has very high noise immunity capacity and overcame the limitation of traditional algorithm with single factor recognition. The recognition rate and precision ratio were greatly improved at the same time.

Automotive Fault Diagnosis Based on the Fuzzy Mathematics

Automobile fault diagnosis is one of the hot issues in detection and diagnosis technology of automobile. The automobile fault has the characteristics of uncertainty and complexity problems. To solve the problems of qualitative description from drivers into quantitative, fuzzy mathematics is introduced. In addition, the fuzzy relationship of automobile fault and fault causes is expressed by setting the membership functions and fuzzy relation matrix. Finally, the qualitative analysis of real cases is present. The fuzzy theory and expert system for automobile fault diagnosis method is proved accurately through the algorithm analysis and real cases.

Fuzzy Hierarchy Analysis of Gravel Pile Stability

This thesis introduces a brief of the development status of thegravel pileand the basic principles, and analysis of vibration displacement stone column foundation treatment influencing factors by the Analytic Hierarchy Process. To compare and analyzed from it, and apply the square root method to calculate their weight; According to the evaluation set structure distribution trapezoidalmembership function, and get the finalmembershipof each index to evaluating set and fuzzy relation matrix; By the analysis of application of a wharf, and find out thecomprehensivescore stabilitygravel pilesystem, we have certain reference from it in the future.

A Study on Integrated Condition Assessment System for Bridge

This paper mechanically applies the thought of recursive hierarchical structure in analytic hierarchy process, by means of fuzzy mathematics, with the investigation, analysis, induction, the fuzzy relation matrix has been found, at the same time, the assignment weight of index is merged into that. Then the integrated condition assessment results of bridge are gained finally. This method greatly reduces the happening of ill-considering the influencing factors, make the results more real, specific and comprehensive, avoid effectively great loss which is caused by the defects of safety and service performance.

Fault Diagnosis of Construction Elevator Based on Fuzzy Recognition

Fault eigenvector, fault fuzzy vector and fuzzy relation matrix of the construction elevator is built on using the fuzzy recognition method in the fault diagnosis system of the elevator. On the basis of every fault membership obtained through fuzzy recognition, the equipment fault is confirmed according to max membership principle. The test shows it can effectively help to estimate cause of fault and to avoid the accidents when the fuzzy recognition method is used.