Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

In this article,the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering.First,an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule.Then,compared to traditional prediction-based ones,two types of fuzzy set-membership filters are proposed to effectively improve filtering performance,where the structure of both filters consists of two parts:prediction and filtering.Under the locally Lipschitz continuous condition of membership functions,unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error.Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state.Finally,the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.

Fuzzy logic controller design with unevenly-distributed membership function for high performance chamber cooling system

Fuzzy logic controller adopting unevenly-distributed membership function was presented with the purpose of enhancing performance of the temperature control precision and robustness for the chamber cooling system.Histogram equalization and noise detection were performed to modify the evenly-distributed membership functions of error and error change rate into unevenly-distributed membership functions.Then,the experimental results with evenly and unevenly distributed membership functions were compared under the same outside environment conditions.The experimental results show that the steady-state error is reduced around 40% and the noise disturbance is rejected successfully even though noise range is 60% of the control precision range.The control precision is improved by reducing the steady-state error and the robustness is enhanced by rejecting noise disturbance through the fuzzy logic controller with unevenly-distributed membership function.Moreover,the system energy efficiency and lifetime of electronic expansion valve(EEV) installed in chamber cooling system are improved by adopting the unevenly-distributed membership function.

Life-cycle cost model and evaluation system for power grid assets based on fuzzy membership degree

Life-cycle cost(LCC)theory can be effectively applied to improve the efficiency and quality of power plant equipment and asset management.However,specific aspects of the LCC calculation and evaluation model require further research for practical application.This paper proposes an LCC assessment model for the management of electric power plant equipment during its service life.A membership function method based on fuzzy logic is used to improve the allocation of modernization and overhaul projects to multiple equipment assets.An LCC assessment model and evaluation system for power equipment are proposed and successfully applied to the equipment and project management of a Guangzhou power plant in the China Southern Power Grid,providing a decision-making mechanism that facilitates efficient operation and optimal utilization of power plant equipment and assets.

The Theory of Membership Degree of Γ-Conclusion in Several n-Valued Logic Systems

Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership degree of formulas A is a consequence of Γ (or Γ-conclusion) in Lukasiewicz n-valued propositional logic systems, Godel n-valued propositional logic system and the R0 n-valued propositional logic systems. The condition and related calculations of formulas A being Γ-conclusion were discussed by extent method. At the same time, some properties of membership degree of formulas A is a Γ-conclusion were given. We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root.

Asymptotically Necessary and Sufficient Quadratic Stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality

Asymptotically necessary and sufficient quadratic stability conditions of Takagi-Sugeno (T-S) fuzzy systems are obtained by utilizing staircase membership functions and a basic inequality. The information of the membership functions is incorporated in the stability analysis by approximating the original continuous membership functions with staircase membership functions. The stability of the T-S fuzzy systems was investigated based on a quadratic Lyapunov function. The asymptotically necessary and sufficient stability conditions in terms of linear matrix inequalities were derived using a basic inequality. A fuzzy controller was also designed based on the stability results. The derivation process of the stability results is straightforward and easy to understand. Case studies confirmed the validity of the obtained stability results.

New Approaches to the Prognosis and Diagnosis of Breast Cancer Using Fuzzy Expert Systems

Breast cancer remains a significant global health challenge, necessitating effective early detection and prognosis to enhance patient outcomes. Current diagnostic methods, including mammography and MRI, suffer from limitations such as uncertainty and imprecise data, leading to late-stage diagnoses. To address this, various expert systems have been developed, but many rely on type-1 fuzzy logic and lack mobile-based applications for data collection and feedback to healthcare practitioners. This research investigates the development of an Enhanced Mobile-based Fuzzy Expert system (EMFES) for breast cancer pre-growth prognosis. The study explores the use of type-2 fuzzy logic to enhance accuracy and model uncertainty effectively. Additionally, it evaluates the advantages of employing the python programming language over java for implementation and considers specific risk factors for data collection. The research aims to dynamically generate fuzzy rules, adapting to evolving breast cancer research and patient data. Key research questions focus on the comparative effectiveness of type-2 fuzzy logic, the handling of uncertainty and imprecise data, the integration of mobile-based features, the choice of programming language, and the creation of dynamic fuzzy rules. Furthermore, the study examines the differences between the Mamdani Inference System and the Sugeno Fuzzy Inference method and explores challenges and opportunities in deploying the EMFES on mobile devices. The research identifies a critical gap in existing breast cancer diagnostic systems, emphasizing the need for a comprehensive, mobile-enabled, and adaptable solution by developing an EMFES that leverages Type-2 fuzzy logic, the Sugeno Inference Algorithm, Python Programming, and dynamic fuzzy rule generation. This study seeks to enhance early breast cancer detection and ultimately reduce breast cancer-related mortality.

基于Membership的高可用性Linux集群

介绍了Ｌｉｎｕｘ集群高可用性（ＨＡ）技术的应用背景和体系结构，重点讲述了集群Ｍｅｍｂｅｒｓｈｉｐ技术可以显著提高集群系统的可用性，并且提出了可配置的Ｍｅｍｂｅｒｓｈｉｐ服务（ＭＢＬＣ）来实现Ｌｉｎｕｘ集群的高可用性的方案。

Stabilization design for continuous-time Takagi-Sugeno fuzzy systems based on new relaxed conditions

This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.

Similarity measure application to fault detection of flight system

Fault detection technique is introduced with similarity measure. The characteristics of conventional similarity measure based on fuzzy number are discussed. With the help of distance measure, similarity measure is constructed explicitly. The designed distance-based similarity measure is applicable to general fuzzy membership functions including non-convex fuzzy membership function, whereas fuzzy number-based similarity measure has limitation to calculate the similarity of general fuzzy membership functions. The applicability of the proposed similarity measure to general fuzzy membership structures is proven by identifying the definition. To decide fault detection of flight system, the experimental data （pitching moment coefficients and lift coefficients） are transformed into fuzzy membership functions. Distance-based similarity measure is applied to the obtained fuzzy membership functions, and similarity computation and analysis are obtained with the fault and normal operation coefficients.

基于Membership拓展的权限机制设计

给出一种基于ASP.NET中的Membership拓展与传统的RBAC机制相结合形成的一种权限机制,它能够实现在Web页面中对于角色与权限的有效控制访问,并且改进了Membership的对权限控制力度不够的缺陷以及传统RBAC机制不能有效利用ASP.NET控件的劣势。最后,在"研究生信息管理系统"项目中实现这种权限机制,充分验证了其优势以及可行性和有效性。

Fuzzy Comprehensive Evaluation for Decision Making of Water Saving Irrigation System

A model of fuzzy comprehensive evaluation for water saving irrigation system (WSIS) decision making is proposed based on establishing an index system affected by six kinds of basic factors including qualitative and quantitative indexes. The object function of WSIS is set up by using the concept of fuzzy membership degree, it is to transform characteristic vector matrix into unify membership matrix and extending the least square method to the least of weighted distance square. The optimum weighted membership degree and the inferior weighted membership degree are used to solve the object function. This method effective solves the problem of classify for fuzzy attributive indexes and the problem of optimum for the set of different attributive indexes. A case study shows that the fuzzy comprehensive evaluation model is reasonable and effective in decision making for water saving irrigation system planning.

Micro-Climate Evaluation System in Thermal Mines

A fuzzy evaluation method was used to evaluate the microclimate in thermal mines. A theoretical model of a microclimate evaluation system was designed and membership functions of the evaluation indices in the system were established. An analytical hierarchy process (AHP) was used to analyze the weight of the evalua- tion indices and their methods of calculation. Software for this evaluation system was developed and used for the evaluation of the microclimate of 714 sections in a mine. It is shown that the evaluation results correspond com- pletely with the actual situation. This evaluation system and the software can be applied in thermal mines.

New Methods of Fitting the Membership Function of Oceanic Water Masses

After reviewing the analytical theories of T S curve, some methods of T S relationship, and fuzzy sets for studying water masses, new methods of fitting the membership function of oceanic water masses are presented based on the characteristics of T S curve family of oceanic water masses. The membership functions of oceanic Subsurface Water Mass with high salinity and Intermediate Water Mass with low salinity are fitted and discussed using the new methods. The proposed methods are useful in analyzing the mixing and modifying processes of these water masses, especially in tracing their sources. The principles and formulae of the new methods and examples are given.

Evaluation of Membership Degree on Conventional Chemical Components in Tobacco from Tobacco Leaf Bases in Yunnan Province Based on Cigarette Brands

[Objective] This study was conducted to investigate the quality condition of chemical components of tobacco in Yunnan. [Method] The C3F samples were collected from 76 base units in Yunnan Province and their conventional chemical components were analyzed, and the evaluation was carded out based on the membership function and hierarchical cluster analysis of cigarette brands H1 and H2 in Yunnan. [Result] The results showed that： （1） Major chemical components of 76 base units were coordinated overall. （2） Total nitrogen of brand H1 was higher than that of the high-quality tobacco leaves by 12.08%; raw tobacco of brands H3 and H2 satisfied the quality requirements of high-quality tobacco in Yunnan; and the total sugar and reducing sugar in flue-cured tobacco of brand H4 were higher those of the high-quality tobacco leaves by 0.76% and 10.3%, respectively. （3） The total sugar, reducing sugar and potassium of tobacco leaves from bases of G1 group were higher than those of tobacco from bases of G2 group by 38.1%, 2.27% and 7.34%, respectively; and total nitrogen and chlorine were lower by 4.69% and 11.11%, respectively; and nicotine contents in tobacco of the two groups were similar. （4） H2 and H3 were not significantly different in main chemical components; H3 and H4 were significantly different in total nitrogen, while other main chemical components were not significant different; and there were no significant differences between H4 and H2. [Conclusion] The quality of tobacco leaves from tobacco base units of G1 and G2 groups was better. Therefore, the evaluation provides theoretical reference for construction of tobacco base units.

Rock burst laws in deep mines based on combined model of membership function and dominance-based rough set

Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific.

Membership Proof and Verification in Authenticated Skip Lists Based on Heap

How to keep cloud data intact and available to users is a problem to be solved. Authenticated skip list is an important data structure used in cloud data integrity verification. How to get the membership proof of the element in authenticated skip list efficiently is an important part of authentication. Kaouthar Blibech and Alban Gabillon proposed a head proof and a tail proof algorithms for the membership proof of elements in the authenticated skip list. However, the proposed algorithms are uncorrelated each other and need plateau function. We propose a new algorithm for computing the membership proof for elements in the authenticated skip list by using two stacks, one is for storing traversal chain of leaf node, the other is for storing authentication path for the leaf. The proposed algorithm is simple and effective without needing plateau function. It can also be applicable for other similar binary hash trees.

Feature Selection Based on Adaptive Fuzzy Membership Functions

Neuro-fuzzy(NF)networks are adaptive fuzzy inference systems(FIS)and have been applied to feature selection by some researchers.However,their rule number will grow exponentially as the data dimension increases.On the other hand,feature selection algorithms with artificial neural networks(ANN)usually require normalization of input data,which will probably change some characteristics of original data that are important for classification.To overcome the problems mentioned above,this paper combines the fuzzification layer of the neuro-fuzzy system with the multi-layer perceptron(MLP)to form a new artificial neural network.Furthermore,fuzzification strategy and feature measurement based on membership space are proposed for feature selection. Finally,experiments with both natural and artificial data are carried out to compare with other methods,and the results approve the validity of the algorithm.

Multi-attribute decision making model based on optimal membership and relative entropy

To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.

Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.

An Approach to Formulation of FNLP with Complex Piecewise Linear Membership Functions

Traditionally, extra binary variables are demanded to formulate a fuzzy nonlinear programming(FNLP) problem with piecewise linear membership functions(PLMFs). However, this kind of methodology usually suffers increasing computational burden associated with formulation and solution, particularly in the face of complex PLMFs. Motivated by these challenges, this contribution introduces a novel approach free of additional binary variables to formulate FNLP with complex PLMFs, leading to superior performance in reducing computational complexity as well as simplifying formulation. A depth discussion about the approach is conducted in this paper, along with a numerical case study to demonstrate its potential benefits.