Diagnosis Problem Solving Using Fuzzy Relations

This paper deals with the restoration and the identification of the causes (diagnoses) through the observed effects (symptoms) on the basis of fuzzy relations and Zadeh's compositional rule of inference. We propose an approach for building fuzzy systems of diagnosis, which enables solving fuzzy relational equations together with design and tuning of fuzzy relations on the basis of expert and experimental information. The essence of tuning consists of the selection such membership functions for fuzzy causes and effects, and also fuzzy relations, which minimize the difference between model and experimental results of diagnosis. The genetic algorithm is used for solving the optimization problem. The proposed approach is illustrated by the computer experiment and the real example of diagnosis.     

Using Fuzzy Ontology to Improve Similarity Assessment: Method and Evaluation

Assessing semantic similarity is a fundamental requirement for many AI applications. Crisp ontology (CO) is one of the knowledge representation tools that can be used for this purpose. Thanks to the development of semantic web, CO‐based similarity assessment has become a popular approach in recent years. However, in the presence of vague information, CO cannot consider uncertainty of relations between concepts. On the other hand, fuzzy ontology (FO) can effectively process uncertainty of concepts and their relations. This paper aims at proposing an approach for assessing concept similarity based on FO. The proposed approach incorporates fuzzy relation composition in combination with an edge counting approach to assess the similarity. Accordingly, proposed measure relies on taxonomical features of an ontology in combination with statistical features of concepts. Furthermore, an evaluation approach for the FO‐based similarity measure named as FOSE is proposed. Considering social network data, proposed similarity measure is evaluated using FOSE. The evaluation results prove the dominance of proposed approach over its respective CO‐based measure.     

Algorithm and axiomatization of rough fuzzy sets based finite dimensional fuzzy vectors

Rough sets, proposed by Pawlak and rough fuzzy sets proposed by Dubois and Prade were expressed with the different computing formulas that were more complex and not conducive to computer operations. In this paper, we use the composition of a fuzzy matrix and fuzzy vectors in a given non-empty finite universal, constitute an algebraic system composed of finite dimensional fuzzy vectors and discuss some properties of the algebraic system about a basis and operations. We give an effective calculation representation of rough fuzzy sets by the inner and outer products that unify computing of rough sets and rough fuzzy sets with a formula. The basis of the algebraic system play a key role in this paper. We give some essential properties of the lower and upper approximation operators generated by reflexive, symmetric, and transitive fuzzy relations. The reflexive, symmetric, and transitive fuzzy relations are characterized by the basis of the algebraic system. A set of axioms, as the axiomatic approach, has been constructed to characterize the upper approximation of fuzzy sets on the basis of the algebraic system.     

Algorithm and axiomatization of rough fuzzy sets based finite dimensional fuzzy vectors

Rough sets, proposed by Pawlak and rough fuzzy sets proposed by Dubois and Prade were expressed with the different computing formulas that were more complex and not conducive to computer operations. In this paper, we use the composition of a fuzzy matrix and fuzzy vectors in a given non-empty finite universal, constitute an algebraic system composed of finite dimensional fuzzy vectors and discuss some properties of the algebraic system about a basis and operations. We give an effective calculation representation of rough fuzzy sets by the inner and outer products that unify computing of rough sets and rough fuzzy sets with a formula. The basis of the algebraic system play a key role in this paper. We give some essential properties of the lower and upper approximation operators generated by reflexive, symmetric, and transitive fuzzy relations. The reflexive, symmetric, and transitive fuzzy relations are characterized by the basis of the algebraic system. A set of axioms, as the axiomatic approach, has been constructed to characterize the upper approximation of fuzzy sets on the basis of the algebraic system.     

A fuzzy reasoning based diagnosis system for X control charts

This paper describes a new diagnosis system, which is based on fuzzy reasoning to monitor the performance of a discrete manufacturing process and to justify the possible causes. The diagnosis system consists chiefly of a knowledge bank and a reasoning mechanism. The knowledge bank provides knowledge of the membership functions of unnatural symptoms that are described by Nelson's rules on X control charts and knowledge of cause-symptom relations. We develop an approach called maximal similarity method (MSM) for knowledge acquisition to construct the fuzzy cause-symptom relation matrix. Through the knowledge bank, the diagnosis system can first determine the degrees of an observation fitting each unnatural symptom. Then, using the fuzzy cause-symptom relation matrix, we can diagnose the causes of process instability. In conclusion we provide a numerical example to illustrate the system.     

A new time invariant fuzzy time series forecasting method based on particle swarm optimization

In the analysis of time invariant fuzzy time series, fuzzy logic group relationships tables have been generally preferred for determination of fuzzy logic relationships. The reason of this is that it is not need to perform complex matrix operations when these tables are used. On the other hand, when fuzzy logic group relationships tables are exploited, membership values of fuzzy sets are ignored. Thus, in defiance of fuzzy set theory, fuzzy sets’ elements with the highest membership value are only considered. This situation causes information loss and decrease in the explanation power of the model. To deal with these problems, a novel time invariant fuzzy time series forecasting approach is proposed in this study. In the proposed method, membership values in the fuzzy relationship matrix are computed by using particle swarm optimization technique. The method suggested in this study is the first method proposed in the literature in which particle swarm optimization algorithm is used to determine fuzzy relations. In addition, in order to increase forecasting accuracy and make the proposed approach more systematic, the fuzzy c-means clustering method is used for fuzzification of time series in the proposed method. The proposed method is applied to well-known time series to show the forecasting performance of the method. These time series are also analyzed by using some other forecasting methods available in the literature. Then, the results obtained from the proposed method are compared to those produced by the other methods. It is observed that the proposed method gives the most accurate forecasts.     

多粒化的模糊粗糙集代数

众所周知,一个粗糙集代数是由一个集合代数加上一对近似算子构成的。首先利用公理化的方法探讨经典的多粒化模糊粗糙集代数系统,可知经典的多粒化模糊粗糙集代数没有很好的性质;其次,引入 具有最小(大)元的等价关系的定义,并给出了基于具有最小(大)元等价关系的多粒化模糊近似算子的概念,在此基础上讨论了模糊粗糙集代数的性质,并得到了诸多结果。     

模糊相似关系下变精度模糊粗糙集

经典变精度模糊粗糙集模型是基于模糊等价关系建立的.在实际应用中,模糊等价关系很难直接构造,需要通过求模糊相似关系的传递闭包生成.对模糊关系的这种改造会丢失较多有价值的信息,而且还增大了模糊粗糙集应用的计算复杂度.基于模糊逻辑算子构造2个模糊集的相对错误包含度,构造性地提出基于模糊相似关系的变精度模糊粗糙集模型,研究了该模型的性质.该模型一方面具有变精度粗糙集的优点,对噪声数据具有很好的容错能力,另一方面是基于模糊相似关系建立的,其应用范围更为广泛.     

Adaptive diagnostic system based on fuzzy relations

Causes (diagnoses) are retrieved and identified using observed effects (symptoms) based on fuzzy relations and Zadeh’s compositional rule of inference. An approach to designing adaptive fuzzy diagnostic systems is proposed. It allows solving fuzzy logic equations and designing and adjusting fuzzy relations using expert and experimental information. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 135–150, July–August 2009.     

Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making

Interval-valued hesitant fuzzy information aggregation plays an important role in interval-valued hesitant fuzzy set theory, which has received more and more attention in recent years. In this paper, we investigate interval-valued hesitant fuzzy multi-attribute group decision-making problems in which there exists a prioritization relationship among the attributes. Firstly, we introduce some Einstein operational laws on interval-valued hesitant fuzzy sets, and discuss some relations of these operations. Then, we develop two interval-valued hesitant fuzzy prioritized aggregation operators with the help of Einstein operations, such as the interval-valued hesitant fuzzy Einstein prioritized weighted average (IVHFEPWA) operator and the interval-valued hesitant fuzzy Einstein prioritized weighted geometric (IVHFEPWG) operator, whose desirable properties are investigated in detail. We further analyze the relationship between these proposed operators and the existing interval-valued hesitant fuzzy prioritized aggregation operators. Moreover, an approach to interval-valued hesitant fuzzy multi-attribute group decision making is given on the basis of the proposed operators. Finally, a numerical example is provided to demonstrate their effectiveness.     

模糊聚类分析在突发事件应急物资分类中应用

为了对应急物资进行合理分类,提出了基于模糊聚类的应急物资分类方法。分析了传统分类方法存在的问题,给出了模糊相似关系和模糊等价关系的概念和求模糊等价矩阵的方法,建立了应急物资分类指标体系,在此基础上提出了基于模糊聚类的应急物资分类方法。最后通过算例验证了该方法的有效性。     

基于模糊逻辑和组合证据理论的信息融合技术在网络管理中的应用

研究基于模糊逻辑和组合证据理论的综合信息融合技术在网络管理中的应用．研究了用于网络管理的来源于多信息源的关联规则的融合方法和推理机制，以及故障与故障原因的模糊关系和模糊规则的融合方法及推理机制；在故障定位方面，采用组合证据理论对网络专家、规则推理和模糊推理所给出的故障原因进行融合得出综合的诊断结果。     

Using multiplicative neuron model to establish fuzzy logic relationships

Determination of fuzzy logic relationships between observations is quite effective on the forecasting performance of fuzzy time series approaches. In various studies available in the literature, it has been seen that utilizing artificial neural networks for establishing fuzzy relations increase the forecasting accuracy. In this study, a novel high order fuzzy time series forecasting approach in which multiplicative neuron model is used to define fuzzy relations is proposed in order to reach high forecasting level. Also, particle swarm optimization method is utilized to train multiplicative neuron model. In order to show forecasting performance of the proposed method, it is applied to a well-known data Taiwan future exchange and the results produced by the proposed approach is compared to those obtained from other fuzzy time series forecasting models. As a result of the implementation, it is observed that the proposed approach gives the best forecasts for Taiwan future exchange time series.     

On the generalization of fuzzy rough sets

Rough sets and fuzzy sets have been proved to be powerful mathematical tools to deal with uncertainty, it soon raises a natural question of whether it is possible to connect rough sets and fuzzy sets. The existing generalizations of fuzzy rough sets are all based on special fuzzy relations (fuzzy similarity relations, T-similarity relations), it is advantageous to generalize the fuzzy rough sets by means of arbitrary fuzzy relations and present a general framework for the study of fuzzy rough sets by using both constructive and axiomatic approaches. In this paper, from the viewpoint of constructive approach, we first propose some definitions of upper and lower approximation operators of fuzzy sets by means of arbitrary fuzzy relations and study the relations among them, the connections between special fuzzy relations and upper and lower approximation operators of fuzzy sets are also examined. In axiomatic approach, we characterize different classes of generalized upper and lower approximation operators of fuzzy sets by different sets of axioms. The lattice and topological structures of fuzzy rough sets are also proposed. In order to demonstrate that our proposed generalization of fuzzy rough sets have wider range of applications than the existing fuzzy rough sets, a special lower approximation operator is applied to a fuzzy reasoning system, which coincides with the Mamdani algorithm.     

Human–machine interface in bioprosthesis control using EMG signal classification

Abstract: We present a concept of human–machine interface intended for the task of bioprosthesis decision control by means of sequential recognition of the patient's intent based on the electromyography (EMG) signal acquired from his/her body. The EMG signal characteristics, the problem of processing the signals including acquisition and feature extraction and their classification are discussed. The contextual (sequential) recognition via fuzzy relations for the classification of the patient's intent is considered and the implied decision algorithms are presented. In the proposed method, the fuzzy relation is determined on the basis of the learning set as a solution of an appropriate optimization problem and then this relation is used in the form of a matrix of membership degrees at successive instants of the sequential decision process. Three algorithms of sequential classification which differ from one another in the sets of input data and procedure are described. The proposed algorithms were experimentally tested in the recognition of phases of the grasping process of the hand on the basis of the EMG signal, where the real-coded genetic algorithm was used as an optimization procedure. The concept of the measurement stand which was the source of information exploited in the experimental investigations of the algorithms is also described.     

Solving fuzzy multiple objective generalized assignment problems directly via bees algorithm and fuzzy ranking

In this paper, a direct solution approach for solving fuzzy multiple objective generalized assignment problems is proposed. In the problem, the coefficients and right hand side values of the constraints and the objective function coefficients are defined as fuzzy numbers. The addressed problem also has a multiple objective structure where the goals are determined so as to minimize the total cost and the imbalance between the workload of the agents. The direct solution approach utilizes the fuzzy ranking methods to rank the objective function values and to determine the feasibility of the constraints within a metaheuristic search algorithm, known as bees algorithm. Different fuzzy ranking methods, namely signed distance, integral value and area based approach are used in bees algorithm. For the computational study, the effects of these fuzzy ranking methods on the quality of the solutions are also analyzed.     

Fault diagnosis and cause analysis using fuzzy evidential reasoning approach and dynamic adaptive fuzzy Petri nets

Fault diagnosis is of great importance to all kinds of industries in the competitive global market today. However, as a promising fault diagnosis tool, fuzzy Petri nets (FPNs) still suffer a couple of deficiencies. First, traditional FPN-based fault diagnosis methods are insufficient to take into account incomplete and unknown information in diagnosis process. Second, most of the fault diagnosis methods using FPNs are only concerned with forward fault diagnosis, and no or less consider backward cause analysis. In this paper, we present a novel fault diagnosis and cause analysis (FDCA) model using fuzzy evidential reasoning (FER) approach and dynamic adaptive fuzzy Petri nets (DAFPNs) to address the problems mentioned above. The FER is employed to capture all types of abnormal event information which can be provided by experts, and processed by DAFPNs to identify the root causes and determine the consequences of the identified abnormal events. Finally, a practical fault diagnosis example is provided to demonstrate the feasibility and efficacy of the proposed model.     

Abductive case‐based reasoning

This article introduces abductive case‐based reasoning (CBR) and attempts to show that abductive CBR and deductive CBR can be integrated in clinical process and problem solving. Then it provides a unified formalization for integration of abduction, abductive CBR, deduction, and deductive CBR. This article also investigates abductive case retrieval and deductive case retrieval using similarity relations, fuzzy similarity relations, and similarity metrics. The proposed approach demonstrates that the integration of deductive CBR and abductive CBR is of practical significance in problem solving such as system diagnosis and analysis, and will facilitate research of abductive CBR and deductive CBR. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 957–983, 2005.     

Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making

Preference relations are a powerful quantitative decision approach that assists decision makers in expressing their preferences over alternatives. In real-life applications, decision makers may not be able to provide exact preference information with crisp numbers. To solve this problem, a hesitant-intuitionistic fuzzy number (Hesitant-IFN) is proposed in this paper, and a proposal for the hesitant-intuitionistic fuzzy preference relation (Hesitant-IFPR) and its complementary form (Hesitant-IFCPR) for uncertain preference information are presented. Compared with other preference relations, the proposed relations use hesitant fuzzy elements (HFEs) to express the priority intensities of decision makers and produce the corresponding non-priority intensities by a conversion formula. In addition, we have deduced the operational laws and comparative methods of Hesitant-IFNs and used such information to investigate the corresponding aggregation operators and the approximate consistency tests. Next, we have constructed a group decision-making approach under a hesitant-intuitionistic fuzzy environment. Finally, two case studies are presented to illustrate the preference relations, the approximate consistency tests and the group decision method.     

On group decision making with four formats of incomplete preference relations

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in four formats of incomplete preference relations, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations, incomplete additive linguistic preference relations, incomplete multiplicative linguistic preference relations. In order to make the collective opinion close each decision maker’s opinion as near as possible, an optimization model is constructed to integrate the four different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.