Expert Elicitation of Fuzzy Membership Functions of Linguistic Terms: A Fire Evacuation Case Study

The linguistic interface is a group of fuzzy sets and their corresponding membership functions applied to define the linguistic terms used in fuzzy modeling, granular computing and computing with words. The fuzzy C-means algorithm (FCM) is widely used in the generation of membership functions for linguistic terms from historical data. However, most of FCM-based membership function generation algorithms and their variants consider little on the transparency or the understandability of the resulting membership functions. This paper proposes a genetic pre-shaped fuzzy C-means algorithm (GPFCM) to generate transparent membership functions for linguistic terms in linguistic interfaces. The proposed algorithm will preserve predefined transparent shapes of membership functions during the optimization process of the clustering algorithm. To avoid local optimality, the genetic algorithm is applied to solve the optimization problem in the clustering algorithm. Numeric experiments based on data collected in a real civil project demonstrate the feasibility and superiority of the proposed new algorithm. The classification problems solved by fuzzy decision trees based on different linguistic interfaces are provided to demonstrate the advantages of the proposed linguistic interface generation method.

Determining contingency reserve is critical to project risk management. Classic methods of determining contingency reserve significantly rely on historical data and fail to effectively incorporate certain types of uncertainties such as vagueness, ambiguity, and subjectivity. In this paper, an interval type-2 fuzzy risk analysis model (IT2FRAM) is introduced in order to determine the contingency reserve. In IT2FRAM, the membership functions for the linguistic terms used to describe the probability, impact of risk and the opportunity events are developed, optimized, and aggregated using interval type-2 fuzzy sets and the principle of justifiable granularity. IT2FRAM is an extension of a fuzzy arithmetic-based risk analysis method which considers such uncertainties and addresses the limitations of probabilistic and deterministic techniques of contingency determination methods. The contribution of IT2FRAM is that it considers the opinions of several subject matter experts to develop the membership functions of linguistic terms. Moreover, the effect of outlier opinions in developing the membership functions of linguistic terms are reduced. IT2FRAM also enables the aggregation of non-linear membership functions into trapezoidal membership functions. A hypothetical case study is presented in order to illustrate the application of IT2FRAM in Fuzzy Risk Analyzer© (FRA©), a risk analysis software.

SummaryThis chapter proposes a fuzzy data-mining algorithm for extracting both association rules and membership functions from quantitative transactions. The number of membership functions for each item is not predefined, but can be dynamically adjusted. A GA-based framework for finding membership functions suitable for mining problems is proposed. The encoding of each individual is divided into two parts. The control genes are encoded into bit strings and used to determine whether membership functions are active or not. The parametric genes are encoded into real-number strings to represent membership functions of linguistic terms. The fitness of each set of membership functions is evaluated using the fuzzy-supports of the linguistic terms in the large 1-itemsets and the suitability of the derived membership functions. The suitability of membership functions considers overlap, coverage and usage factors.

The shapes of terms used in fuzzy systems have adopted several 'conventions'. Terms are almost invariably normalised (having a maximum membership value of 1), convex (having a single maximum or plateau maxima) and distinct (being restricted in their degree of overlap: often expressed as some variation on the concept that all membership values at any point in the universe of discourse sum to I across that universe). The shape of these terms are generated by certain accepted membership functions: piecewise linear functions (with restrictions), Gaussians or Sigmoids are almost exclusively used. As such these constitute only a small subset of the total set of possible shapes of terms. These conventions are largely empirical or are justified by arguments based on what might loosely be called 'fuzzy control principles'. The paper highlights a number of membership functions that developers of fuzzy systems outside the paradigm of fuzzy control may consider as alternatives. In particular, we highlight subsumed fuzzy sets, discuss the merits of non-convex fuzzy sets and present a medical application where sub-normal fuzzy sets have been used. These ideas are reinforced by examples.

Contemporary research in the field of creation and development of intelligent systems based on fuzzy logic is carried out mainly in the direction of developing highly efficient methods for their synthesis and structural-parametric optimization. In recent years, due to the intensive development of information technologies and computer hardware, bioinspired intelligent techniques of global search are quite promising for solving problems of synthesis and optimization of fuzzy systems, which include evolutionary and swarm methods, that simulate the processes of natural selection, as well as collective behavior of various groups of social animals, insects and microorganisms in nature. This paper is devoted to the development and study of a method of optimal membership functions search for fuzzy systems based on bioinspired evolutionary algorithms of global optimization. The obtained method allows finding the optimal membership functions of linguistic terms at solving the compromise problems of multicriteria structural optimization of various fuzzy systems in order to increase their efficiency, as well as to reduce the degree of complexity of further parametric optimization. In the proposed method for finding the global optimum of the problem being solved, the iterative procedures are carried out on the basis of combination of several different bioinspired evolutionary algorithms with subsequent analysis of the results obtained and the choice of the best variant of the membership function vector. The paper outlines the theoretical foundations and information model for the implementation of the computational step-by-step method for structural optimization of fuzzy systems, as well as presents various options for carrying out its search procedures. In particular, the features of the application and adaptation to the search problem to be solved of such bioinspired evolutionary algorithms as genetic, artificial immune systems and biogeographic are discussed.

Fuzzy environmental monitoring for the quality assessment: Detailed feasibility study for the Karun River basin, Iran

Identification of the real risk factors of diabetes is still very much inconclusive. In this paper, fuzzy rules based system was devised to identify risk factors of diabetes. The system consists of five input variables: Body Mass Index, age, blood pressure, Creatinine, and serum cholesterol and one output variable: level of risk. Three Gaussian membership functions for linguistic terms are defined for each input variable. The level of risk is defined using three triangular membership functions to represent output variable. Based on the information from patients’ clinical audit reports, the system was used to classify the level of risk of fifty patients that currently undergoing regular diagnosis for diabetes treatment. The system successfully classified the risk into three levels of Low, Medium and High where three main contributing factors toward developing diabetes were identified.<br /> The three risk factors are age, blood pressure and serum cholesterol.<br /> The multi-input system that characterised by IF-THEN fuzzy rules provide easily interpretable result for identifying predictors of diabetes. Research to establish reproducibility and validity of the findings are left for future works.

Terms used in fuzzy systems are almost invariably normalised, convex and distinct. The shapes of these terms are generated by certain accepted membership functions: piecewise linear functions, Gaussians or Sigmoids are almost exclusively used. This paper extends previous work in which it was suggested that non-convex membership functions might be considered for use in the context of modelling human decision making utilising fuzzy expert systems. In particular, the merits of non-convex fuzzy sets are discussed and a case study is presented to investigate inferencing with non-convex fuzzy sets in a practical implementation. It is shown that it is indeed possible to build a fuzzy expert system featuring usual Mamdani style fuzzy inference in which a time-related non-convex fuzzy set is used together with 'traditional' fuzzy sets. An examination is made of the resultant output surface generated by four different sub-classes of non-convex membership functions.

Because of the lack or incompleteness of data, a number of maritime risk studies based on fuzzy rule‐based approaches have been proposed. However, two drawbacks can be identified in such approaches. The first is the low degree of discrimination of risk results because of the membership function distribution of the linguistic terms describing inputs. The lack of discrimination becomes degenerative in circumstances where the membership functions of linguistic terms are disproportionately distributed. The second is the lack of consideration for different effects of risk results caused by input weights because of the loss of information from the inputs. By developing a new mechanism for constructing rules and fuzzy conclusions, a risk modelling capable of overcoming such difficulties is proposed. The methodology is validated using two case studies selected from the literature. It is concluded that the framework is able to provide better discrimination of risk results. Risk outcomes can be generated with confidence regardless of the membership function shapes of linguistic terms in both the antecedent and consequent parts. It also has the feature that enables risk results to be sensitive to the minor alterations of input weights.

Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations

In real-world database, most attribute values of objects are numerical, numeral is too detail to obtaining good information or decision. Hence, linguistic rules of a set of data would be very desirable and human consistent. Based on a new aggregation operator for aggregating linguistic terms, extracting linguistic rules are presented. Due to obtain a linguistic rule with higher truth degree, genetic algorithm is used to optimize the number and membership functions of linguistic terms.

This chapter is devoted to the development and research of intelligent information technology (IIT) for structural optimization of fuzzy systems (FS) based on the evolutionary search of the optimal membership functions. The proposed IIT uses a combination of different (two or more) bioinspired evolutionary algorithms and allows finding the optimal membership functions of linguistic terms at solving the compromise problems of multi-criteria structural optimization of various FSs to increase their efficiency, as well as to reduce the degree of complexity of further parametric optimization. To study the effectiveness of the considered IIT, the search of the optimal membership functions is conducted for a FS of the multi-purpose mobile robot (MR) designed to move along inclined and vertical ferromagnetic surfaces, with the implementation of three evolutionary algorithms: genetic, artificial immune systems, biogeographic. The analysis of the obtained results showed that the usage of the proposed IIT gives the opportunity to significantly increase the efficiency of the MR control, as well as to reduce the total number of parameters at further parametric optimization of linguistic terms, which confirms its high efficiency.

Web services provide a promising solution to an age old need of fast and flexible information sharing among people and businesses. One of the key research issues in web services is selection of most pertinent web services. Selection of web service has become a tedious job because of the increasing number of service providers providing services with similar functionality. Therefore, a framework for selection and discovery of web service that can meet the non-functional requirements is needed. In this work, we have developed a selection tool (WSS-NFP) for web services which can rank services based on their non functional properties such as performance, delay etc. We have used soft computing techniques for selection and discovery of web services based on non functional properties. These properties are fuzzy in nature. A tool is developed and implemented that is generic in nature and can be customized for any application domain. As a core of this tool, it consists of Fuzzy System for ranking web services and Neural Network for fine tuning the membership functions for linguistic terms. Appropriate and fine tuned membership functions help in minimizing the output error measure and maximizing the performance index of the proposed tool. This tool is basically a Neuro-Fuzzy system for ranking web services of any domain.

The work is devoted to the problems of modeling systems with incomplete or complex mathematical description using the fuzzy logic apparatus. The object of modeling is the heat-recovery boiler of the gas turbine power station. The object is represented as a complex, thermodynamic system with non-stationary dynamics and a variety of forms of communication of input and output parameters, which influence the heat exchange processes. Due to the complex specifics of the system or the conditions of incomplete information about the object, the creation of an adequate mathematical description using the methods of the classical theory of automatic control becomes a difficult task. The use of the apparatus of fuzzy logic for modeling objects with complex dynamics has several advantages: they function well in conditions of incomplete information about the object of research, do not require a strictly mathematical description of the object, have the ability to adjust existing models without making many changes to them. Having information about the processes in the object of research, knowing the degree of influence of input parameters on the output characteristics of the object and knowing the limits of changing parameters, one can create a model that will describe the dynamic characteristics of the object with a sufficient degree of adequacy by means of the fuzzy logic apparatus. As a result of the research, a model of a heat recovery boiler was developed using a fuzzy logic apparatus. Linguistic variables, membership functions of linguistic terms, focused on the subsequent solution of the identification problem are defined. A rule base has been developed to describe the behavior of the model. The method of defuzzification of output linguistic variables is selected. The identification of a fuzzy model based on historical trend curve in equipment operation has been carried out.

Modeling risk management systems in construction projects is a complex process because of various internal and external factors and their interrelationships. Fuzzy system dynamics (FSD) have been commonly employed to model and analyze construction risk management systems. To run FSD simulation models, all hard (objective) and soft (subjective) causal relationships between variables must be quantified. However, a research gap exists regarding structured methods for constructing soft causal relationships in FSD models. This paper proposes an adaptive hybrid model consisting of fuzzy analytical hierarchy process, weighted principle of justifiable granularity, and fuzzy aggregation operators to determine crisp values of causality degree for soft (subjective) causal relationships in FSD modeling of construction risk analysis. The proposed model is implemented in analyzing construction risks of a windfarm project to illustrate its applicability. The proposed model generates two results: (1) optimized membership functions for linguistic terms representing the causality degree of soft relationships and (2) the crisp value for the causality degree of soft relationships. The contribution of study is to propose a structured model to improve efficiency and effectiveness of developing FSD quantitative modeling by addressing soft causal relationships between different variables in FSD models and considering multiple risk expertise of heterogeneous experts in construction risk assessment.