Use Of Fuzzy Sets Research Articles

An Ecological Framework for Evaluating Map Errors Using Fuzzy Sets

The use of fuzzy sets to assess uncertainty in land-use/cover maps provides a robust conceptual framework for examining unique characteristics of map error. By recognizing the possibility of gradations of error, fuzzy sets can be used to assess errors due to class similarity, or the sensitivity of the map legend to class boundaries. Building on the theoretical work of Gopal and Woodcock (1994), we present a practical methodology for assessing map errors using fuzzy sets. A key component of our methodology focuses on improving the decision-making process map experts assume when conducting a fuzzy set assessment of map errors. Using an ecological context to define varying levels of land-cover class similarity, we demonstrate how a decision framework guides the map experts’ decisions and provides a more meaningful assessment of map errors. Our methodology differs from traditional fuzzy set error assessment methods in that the map expert evaluates misclassifications within the error matrix (off-diagonal cells) rather than individual reference sites. Advantages to a matrixbased approach include a reduction in the time required by map experts to evaluate map errors, and a relatively simple means of conveying map error information to the map user. We conclude that establishing criteria for determining multiple set memberships in a fuzzy set error assessment is an important methodological procedure that is commonly overlooked. Our methodology, designed to explicitly identify land-cover class similarities based on ecological criteria, serves as a practical example of how to address this issue.

Using fuzzy numbers to propagate uncertainty in matrix-based LCI

Background, aim, and scope Analysis of uncertainties plays a vital role in the interpretation of life cycle assessment findings. Some of these uncertainties arise from parametric data variability in life cycle inventory analysis. For instance, the efficiencies of manufacturing processes may vary among different industrial sites or geographic regions; or, in the case of new and unproven technologies, it is possible that prospective performance levels can only be estimated. Although such data variability is usually treated using a probabilistic framework, some recent work on the use of fuzzy sets or possibility theory has appeared in the literature. The latter school of thought is based on the notion that not all data variability can be properly described in terms of frequency of occurrence. In many cases, it is necessary to model the uncertainty associated with the subjective degree of plausibility of parameter values. Fuzzy set theory is appropriate for such uncertainties. However, the computations required for handling fuzzy quantities has not been fully integrated with the formal matrix-based life cycle inventory analysis (LCI) described by Heijungs and Suh (2002).

A fuzzy decision support system for meta-evaluation a new approach and a case study performed in Brazil

This paper presents a new methodology for meta-evaluation that makes use of fuzzy sets and fuzzy logic. It is composed of a data collection instrument and of a hierarchical fuzzy inference system. The advantages of the proposed methodology are: (i) the instrument, which allows intermediate answers; (ii) the inference process ability to adapt to specific needs; and (iii) transparency, through the use of linguistic rules that facilitate both the understanding and the discussion of the whole process. The rules are based on guidelines established by the Joint Committee on Standards for Educational Evaluation (1994) and also represent the view of experts. The system can provide support to evaluators that may lack experience in meta-evaluation. A case study is presented as a validation of the proposed methodology.

A general concept for solving linear multicriteria programming problems with crisp, fuzzy or stochastic values

For modelling imprecise data the literature offers two different methods: either the use of probability distributions or the use of fuzzy sets. In our opinion these two concepts should be used in parallel or in combination, dependent on the real situation. Moreover, in many economic problems, the well-known probabilistic or fuzzy solution procedures are not suitable because the stochastic variables do not have a simple classical distribution and the fuzzy values are not fuzzy intervals. For example, in case of investment problems the coefficients may often be described by means of more complex distributions or more general fuzzy sets. In this case we propose to distinguish several scenarios and to describe the parameters of the different scenarios by fuzzy intervals. For solving such stochastic linear programs with fuzzy parameters we propose a new method, which retains the original objective functions dependent on the different states of nature. It is based on the integrated chance constrained program introduced by Klein Haneveld [On integrated chance constraints, in: Gargnano (Ed.), Stochastic Programming, Springer, Berlin, 1986, pp. 194–209] and the interactive solution process FULPAL, see Rommelfanger [Fuzzy Decision Support-Systeme - Entscheiden bei Unschärfe, second ed., Springer, Berlin, Heidelberg, 1994; FULPAL: an interactive method for solving multiobjective fuzzy linear programming problems, in: R. Slowinski, J. Teghem (Eds.), Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, Reidel Publishing Company, Dordrecht, 1990, pp. 279–299; FULPAL 2.0—an interactive algorithm for solving multicriteria fuzzy linear programs controlled by aspiration levels, in: D. Scheigert (Ed.), Methods of Multicriteria Decision Theory, Pfalzakademie Lamprecht, 1995, pp. 21–34; The advantages of fuzzy optimization models in practical use, Fuzzy Optim. Decision Making 3 (2004) 295–310] and Rommelfanger and Slowinski [Fuzzy linear programming with single or multiple objective functions, in: R. Slowinski (Ed.), Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer Academic Publishers, Norwell, MA, 1998, pp. 179–213]. An extensive numerical example illustrates the efficiency and the generality of the proposed new method.

Models and methods of decision making in fuzzy environment and their applications to power engineering problems

AbstractResults of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems are presented. Two types of situations which need the application of a multicriteria approach are classified. According to this, two classes of models (〈X, M〉 and 〈X, R〉 models) are considered with utilizing the Bellman–Zadeh approach to decision making in a fuzzy environment and techniques for modelling of fuzzy preference relations for their analysis. The application of the Bellman–Zadeh approach for solving 〈X, M〉 problems conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analysing associated maxmin problems. Analysis of 〈X, R〉 models is considered as part of a general approach to solving problems with fuzzy coefficients. Three techniques for processing of fuzzy preferences relations are considered. The first technique is associated with building and analysing a membership function of a subset of non‐dominated alternatives considering all criteria simultaneously. The second technique is of a lexicographic character and consists in step‐by‐step consideration of criteria. The third technique is based on aggregating membership functions of subsets of non‐dominated alternatives for each criterion. The results of the paper are universally applicable and are already being used to solve power engineering problems. It is illustrated by considering problems of multicriteria power and energy shortage allocation, multicriteria power system operation, and substation planning with considering criteria of quantitative as well as of qualitative character. Copyright © 2007 John Wiley & Sons, Ltd.

Mathematical Modelling of Observer in Physical Systems

In this paper a mathematical model for a one-dimensional observer by the use of fuzzy sets is studied. A realistic approach to the problem of unity by using of relative metrics on relative manifolds is presented. A driven system of Chua’s diode contains an observer as a relative vector field is considered.

Relative vector fields

In this paper relative vector fields by the use of fuzzy sets are presented. A representation for relative vector fields at non-singular points is deduced. Poisson bracket product and Frobenius theorem for relative vector fields are extended.

From vagueness in medical thought to the foundations of fuzzy reasoning in medical diagnosis

This article delineates a relatively unknown path in the history of medical philosophy and medical diagnosis. It is concerned with the phenomenon of vagueness in the physician's "style of thinking" and with the use of fuzzy sets, systems, and relations with a view to create a model of such reasoning when physicians make a diagnosis. It represents specific features of medical ways of thinking that were mentioned by the Polish physician and philosopher Ludwik Fleck in 1926. The paper links Lotfi Zadeh's work on system theory before the age of fuzzy sets with system-theory concepts in medical philosophy that were introduced by the philosopher Mario Bunge, and with the fuzzy-theoretical analysis of the notions of health, illness, and disease by the Iranian-German physician and philosopher Kazem Sadegh-Zadeh. Some proposals to apply fuzzy sets in medicine were based on a suggestion made by Zadeh: symptoms and diseases are fuzzy in nature and fuzzy sets are feasible to represent these entity classes of medical knowledge. Yet other attempts to use fuzzy sets in medicine were self-contained. The use of this approach contributed to medical decision-making and the development of computer-assisted diagnosis in medicine. With regard to medical philosophy, decision-making, and diagnosis; the framework of fuzzy sets, systems, and relations is very useful to deal with the absence of sharp boundaries of the sets of symptoms, diagnoses, and phenomena of diseases. The foundations of reasoning and computer assistance in medicine were the result of a rapid accumulation of data from medical research. This explosion of knowledge in medicine gave rise to the speculation that computers could be used for the medical diagnosis. Medicine became, to a certain extent, a quantitative science. In the second half of the 20th century medical knowledge started to be stored in computer systems. To assist physicians in medical decision-making and patient care, medical expert systems using the theory of fuzzy sets and relations (such as the Viennese "fuzzy version" of the Computer-Assisted Diagnostic System, CADIAG, which was developed at the end of the 1970s) were constructed. The development of fuzzy relations in medicine and their application in computer-assisted diagnosis show that this fuzzy approach is a framework to deal with the "fuzzy mode of thinking" in medicine.

A fuzzy approach to Markov decision processes with uncertain transition probabilities

In this paper, Markov decision models with uncertain transition matrices, which allow a matrix to fluctuate at each step in time, is described by the use of fuzzy sets. We find a Pareto optimal policy maximizing the infinite horizon fuzzy expected discounted reward (FEDR) over all stationary policies under some partial order. The Pareto optimal policies are characterized by maximal solutions of an optimal inclusion including efficient set-functions. As a numerical example, a machine maintenance problem is considered.

Modelling the deterioration of buried infrastructure as a fuzzy Markov process

Research Article| March 01 2006 Modelling the deterioration of buried infrastructure as a fuzzy Markov process Yehuda Kleiner; Yehuda Kleiner 1Senior Research Officer and Group Leader, Institute for Research in Construction, National Research Council Canada (NRC), 1200 Montreal Road, Building M-20Ottawa, ON Canada K1A 0R6 Phone: 1-613-993-3805 Fax: 1-613-954-5984 yehuda.kleiner@nrc-cnrc.gc.ca E-mail: yehuda.kleiner@nrc-cnrc.gc.ca Search for other works by this author on: This Site PubMed Google Scholar Rehan Sadiq; Rehan Sadiq 2Research Officer, Institute for Research in Construction, National Research Council Canada (NRC), 1200 Montreal Road, Building M-20Ottawa, ON, Canada K1A 0R6 Phone: 1-613-993-6282 Fax: 1-613-954-5984 rehan.sadiq@nrc-cnrc.gc.ca Search for other works by this author on: This Site PubMed Google Scholar Balvant Rajani Balvant Rajani 3Principal Research Officer, Institute for Research in Construction, National Research Council Canada (NRC), 1200 Montreal Road, Building M-20Ottawa, ON Canada K1A 0R6 Phone: 1-613-993-3810 Fax: 1-613-954-5984 balvant.rajani@nrc-cnrc.gc.ca Search for other works by this author on: This Site PubMed Google Scholar Journal of Water Supply: Research and Technology-Aqua (2006) 55 (2): 67–80. https://doi.org/10.2166/aqua.2006.074 Article history Received: August 23 2005 Accepted: December 08 2005 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Share Icon Share Twitter LinkedIn Tools Icon Tools Cite Icon Cite Permissions Search Site Search nav search search input Search input auto suggest search filter All ContentAll JournalsThis Journal Search Advanced Search Citation Yehuda Kleiner, Rehan Sadiq, Balvant Rajani; Modelling the deterioration of buried infrastructure as a fuzzy Markov process. Journal of Water Supply: Research and Technology-Aqua 1 March 2006; 55 (2): 67–80. doi: https://doi.org/10.2166/aqua.2006.074 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Dearth of data is the greatest acknowledged obstacle to the deterioration modeling of the buried infrastructure assets. In the last two decades numerous models have been proposed with a greater emphasis on Markovian Deterioration Processes (MDP). The MDP requires that the condition of the deteriorating system be encoded as an ordinal condition rating, based on numerous distress indicators obtained possibly from direct and indirect observations, as well as from non-destructive tests. The encoding of distress indicators into condition rating is inherently imprecise and involves subjective judgment. This imprecision is not considered, let alone propagated in the traditional application of the MDP.In this paper a new approach is presented to model the deterioration of buried infrastructure assets using a fuzzy rule-based, non-homogeneous Markov process. This deterioration model yields the ‘possibility’ of failure at every time step along the life of the asset. The use of fuzzy sets and fuzzy techniques help to incorporate the inherent imprecision and subjectivity of the data, as well as to propagate these attributes throughout the model, yielding more realistic results.This paper is the first of two companion papers that describe a complete method of managing failure risk of large buried infrastructure assets. The second companion paper describes how the condition ratings along the life of the asset are converted to risk values and how effective decisions can be made about the renewal and/or scheduling the next inspection of the asset. condition rating, deterioration, failure risk, fuzzy Markov, infrastructure, large water mains This content is only available as a PDF. © NRC 2006 You do not currently have access to this content.

Failure risk management of buried infrastructure using fuzzy-based techniques

Research Article| March 01 2006 Failure risk management of buried infrastructure using fuzzy-based techniques Yehuda Kleiner; Yehuda Kleiner 1Senior Research Officer and Group Leader, Institute for Research in Construction, National Research Council Canada (NRC), 1200 Montreal Road, Building M-20Ottawa, ON Canada K1A 0R6, Phone: 1-613-993-3805 Fax: 1-613-954-5984 e-mail: yehuda.kleiner@nrc-cnrc.gc.ca E-mail: yehuda.kleiner@nrc-cnrc.gc.ca Search for other works by this author on: This Site PubMed Google Scholar Balvant Rajani; Balvant Rajani 2Principal Research Officer, Institute for Research in Construction, National Research Council Canada (NRC), 1200 Montreal Road, Building M-20Ottawa, ON Canada K1A 0R6, Phone: 1-613-993-3810 Fax: 1-613-954-5984 e-mail: balvant.rajani@nrc-cnrc.gc.ca Search for other works by this author on: This Site PubMed Google Scholar Rehan Sadiq Rehan Sadiq 3Research Officer, Institute for Research in Construction, National Research Council Canada (NRC), 1200 Montreal Road, Building M-20, Ottawa, ON Canada K1A 0R6, Phone: 1-613-993-6282 Fax: 1-613-954-5984 e-mail: rehan.sadiq@nrc-cnrc.gc.ga Search for other works by this author on: This Site PubMed Google Scholar Journal of Water Supply: Research and Technology-Aqua (2006) 55 (2): 81–94. https://doi.org/10.2166/aqua.2006.075 Article history Received: August 28 2005 Accepted: December 08 2005 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Cite Icon Cite Permissions Search Site Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsThis Journal Search Advanced Search Citation Yehuda Kleiner, Balvant Rajani, Rehan Sadiq; Failure risk management of buried infrastructure using fuzzy-based techniques. Journal of Water Supply: Research and Technology-Aqua 1 March 2006; 55 (2): 81–94. doi: https://doi.org/10.2166/aqua.2006.075 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex The effective management of failure risk of buried infrastructure assets requires knowledge of their current condition, their rate of deterioration, the expected consequences of their failure and the owner's (decision-maker) risk tolerance. Fuzzy-based techniques seem to be particularly suited to modeling the deterioration of buried infrastructure assets, for which data are scarce, cause-effect knowledge is imprecise and observations and criteria are often expressed in vague (linguistic) terms (e.g., ‘good’, ‘fair’ ‘poor’ condition, and so on). The use of fuzzy sets and fuzzy-based techniques helps to incorporate inherent imprecision, uncertainties and subjectivity of available data, as well as to propagate these attributes throughout the model, yielding more realistic results.This paper is the second of two companion papers that describe an entire method of managing risk of large buried infrastructure assets. The first companion paper describes the deterioration modeling of buried infrastructure assets, using a fuzzy rule-based, non-homogeneous Markov process. This paper describes how the fuzzy condition rating of the asset is translated into a possibility of failure. This possibility of failure is combined with the fuzzy failure consequences to obtain fuzzy risk of failure throughout the life of the pipe. This life-risk curve can be used to make effective decisions on pipe renewal. These decisions include when to schedule the next inspection and condition assessment or alternatively, when to renew a deteriorated pipe, and what renewal alternative should be selected. buried pipes, condition rating, deterioration, failure risk, fuzzy, infrastructure, renewal decision, risk management This content is only available as a PDF. © NRC 2006 You do not currently have access to this content.

Reliability assessment method for pressure piping containing circumferential defects based on fuzzy probability

Randomness of the assessment parameters and fuzzy failure areas both exist in the reliability assessment of pressure piping containing circumferential defects. The use of fuzzy sets is considered in this context. It is pointed out that the failure probability of pressure piping containing circumferential defects is in fact a fuzzy failure probability, and a method to compute the fuzzy failure probability of pressure piping is proposed. Numerical examples that consider the fuzzy failure areas of pressure piping can have an effect on reliability estimation of pressure piping containing defects, and different assessment results can sometimes be obtained. Compared with the conventional reliability estimation method, which neglects the existence of fuzzy failure areas, the method proposed in this paper provides a more complete assessment of pressure piping containing defects.

On the representation, measurement, and discovery of fuzzy associations

The use of fuzzy sets to describe associations between data extends the types of relationships that may be represented, facilitates the interpretation of rules in linguistic terms, and avoids unnatural boundaries in the partitioning of the attribute domains. In addition, the partial membership values provide a method for incorporating the distribution of the data into the assessment of a rule. This paper investigates techniques to identify and evaluate associations in a relational database that are expressible by fuzzy if-then rules. Extensions of the classical confidence measure based on the /spl alpha/-cut decompositions of the fuzzy sets are proposed to incorporate the distribution of the data into the assessment of a relationship and identify robustness in an association. A rule learning strategy that discovers both the presence and the type of an association is presented.

Code performance assessment: application to the pull-out strength of concrete

This paper deals with the investigation into the best fitted program for solving a particular problem. We present a general method to assess the efficiency of a code in the general context where both experimental results (due to problems of experimental reproducibility and/or sample size) and theoretical results (predicted by the computer code) are uncertain. This method is based on the use of fuzzy sets to represent partial results and on a method to aggregate them into a global confidence degree. This method is applied to the problem of the pulling steel plugs out of a block of concrete or masonry, the code being based on limit analysis theory.

Use of Fuzzy Sets to Evaluate Driver Perception of Variable Message Signs

Current methods for evaluating the quality of service provided by a variable message sign (VMS) may not yield results that represent the satisfaction drivers experience because these techniques cannot represent the variability and complexity of human perception with great fidelity. To solve those problems, a new method that applies fuzzy set theory was developed. Results of a preexisting survey of VMS service quality were reanalyzed with this method. For this application, two membership functions were constructed with two different experimental methods: interval estimation and pairwise comparison. Specifically, construction of the second membership function used Saaty's eigenvector method. These two membership functions employ five linguistic statements to represent the degree of satisfaction and relative importance of six performance criteria. Quality of VMS service perceived by an individual driver was evaluated with the concept of the fuzzy weighted average. A set of 322 quality measures was computed, and they were aggregated and transformed into a single percentage value with the use of an arithmetic fuzzy mean. The defuzzified final value indicates the degree of satisfaction with VMS service perceived by a group of participating drivers, taking into consideration the variance of human perception and the degree of importance of the six criteria. By employing the proposed method, the quality of VMS service as subjectively perceived by humans and influenced by various exogenous factors can be evaluated while still considering the subjective and complicated manner of human thinking.

Use of Fuzzy Sets and the Possibility Category in the Problems of Character Recognition

Use of Fuzzy Sets and the Possibility Category in the Problems of Character Recognition

Use of Fuzzy Sets to Evaluate Driver Perception of Variable Message Signs

Current methods for evaluating the quality of service provided by a variable message sign (VMS) may not yield results that represent the satisfaction drivers experience because these techniques cannot represent the variability and complexity of human perception with great fidelity. To solve those problems, a new method that applies fuzzy set theory was developed. Results of a preexisting survey of VMS service quality were reanalyzed with this method. For this application, two membership functions were constructed with two different experimental methods: interval estimation and pairwise comparison. Specifically, construction of the second membership function used Saaty's eigenvector method. These two membership functions employ five linguistic statements to represent the degree of satisfaction and relative importance of six performance criteria. Quality of VMS service perceived by an individual driver was evaluated with the concept of the fuzzy weighted average. A set of 322 quality measures was computed, ...

Visual acuity of vision tested by fuzzy logic: An application in ophthalmology as a step towards a telemedicine project

Abstract This paper deals with the application of a soft computing technique to a medical project. The application consists in connecting a patient to an ophthalmologist situated in a hospital or to a specialized web center through a telecommunication network. The patient may be at home or at any other place agreed upon for that teleconsultation. The aim of the study concerns the evaluation of a patient's visual acuity, using web-based medical advice. Indeed an ophthalmologist actually requires specific equipment, available only in medical centers and used by specialized staff. This situation leads to limit the number of patients being examined by the physician and so to extend the waiting time necessary before you can get an appointment (you have to wait between 8 and 10 months at the moment in France). So, public health services have an interest in making these tests available to the patients, in schools, firms, at home and so on, the tests being implemented remotely by competent personnel thanks to modern means of telecommunication. In order to achieve this, a certain number of tests are made, during which optotypes (or letters of different sizes) are presented to the patient. We propose an algorithmic treatment of the binary answers, based on the use of fuzzy sets, in order to eliminate the different mistakes (voluntary or not) that can be made. This algorithm also allows to assess the quality of the examination by measuring the inaccuracy of the visual acuity. This work must be considered as a pioneering telemedicine project, and particularly as a way of developing expert systems able to generate medical advice without the physician's actual presence.

Sectors associations and similarities in input-output systems: An application of dual scaling and fuzzy logic to Canada and the United States

Various authors addressed interindustry linkages in the context of input-output systems, however many focused on the identification of key sectors in the economy. Sonis et al. (1996) offered as a field of influence theory an alternative approach focusing on the analytical importance of elements and combinations of elements. In an attempt to further the understanding of the linkages in an input-output system, the objective of this paper is to examine the cluster structure of sales and purchases profiles when the principle of ‘excluded middle’ is violated by the use of fuzzy sets. The identification of fuzzy clusters is based on an analysis to derive an alternative decomposition of␣interindustry flows (Dridi and Hewings 2002), it is a complementary approach to the so-called ‘Matrioshka principal’ (Sonis and Hewings 1990) and will be presented first; the approach looks into the hierarchy of the statistical dependence between supply and demand in input-output systems. The analysis on the cluster structure and the interindustry flows is conducted using the data analysis technique known as dual scaling (Nishisato 1980, 1994). Results of the analysis will be illustrated using input-output tables of the US and Canada.

Fuzzy sets and models of decision making

Results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented. Much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems. The application of a multicriteria approach is needed to solve 1. (1)|problems in which solution consequences cannot be estimated on the basis of a single criterion, that involves the necessity of analyzing a vector of criteria, and 2. (2)|problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so-called decision uncertainty regions, and the application of additional criteria can serve as a convincing means to contract these regions. According to this, two classes of models (〈 X, M〉 and 〈 X, R〉 models) are considered with applying the Bellman-Zadeh approach and techniques of fuzzy preference relations to their analysis. The consideration of 〈 X, R〉 models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients. This approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. It allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve problems of power engineering.