Application Of Fuzzy Set Theory Research Articles

Applications of Possibility and Evidence Theory in Civil Engineering

This article is devoted to applications of fuzzy set theory, possibility theory and evidence theory in civil engineering, presenting current work of a group or researchers at the University of Innsbruck. We argue that these methods are well suited for analyzing and processing the parameter uncertainties arising in soil mechanics and construction management. We address two specific applications here: finite element computations in foundation engineering and a queueing model in earth work.

APPLICATIONS OF POSSIBILITY AND EVIDENCE THEORY IN CIVIL ENGINEERING

This article is devoted to applications of fuzzy set theory, possibility theory and evidence theory in civil engineering, presenting current work of a group or researchers at the University of Innsbruck. We argue that these methods are well suited for analyzing and processing the parameter uncertainties arising in soil mechanics and construction management. We address two specific applications here: finite element computations in foundation engineering and a queueing model in earth work.

Application of fuzzy sets with different t-norms in the interpretation of portfolio matrices in strategic management

The possible application of fuzzy sets theory in strategic management to the problem of portfolio matrices analysis, used for strategy alternative(s) formulation and selection is described. The values of membership functions of input variables into portfolio matrices are combined with different t-norms: (a) T M(x,y)= min(x,y) ; (b) T P(x,y)=xy ; (c) Sugeno's λ t-norms; (d) Hamacher's t-norm family, for investigating possible different results, but the recommended strategy selection remained the same for all applied t-norms.

A fuzzy set approach for modelling time in GIS

This paper describes an application of fuzzy set theory to perform temporal interpolation in a raster GIS database. Specific fuzzy membership functions have been derived to simulate spatial changes between consecutive snapshots registered in the database. The proposed approach is tested on a very dynamic rural-urban environment of Montreal Metropolitan area in Quebec, Canada, covering the period from 1956 to 1986 with a temporal resolution of ten years. A user friendly software package named FUZZY_TEMP was developed and integrated in the GRASS4.1 environment in order to perform the implementation of the developed concepts.

Fuzzy dynamical systems in epidemic modelling

Proposes an application of fuzzy set theory to model epidemiological problems. Fuzzy logic has been revealed as a powerful predictive tool in the epidemiology of infectious diseases and some ideas are presented on how this could be done. This work presents an attempt to model the dynamics of rabies among a population of partially vaccinated dogs. This study demonstrates how a dynamical system can be modelled by fuzzy linguistic rules compared to the classical differential equations approach. The results are very encouraging and the approach through a more complex dynamical system is discussed in the final section.

Multireservoir System Optimization using Fuzzy Mathematical Programming

For a multireservoir system, where the number of reservoirs is large, the conventional modelling by classical stochastic dynamic programming (SDP) presents difficulty, due to the curse of dimensionality inherent in the model solution. It takes a long time to obtain a steady state policy and also it requires large amount of computer storage space, which form drawbacks in application. An attempt is made to explore the concept of fuzzy sets to provide a viable alternative in this context. The application of fuzzy set theory to water resources systems is illustrated through the formulation of a fuzzy mathematical programming model to a multireservoir system with a number of upstream parallel reservoirs, and one downstream reservoir. The study is aimed to minimize the sum of deviations of the irrigation withdrawals from their target demands, on a monthly basis, over a year. Uncertainty in reservoir inflows is considered by treating them as fuzzy sets. The model considers deterministic irrigation demands. The model is applied to a three reservoir system in the Upper Cauvery River basin, South India. The model clearly demonstrates that, use of fuzzy linear programming in multireservoir system optimization presents a potential alternative to get the steady state solution with a lot less effort than classical stochastic dynamic programming.

Application of fuzzy sets and cognitive maps to incorporate social science scenarios in integrated assessment models: A case study of urbanization in Ujung Pandang, Indonesia.

Decision–support systems in the field of integrated water management could benefit considerably from social science knowledge, as many environmental changes are human-induced. Unfortunately the adequate incorporation of qualitative social science concepts in a quantitative modeling framework is not straightforward. The applicability of fuzzy set theory and fuzzy cognitive maps for the integration of qualitative scenarios in a decision–support system was examined for the urbanization of the coastal city of Ujung Pandang, Indonesia. The results indicate that both techniques are useful tools for the design of integrated models based on a combination of concepts from the natural and social sciences.

Grade of membership models in low dimensions

Grade of Membership (GoM) Models have always been presented by their inventors as statistical applications of fuzzy set theory. This paper develops an alternative formulation, recasting GoM as a geometric dimensionality-reduction technique in terms of an underlying family of metrics, exposing a close relationship with Principal Components. The geometric viewpoint facilitates intuitive understanding and guides an investigation into the robustness of GoM estimates to violations of assumption, with test cases drawn from the National Survey of Families and Households. Analysis is restricted to visualizable, low-dimensional cases with two pure types and 3 to 9 dichotomous variables, and to “conditional” GoM, the version more commonly used but less commonly studied. In these low-dimensional settings, I find GoM to be a successful technique for recovering an underlying gradient among individuals when such a gradient is actually present. GoM is only moderately sensitive to moderate violations in its assumptions. In the cases studied, GoM solutions turn out to be remarkably close to Principal Component solutions.

Renewal reward processes with fuzzy rewards and their applications to T-age replacement policies

The application of fuzzy set theory to renewal reward processes is proposed in this paper. The reward is modeled as a fuzzy random variable. A theorem which presents the long-run average fuzzy reward per unit time is stated. A procedure to obtain the best T-age replacement policy with fuzzy cost structure is developed. The original problem is transformed into a nonlinear program in order to evaluate the membership of the long-run average fuzzy cost per unit time.

Application of Fuzzy Set Theory in the Scheduling of a Tandem Cold-Rolling Mill

In a tandem cold-rolling mill, a strip is successively reduced in gauge at each stand as it passes through the mill. The optimal scheduling of a tandem mill is an important but difficult task. In this work, a scheduling problem is considered as an optimization problem which minimizes the total specific power and satisfies certain constraints. Since the material properties and friction coefficient are not known precisely, they are treated as fuzzy numbers. The fuzzy set theory is applied to find out an optimum drafting pattern. The methodology is illustrated by means of a few examples. It is observed that the schedule in which the maximum reduction is achieved in the first pass results in minimum specific power; however, its reliability is poor. Optimization using fuzzy set theory provides a solution which meets the twin requirements of high reliability and minimum power. [S1087-1357(00)00902-3]

An Application of Fuzzy Decision-Making Method in Examining the Quality of Residential Environment

Central to the paradigm of decision making is the assumption, often unstated, that each of the judgements called for in an analysis can be represented accurately by a single precise number. Indeed, if the decisionmaker consistently satisfied Savage axioms, that would be the case. But, as Savage himself noted, judgments of the magnitude of personal probabilities are generally somewhat vague. The problem here is how to handle imprecision. Zadeh has argued strongly for over a decade that applications of systems science to the study of systems involving humans are often unsuccessful primarily because the methodologies used demand very high levels of precision in measuring variables and in describing how they are related. In group decision-making, it seems rather important to analyze the group dynamics and to refine the information available for decisionmakers to help their mutual understanding. Therefore in this study, uncertainty in input variables and its impact on results are characterized with an application of fuzzy set theory. The methodological focus of this study is on making decisions when there are conflicting objectives and the value of each input variable is uncertain. With this in mind, this study was conducted with the following purpose: to evaluate the quality of the residential environment using both crisp and fuzzy set, and to examine the usefulness of the fuzzy set through the comparison of the evaluation results. In addition, the stated method was applied to the assessment of the residential environment in the urban core of Seoul in Korea.

The application of fuzzy set theory to cognitive workload evaluation of electronic circuit board inspectors

The application of fuzzy set theory to cognitive workload evaluation of electronic circuit board inspectors

A Bayesian Evaluation of Fuzzy Logic in a Classification Problem

Models based on fuzzy sets are increasingly being used in academic and industrial research and applications, primarily for data analysis and systems control. The possible consequences of their popular use necessitate their evaluation from a probabilistic viewpoint. In this paper, a simple fuzzy logic model is translated into a Bayesian setting and used to address a discrimination and attribution (or classification) problem. Probabilistic tools and concepts are then employed to evaluate the fuzzy-set paradigm. The translation suggests that applications of fuzzy-set theory may suffer from many serious problems, primarily due to the unobservability of the fuzzy-set membership vector and to the poor structure of the fuzzy-set model. These difficulties are illustrated using the well-known Fisher iris data. For example, Table 11 suggests that fuzzy-set models may find probabilistic mixtures only when the evidence is thoroughly overwhelming in Bayesian models

Dynamical Behavior of Fuzzy Logic Based Velocity Control Autopilot with Respect to Changes in Linguistic Variables Membership Functions Shape

Recently, fuzzy control has become one of the most attractive areas of fuzzy set theory applications. 3,10 As it provides an effective way to approximate inexact nature of human thinking, this theory is an appropriate tool for converting linguistically expressed expert's knowledge about a given process control into mathematically defined control strategy. This is made by means of the so called linguistic values, which are fuzzy sets over given universe of discourse of corresponding linguistic variable. The membership functions, which describe this linguistic values, as a rule, are defined by some bell-shaped function. Several nonlinear definitions of this functions are known, 2 but most researchers prefer to use simple linear triangular or trapezoidal functions. Usually in fuzzy controller synthesis membership functions shape is defined in advance and then only their position in the universe of discourse is tuned.

Decision making in energy planning: the ELECTRE multicriteria analysis approach compared to a FUZZY-SETS methodology

Every planning activity generally requires to make some choices. After a preliminary analysis of the sector under examination, a forecast of trends of input–output items, the planner must define an action plan voted to arrange all the strategies and specific interventions able to fit demand and supply during the planned time. The redaction of an action plan implies a strong effort in order to synthesize either suggestions coming from the analysis phases either all the constraints linked to technical choices. In the same time, a large number of “external” variables plays a role in orienting decision making. Some of these can be handled by numerical models (economic cost-benefit analyses, market penetration strategies, environmental impacts). Other aspects, concerning social and cultural impact, political drawbacks, aesthetic aspects, etc., can be analysed only in a qualitative way, or are subjected to a not-objective judgement. This paper aims of introducing a methodological tool able to “organize” and “synthesize” the large set of variables coming from several specific judgements (or assessments) helping the “decision maker” to read the complex problem, understand it and make choices. Previous works of the authors have presented possible applications of “multicriteria-analysis”. In particular, the ELECTRE methods family, (Roy, B., Me ́thodologie multicrite ̀re d'aide a ̀ la de ́cision, Economica, coll. ``Gestion'', Paris, 1985) will be presented under the point of view of energy planning application. It consists in a “flexible” ranking method which takes into account the uncertainties of all the specific assessments, the qualitative nature of some indexes, the weight of the preferences or willingness systems of the decision maker. On the other hand, similar results can be obtained through the application of fuzzy sets theory (Zimmermann, H. J., Fuzzy set Theory and its Application. Kluver Academic Publisher, 1987). A decision making support method, based on fuzzy logic is here tested and compared to the previous one. A case study developed by authors will show differences among these two different approachs. It is focused on the development of a renewable energy diffusion strategies plan. Advantages and drawbacks of both methods will be explored and some suggestions will be proposed.

Application of Fuzzy Set Theory in the Safe Ship Control Process

In this paper, collision avoidance with many targets in open sea is treated as a problem of optimal control using the fuzzy set theory. Optimal safe ship trajectory in collision situation is presented as multistage decision-making in a fuzzy environment. The Collision Avoidance Regulations, the manoeuvrability parameters of the ship and the navigator’s subjective assessment in making a decision are taken under consideration in the process model. To prove application of the proposed conception two examples are simulated and presented in a graphical form.

On the decomposition problem of fuzzy sets

In this paper, we consider an important problem that is frequently encountered and yet almost universally ignored both in the application and in the theoretic studies of fuzzy sets. We refer to this problem as the decomposition of fuzzy sets. In nearly all applications of fuzzy sets theory (e.g., fuzzy decision making, fuzzy control, fuzzy forecasting, etc.), the output is, in general, a fuzzy set; this is then defuzzified before it is applied. Although defuzzification may be necessary if a crisp quantity is definitely needed, when a fuzzy output is appropriate, desired or required in an application, then the defuzzification step becomes unnecessary. Yet, in this case, one finds that it is some times difficult to correctly interpret a fuzzy quantity or identify the true meaning of this fuzzy output using a family of predefined fuzzy sets. Thus, how to match the fuzzy output and the predefined fuzzy sets is the problem of concern in this paper. To address this problem, we first present and review some definitions and then proceed with an investigation of the preliminary properties of these concepts, complementing them with illustrative examples. Finally, we propose some algorithms for the solution of this problem.

Fuzzy logic and inflammatory protein variations

This tutorial style paper has been written for physicians and biologists who are not necessarily familiar with fuzzy set theory and biomedical applications. The field is introduced in the framework of medical diagnosis problems and illustrated with an application to inflammatory protein variations. The model is of special interest in the processing of borderline cases, allowing a graded assignment of diagnoses to patients. Relationships between signs and diagnoses are interpreted as labels of fuzzy sets and it is shown how diagnoses can be derived from soft matching processes. In cases of poor diagnostic classification, appropriate weights are introduced, acting on characterizations of signs, in order to decrease their relative influence. As a consequence, when pattern matching is achieved, the final ranking of inflammatory syndromes assigned to a given patient might change to better fit the actual classification.

Fuzzy set theory applications in production management research: a literature survey

Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This paper provides a survey of the application of fuzzy set theory in production management research. The literature review that we compiled consists of 73 journal articles and nine books. A classification scheme for fuzzy applications in production management research is defined. We also identify selected bibliographies on fuzzy sets and applications.

An application of fuzzy set theory to inventory control models

A method for solving an inventory control problem, of which input data are described by triangular fuzzy numbers will be presented here. The continuous review model of the inventory control problem with fuzzy input data will be focused in, and a new solution method will be presented. For the reason that the result should be a fuzzy number because of fuzzy input data, and the certain number about order quantity is prefered in the real-world, it is necessary to transform the fuzzy result to crisp one. The interval mean value concept is used here to help to solve this problem. Under the condition of total cost minimum, the interval order quantity maximum can be obtained.