Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

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Fuzzy Set Theory - and Its Applications

Introduction to linear and nonlinear programming

This chapter contains sections titled: Combinatorial Optimization, The ACO Metaheuristic, How Do I Apply ACO?, Other Metaheuristics, Bibliographical Remarks, Things to Remember, Thought and Computer Exercises

https://wwwmayr.informatik.tu-muenchen.de/lehre/1999SS/optprak/BC.04-DorDic-NIO99.pdf

The ant colony optimization meta-heuristic

This study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set. Assessment of cluster validity is based on performance measures using hypervolume and density criteria. An algorithm is derived from a combination of the fuzzy K-means algorithm and fuzzy maximum-likelihood estimation. The unsupervised fuzzy partition-optimal number of classes algorithm performs well in situations of large variability of cluster shapes, densities, and number of data points in each cluster. The algorithm was tested on different classes of simulated data, and on a real data set derived from sleep EEG signal. >

Unsupervised optimal fuzzy clustering

OR/MS research in disaster operations management

Mathematical aspects of scheduling and applications

Fuzzy dynamic programming: main developments and applications

This paper considers the two different flow shop scheduling problems that arise when, in a two machine problem, one machine is characterized by sequence dependent setup times. The objective is to determine a schedule that minimizes makespan. After establishing the optimally of permutation schedules for both of these problems, an efficient dynamic programming formulation is developed for each of them. Each of these formulations is shown to be comparable, from a computational standpoint, to the corresponding formulation of the traveling salesman problem. Then, the relative merits of the dynamic programming and branch and bound approaches to these two scheduling problems are discussed.

Two machine flow shop scheduling problems with sequence dependent setup times: A dynamic programming approach

On the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems

Ward beds are a primary resource under the control of hospital management. We develop a method for determining an optimum distribution of beds in a ward by assuming that ward patients can be classified into two categories, that admissions follow Poisson distribution, and that length of stay in the ward follows the negative exponential distribution. After defining a cut-off level as "the number of beds beyond which type 2 non-serious patients are not admitted," we develop a system of differential and difference birth and death process equations for the process. An objective function made up of shortage and holding costs is then developed and optimized for various values of cut-off priority level. An application of this model to a university teaching hospital in Cleveland is illustrated. The model is then extended to a situation where overflows are temporarily housed in a buffer accommodation or inappropriate ward.

Augustine O. Esogbue

Papers

Mathematical aspects of scheduling and applications

Fuzzy dynamic programming: main developments and applications

Two machine flow shop scheduling problems with sequence dependent setup times: A dynamic programming approach

On the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems

A Stochastic Model for an Optimal Priority Bed Distribution Problem in a Hospital Ward