James J. Buckley Knihy

What happens when a school administrator becomes involved in solving the crime perpetrated against one of his teachers? Ed Pearson finds out as he uncovers clue after clue about what may have occurred to the faculty member whose body lies for days undiscovered. Although at first, the press jokingly refers to him as their local Sherlock Holmes, they eventually realize that without his help, the murder case will not be solved.

Set in 1850, the story follows Thad Perkins, a US seaman entangled in a web of espionage under President Millard Fillmore's new spy network. As he navigates dangerous assassination attempts, Thad's life and the safety of those around him become increasingly at risk, with some becoming unintended victims in the chaos. The narrative explores themes of loyalty, danger, and the high stakes of covert operations during a tumultuous period in American history.

This book aims to introduce Monte Carlo methods for finding approximate solutions to fuzzy optimization problems, an area lacking established algorithms compared to crisp optimization. It addresses key topics such as the comparison of fuzzy numbers and the evaluation of max/min values for fuzzy objective functions. The structure of the book is divided into four parts: Part I serves as an introduction, covering Chapters 1-5; Part II, spanning Chapters 6-16, applies the Monte Carlo method to fuzzy optimization problems; Part III, consisting of Chapters 17-27, discusses unresolved fuzzy optimization challenges where the Monte Carlo method has yet to be applied; and Part IV offers a summary, conclusions, and suggestions for future research. In Part I, readers will become acquainted with fuzzy sets, with Chapter 2 providing the essential concepts needed for the book. For those new to fuzzy sets and fuzzy logic, a preliminary introduction is suggested. Additionally, Chapter 2 includes three significant topics related to fuzzy sets: Section 2.5 discusses past approaches to determining max/min values for fuzzy sets representing objective functions in fuzzy optimization. This foundational knowledge is crucial for understanding the subsequent applications and discussions throughout the book.

This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications, Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson, binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.

Simulating Fuzzy Systems demonstrates how many systems naturally become fuzzy systems and shows how regular (crisp) simulation can be used to estimate the alpha-cuts of the fuzzy numbers used to analyze the behavior of the fuzzy system. This monograph presents a concise introduction to fuzzy sets, fuzzy logic, fuzzy estimation, fuzzy probabilities, fuzzy systems theory, and fuzzy computation. It also presents a wide selection of simulation applications ranging from emergency rooms to machine shops to project scheduling, showing the varieties of fuzzy systems.

The book is structured into four main parts focusing on fuzzy statistics. The first part introduces fuzzy estimation, including the construction of fuzzy estimators for normal distributions. The second part delves into fuzzy hypothesis testing, applying fuzzy estimators in statistical tests. The third part covers fuzzy regression and prediction, starting with fuzzy correlation and progressing through simple and multiple linear regression. Each section builds on the previous one, emphasizing the use of crisp data from random samples to develop fuzzy models.

1.1 Introduction This book is written in five major divisions. The first part is the introduc tory chapters consisting of Chapters 1-3. In part two, Chapters 4-10, we use fuzzy probabilities to model a fuzzy queuing system . We switch to employ ing fuzzy arrival rates and fuzzy service rates to model the fuzzy queuing system in part three in Chapters 11 and 12. Optimization models comprise part four in Chapters 13-17. The final part has a brief summary and sug gestions for future research in Chapter 18, and a summary of our numerical methods for calculating fuzzy probabilities, values of objective functions in fuzzy optimization, etc., is in Chapter 19. First we need to be familiar with fuzzy sets. All you need to know about fuzzy sets for this book comprises Chapter 2. Two other items relating to fuzzy sets, needed in Chapters 13-17, are also in Chapter 2: (1) how we plan to handle the maximum/minimum of a fuzzy set; and (2) how we will rank a finite collection of fuzzy numbers from smallest to largest.

In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.

The book aims at surveying results in the application of fuzzy sets and fuzzy logic to economics and engineering. New results include fuzzy non-linear regression, fully fuzzified linear programming, fuzzy multi-period control, fuzzy network analysis, each using an evolutionary algorithm; fuzzy queuing decision analysis using possibility theory; fuzzy differential equations; fuzzy difference equations; fuzzy partial differential equations; fuzzy eigenvalues based on an evolutionary algorithm; fuzzy hierarchical analysis using an evolutionary algorithm; fuzzy integral equations. Other important topics covered are fuzzy input-output analysis; fuzzy mathematics of finance; fuzzy PERT (project evaluation and review technique). No previous knowledge of fuzzy sets is needed. The mathematical background is assumed to be elementary calculus.

The primary purpose of this book is to present information about selected topics on the interactions and applications of fuzzy + neural. Most of the discussion centers around our own research in these areas. Fuzzy + neural can mean many things: (1) approximations between fuzzy systems and neu ral nets (Chapter 4); (2) building hybrid neural nets to equal fuzzy systems (Chapter 5); (3) using neura. l nets to solve fuzzy problems (Chapter 6); (4) approximations between fuzzy neural nets and other fuzzy systems (Chap ter 8); (5) constructing hybrid fuzzy neural nets for certain fuzzy systems (Chapters 9, 10); or (6) computing with words (Chapter 11). This book is not intend to be used primarily as a text book for a course in fuzzy + neural because we have not included problems at the end of each chapter, we have omitted most proofs (given in the references), and we have given very few references. We wanted to keep the mathematical prerequisites to a minimum so all longer, involved, proofs were omitted. Elementary dif ferential calculus is the only prerequisite needed since we do mention partial derivatives once or twice.