Fuzzy sets were for a long time not accepted by the AI community. Now they have become highly evolved and their techniques are well established. This book will teach the reader how to construct a fuzzy expert system to solve real-world problems. After a general discussion of expert systems, the basic fuzzy math required is presented first, requiring little more math background than high-school algebra. This book will fill a void in the market because although there are many books on expert systems, none devote more than a few pages to the notion of fuzzy sets and their applications in this...

1. 1 Introduction This book is written in two major parts. The ?rst part includes the int- ductory chapters consisting of Chapters 1 through 6. In part two, Chapters 7-26, we present the applications. This book continues our research into simulating fuzzy systems. We started with investigating simulating discrete event fuzzy systems ( 7], 13], 14]). These systems can usually be described as queuing networks. Items (transactions) arrive at various points in the s- tem and go into a queue waiting for service. The service stations, preceded by a queue, are connected forming a network of queues...

Combines material from "Fuzzy Probabilities: New Approach and Applications, Physica-Verlag, 2003" and "Fuzzy Statistics, Springer, 2004". This book includes three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions.

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...

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...

1. 1 Introduction This book is written in two major parts. The ?rst part includes the int- ductory chapters consisting of Chapters 1 through 6. In part two, Chapters 7-26, we present the applications. This book continues our research into simulating fuzzy systems. We started with investigating simulating discrete event fuzzy systems ( 7], 13], 14]). These systems can usually be described as queuing networks. Items (transactions) arrive at various points in the s- tem and go into a queue waiting for service. The service stations, preceded by a queue, are connected forming a network of queues...

Synopsis: At the same time as Catholic and evangelical Christians have increasingly come to agree on issues that divided them during the sixteenth-century reformations, they seem increasingly to disagree on issues of contemporary "morality" and "ethics." Do such arguments doom the prospects for realistic full communion between Catholics and evangelicals? Or are such disagreements a new opportunity for Catholics and evangelicals to convert together to the triune God's word and work on the communion of saints for the world? Or should our hope be different than simple pessimism or optimism? In...

How can Christians committed to the classical Christian tradition address the issues raised by contemporary Islam? Before a much-needed dialogue between Christians and Muslims is established, Christians need to ask themselves how their Scriptures and traditions might come to bear on such a dialogue. Do the divisions among Catholic and Evangelical Christians fracture the classical Christian tradition in ways that undercut Christian-Muslim dialogue before it has even begun? Or could the classical tradition provide invaluable resources for resolving divisions between Catholic and Evangelical...

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...