Fuzzy probabilities and fuzzy sets for web planning
The main goal of this book is the presentation of fuzzy systems as a tool for Web optimization. The organization of the book is sketched at Chapter 1. Chapter 2 contains necessary basic knowledge in fuzzy set theory. In Chapter 3 the author applies a new method of using fuzzy numbers to model uncertain probabilities. There is shown how fuzzy probabilities can be constructed by means of restricted fuzzy arithmetic from a set of confidence intervals. Restricted fuzzy arithmetic is used in fuzzy Markov chains in Chapter 4. Fuzzy queueing system given as a fuzzy, finite, regular Markov chain is modeled in Chapter 5. All the computations needed to get the numbers for system performance are described in Chapters 6-10. In Chapters 11 and 12, starting with fuzzy numbers for the arrival rate and service rate, the author finds the fuzzy steady probabilities and then the fuzzy numbers for system performance. In all the above modeling methods, the spread of fuzzy numbers for system performance gives the uncertainty in their value. Optimization models are discussed in the next chapters. All considerations start with ignoring revenues/costs. At first, in Chapter 13 there is minimizing fuzzy number representing average response time for the system and there is maximizing fuzzy number for server utilization. Revenues/costs are added in Chapter 14 where server costs, queue costs and revenues to maximize the fuzzy number for profit are considered. The phenomenon identified with web sites, ``burstiness'' and ``long tailed distributions'' are described in Chapters 15 and 16. All sub-optimization models from Chapters 13-16 are put all together into global optimization plan. In all chapters we can find many useful numerical examples. At the end computational algorithms applied in this book are presented. A CD-ROM with starting data and necessary software is requested. The reviewed book is recommended to all researchers of the field of fuzzy systems as a good monograph devoted to fuzzy decision-making.
scientific article; zbMATH DE number 1979567