This book chiefly presents a novel approach referred to as backward fuzzy rule interpolation and extrapolation (BFRI). BFRI allows observations that directly relate to the conclusion to be inferred or interpolated from other antecedents and conclusions. Based on the scale and move transformation interpolation, this approach supports both interpolation and extrapolation, which involve multiple hierarchical intertwined fuzzy rules, each with multiple antecedents. As such, it offers a means of broadening the applications of fuzzy rule interpolation and fuzzy inference. The book deals with the general situation, in which there may be more than one antecedent value missing for a given problem. Two techniques, termed the parametric approach and feedback approach, are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. In addition, to further enhance the versatility and potential of BFRI, the backward fuzzy interpolation method is extended to support -cut based interpolation by employing a fuzzy interpolation mechanism for multi-dimensional input spaces (IMUL). Finally, from an integrated application analysis perspective, experimental studies based upon a real-world scenario of terrorism risk assessment are provided in order to demonstrate the potential and efficacy of the hierarchical fuzzy rule interpolation methodology.

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Intense media coverage of the public pension funding crisis continues to fuel heightened awareness in and debate over public pension benefits. With over $3 trillion in assets currently under management, the ramifications of poor oversight are severe. It is important that practitioners, researchers, and taxpayers be well-advised regarding any concerns, but until now traditional references have provided very little coverage.

State and Local Pension Fund Management provides a basic and systematic discussion of all the major issues facing those responsible for state and local public retirement programs. The author begins with a technical overview that examines the history of the public pension system. He then proceeds to examinations of pension benefit design, actuarial valuation and funding methods, financial reporting, and pension asset investment management.

These technical discussions prepare readers for the second component, which is a focus on policy. The book delves into issues such as managing public pension programs in the political context of public budgeting, pension benefit reforms, and the fairness and sustainability of pension benefits in the public sector. In addition, the author dedicates a chapter to a detailed discussion of other postemployment benefits (OPEBs) such as life, disability, and long-term care insurance, as well as healthcare subsidies. The book concludes by exploring the dilemma over how to ensure financial security for public employees in their retirement without putting additional pressure on state and local government finance.

By understanding the major issues involved in managing retirement benefit programs in the public sector, readers will gainthe knowledge needed to make informed decisions regarding specific fund management. They will also be better able to participate in the debate over the larger issues regarding pension fund policy and reform measures.

This book chiefly presents a novel approach referred to as backward fuzzy rule interpolation and extrapolation (BFRI). BFRI allows observations that directly relate to the conclusion to be inferred or interpolated from other antecedents and conclusions. Based on the scale and move transformation interpolation, this approach supports both interpolation and extrapolation, which involve multiple hierarchical intertwined fuzzy rules, each with multiple antecedents. As such, it offers a means of broadening the applications of fuzzy rule interpolation and fuzzy inference. The book deals with the general situation, in which there may be more than one antecedent value missing for a given problem. Two techniques, termed the parametric approach and feedback approach, are proposed in an attempt to perform backward interpolation with multiple missing antecedent values. In addition, to further enhance the versatility and potential of BFRI, the backward fuzzy interpolation method is extended to support -cut based interpolation by employing a fuzzy interpolation mechanism for multi-dimensional input spaces (IMUL). Finally, from an integrated application analysis perspective, experimental studies based upon a real-world scenario of terrorism risk assessment are provided in order to demonstrate the potential and efficacy of the hierarchical fuzzy rule interpolation methodology.