Abstract
Power flow calculations are one of the most important computational tools for planning and operating electric power systems. After the stabilization of the deterministic power flow calculation methods, the need to capture uncertainty in load definition lead first to the development of probabilistic models, and later to fuzzy approaches able to deal with qualitative declarations and other non-probabilistic information about the value of the loads. Present fuzzy power flow (FPF) calculations use typically incremental techniques, in order to obtain a good approximation of the fuzzy state variables. However, these models and procedures are not entirely satisfactory for the evaluation of the adequacy of the electric transmission system, since they are not completely symmetric. In this paper, we show how to perform the detailed calculation of the state variables of the FPF problem in an exact and symmetrical way, by means of solving multiple optimization problems. The procedure is illustrated using the IEEE 118 test system.

Abstract
Most of the approaches to decision problems under uncertainty are based on decision paradigms, generally associated to an optimization process that leads to a final solution. For the Decision Maker, the basic decision is thus what paradigm to choose, the rest of the procedure being mainly technical. In this paper, a different approach is advocated for this kind of problems. The main idea is to leave prescriptive models in favor of a more flexible approach, where risk related criteria are explicitly considered, conducting to an '' equivalent '' multicriteria (deterministic) model where decision-aid procedures can be used, with a greater involvement of the Decision Maker. The paper discusses first the uncertainty model and then reviews existing paradigms for the single criterion problem under uncertainty. Proposed risk and opportunity attributes come mainly from the analysis of those methodologies and from risk perception studies reports. Some hints about multicriteria aid methods and an illustrative example complete the paper.

Abstract
In response to the soaring energy crisis and the related pollution problems worldwide, it is essential to apply new technologies that use renewable energy sources in both an efficient and environmentally friendly manner. In this way, biomass offers one of the largest potential among renewable energy sources. The aim of this work is to demonstrate a novel fuzzy-based methodology for selecting hybrid energy systems fuelled by biogas. Fuzzy multi-rules and fuzzy multi-sets are used to evaluate the main operational characteristics of five types of renewable sources fuelled by biogas. The possibility of using the methodology for energy storage system evaluation is also assessed. The construction of the fuzzy multirules and fuzzy multi-sets is based on the following methods: Mamdani (fuzzification process), Max-Min (inference process), and Center of Gravity (defuzzification process). Several criteria are used: costs, efficiency, cogeneration, life-cycle, technical maturity, power application range, and environmental impacts. The methodology considers three different settings with two different constraints: costs and environment. One of the most relevant aspects presented by this work is about the previous classification of the criteria. It was created according to the different relevance observed among the attributes. The purpose of the proposed arrangement is to facilitate the understanding of the methodology and to increase the possibility of incorporating the decision makers' preferences on the decision-aid process. These aspects are essential to strengthen the final decision. © Springer-Verlag Berlin Heidelberg 2011.

Abstract
This chapter presents some case studies using fuzzy equivalent uniform annual worth analysis. It includes three case studies and each case is studied for both crisp and fuzzy cases. Trapezoidal fuzzy numbers and correlated, uncorrelated, and partially correlated cash flows are handled in the cases. © 2008 Springer-Verlag Berlin Heidelberg.

Abstract
This chapter first presents arithmetic operations over independent fuzzy numbers and economic concepts review. Then, it gives the techniques for comparing and ordering fuzzy numbers of independent numbers and dependent numbers. It examines fuzzy case with partial correlation. The chapter also includes many numerical applications. © 2008 Springer-Verlag Berlin Heidelberg.

Abstract
Reliability models rarely incorporate the uncertainty that is present in most of the reliability parameters, which is an important limitation for the managers of production system. This paper presents a fuzzy-probabilistic methodology that was developed to analyse production systems. The methodology employs probabilistic theory to represent the stochastic behaviour of the failure and repair processes and fuzzy sets to represent uncertainty in the parameters. This approach is based on a fuzzy reliability analysis from which is possible to obtain the fuzzy downtime function of a system in a given period of analysis. This function is a crucial element to obtain two performance measures: a financial measure (the fuzzy cost concerning failures of a production system) and a quality of service measure (the fuzzy frequency of failure on deliveries), as it will be illustrated in the final part of the paper through a practical example.