EXECUTIVE SUMMARY Government budget is useful for forecasting as it is based on the estimation of a variety of activity volumes. The purpose of this report is to discuss how fuzzy logic can be applied to collect decision information, and how it facilitates the integration of foresight information into capital budgeting process, and how the agents can be constructed. Finally, it elaborates on the limitations of fuzzy logic. Table of Contents EXECUTIVE SUMMARY 1 1.0 INTRODUCTION 1 2.0 FUZZY LOGIC 1 2.1 DIFFERENCE BETWEEN FUZZY LOGIC AND BINARY LOGIC (CRISP) 2 3.0 NEURAL NETWORKS 2 3.1 BAYESIAN NETWORK 3 4.0 UNCERTAIN FACTORS TO CONSIDER DURING BUDGET PREPARATION 3 4.1 INFLATION 3 4.2 GDP 4 4.3 UNEMPLOYEMENT 5 4.4 TAX 5 5.0 FUZZY MODEL 7 5.2 MODEL II 8 6.0 LIMITATIONS OF FUZZY LOGIC 9 7.0 CONCLUSION 10 Reference: 10 1.0 INTRODUCTION Budgeting decisions are the most important decisions made by management. As every year, the budget will be an event that would signal the direction set forth for the growth path of the economy. Formulating large budgets of capital projects is of strategic importance. It often has many unknown or hard-to-estimate risk and potentials difficult to foresee at the initial planning stage. The change can be fundamental, for example, inflation, GDP, unemployment, tax rate, etc. However, such uncertainty and possibility of change in fundamentals of budgeting calls for a proactive management. In this paper we will look at how fuzzy logic will support the capital budgeting process. We will first develop a framework for a budgeting system using fuzzy real option approach. We will then discuss how intelligent agents can be applied to collect decision information and how they can be applied to facilitate the integration of foresight information into a capital budgeting process. 2.0 FUZZY LOGIC Fuzzy logic (FL) was initiated in 1965 by Lotfi A Zadeh. FL is a multi-value logic that has profound influence on the thinking of uncertainty as it challenges not only the probability theory as the sole representation of uncertainty, but also the foundations on which probability theory was based, which allows intermediate values to be defined between conventional evaluations like true/false, yes/no, high/low, etc. (Klir and Yuana, 1995). A fuzzy set theory corresponds to fuzzy logic, and the semantic of fuzzy operators can be understood using a geometric model. The geometric visualisation of fuzzy logic will give us a hint as to the possible connection with neural networks Oderanti FO and DeWilde P., 2011). Further, an example proposed by Zadeh to the neural network community is that of developing a system to park a car. It is straightforward to formulate a set of fuzzy rules for this task, but it is not immediately obvious how to build a network to do the same, nor how to train it. FL is now widely used in many products of industrial and consumer electronics in which a good control system is sufficient, and the issue of optimal control does not necessarily arise. 2.1 DIFFERENCE BETWEEN FUZZY LOGIC AND BINARY LOGIC (CRISP) A crisp relation represents the presence or absence of association, interaction, or interconnectedness between the elements of two or more sets. This concept can be generalised to allow for various degrees or strengths of relation or interaction between elements. Degrees of association can be represented by membership grades in a fuzzy relation in the same way as degrees of set membership represented in the fuzzy set. In fact, just as the crisp set can be viewed as a restricted case of the more general fuzzy set concept, the crisp relation can be considered to be a restricted case of the fuzzy relations. 3.0 NEURAL NETWORKS Neural Networks (NN) are mathematical tools designed to simulate the way in which the human brain performs(?) a specific task, and consist of simple processing units that are only the elements of calculation, and are called neurons or nodes (Nodes, Neurons), which have a characteristic neurological ???. Neurons are joined with communication channels, and information flows, in the structure of arithmetical information, among nodes. It learns through examples on a trial-and-error basis. The goal of this type of network is to create a model that correctly maps an input to the desired one using historical data. However, fuzzy logic answers questions with imprecise information. It deals with reasoning that is approximate rather than fixed and precise. 3.1 BAYESIAN NETWORK Bayesian networks represent a culmination of Bayesian probability theory and causal graphical representations for modeling causal and probabilistic applications. There are two essential problems troubling proponents and adherents of Bayesian networks or probability in general. However, fuzzy logic and Bayesian network differ in the interpretation of membership and, consequently, the calculation of cross-membership. Fuzzy partial membership represents vagueness about the meaning of the classes whi