Discrete fuzzy measures: computational aspects

摘要

Decision-making is a problem-solving activity aimed at reckoning a choice by taking into account a possibly large number of constraints, preferences, beliefs, and costs, among other things. It is a complex discipline that requires sophisticated operators based on solid theory. This book offers a clean and rigorous view of an important class of such operators-discrete fuzzy measures-to help specialists use them correctly, with a closed eye to the computational aspects of their implementation. One important operation in decision-making is aggregation (of preferences, satisfaction degrees, beliefs, and so on), which combines multiple values-coming from several sources-into a single value that can be used to support a decision. In large part, aggregation is obtained by some kind of averaging, like weighted average or other forms of means. In most cases, however, these simple aggregation functions disregard interactions among the sources that provided the values. Nevertheless, interactions are commonplace, so ignoring them may lead to biased aggregations and, consequently, suboptimal decisions.