Multicriteria Decision-Making Under Conditions of Uncertainty

2Notions and Concepts of Fuzzy Sets: An Introduction

In this chapter, we introduce the fundamental concepts of fuzzy sets. We focus on the fundamental ideas of partial membership, which are conveniently quantified through membership functions and membership degrees. Fuzzy sets come as a manifestation of a general idea of information granule. Processing of information granules is realized in the framework of Granular Computing. We present the underlying rationale and next move on to the detailed description of fuzzy sets by discussing the most commonly encountered classes of membership function, and relating these classes to the semantics of fuzzy sets. We elaborate on the basic operations on fuzzy sets (intersection, union, complement, negations) and discuss concepts of fuzzy relations and their main properties, which are of direct relevance in the context of decision‐making.

2.1 Sets and Fuzzy Sets: A Fundamental Departure from the Principle of Dichotomy

Conceptually and algorithmically, fuzzy sets constitute one of the most fundamental and widely influential concepts in science and engineering. The notion of a fuzzy set is highly intuitive and transparent since it captures what really becomes an essence of a way in which a real world is being perceived and described in our everyday activities. We are faced with categories of objects whose belongingness to a given category (concept) is always a matter of degree. There are numerous examples in which we encounter elements ...