# Applying Fuzzy Logic and Fuzzy Methods to Marketing

Laurent Donzé (University of Fribourg, Switzerland) and Andreas Meier (University of Fribourg, Switzerland)
DOI: 10.4018/978-1-4666-2625-6.ch062
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## Abstract

Marketing deals with identifying and meeting the needs of customers. It is therefore both an art and a science. To bridge the gap between art and science, soft computing, or computing with words, could be an option. This chapter introduces fundamental concepts such as fuzzy sets, fuzzy logic, and computing with linguistic variables and terms. This set of fuzzy methods can be applied in marketing and customer relationship management. In the conclusion, future research directions are given for applying fuzzy logic to marketing and customer relationship management.
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## Crisp Sets Vs. Fuzzy Sets

The concept of a set or a collection of objects is common in marketing and relationship management. For instance, all customers with their properties, such as name, age, address, and customer value are stored in the customer database or data warehouse. The objects in the set are called the elements of the set. Traditional data sets are also called ordinary or crisp sets in order to distinguish them from fuzzy sets.

An important notion in set theory is that of membership. If an element x belongs to a set A then xA, otherwise xA. For each element x of a set A there are only two possibilities: either x belongs to A or it does not. The membership rule that characterizes the elements of a set A can be described by the characteristic function. The characteristic function χ takes only two values 1 and 0 or ‘true’ and ‘false’. More precisely: if X is the universal set (universe of discourse) and A is a subset AX then the characteristic function χ of a set A indicates whether or not x belongs to A, i.e., χA: X −> {0,1}. In other words every crisp set is uniquely defined by its characteristic function.

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