Fuzzy Analytic Hierarchy Process and Its Application to E-Marketplace Selection

1. Introduction

Making decision is a part of human daily life. The nature of decision-making includes multiple and usually conflicting criteria. Multi Criteria Decision-Making (MCDM) problems handled under two main headings: Multi Attribute Decision-Making (MADM) and Multi Objective Decision-Making (MODM).

AHP is a widely used multi-criteria decision making approach and has successfully been applied to many practical problems. In spite of its popularity, this method is often criticized for its inability to adequately handle the inherent uncertainty and imprecision associated with the mapping of the DM’s perceptions to exact numbers. Traditional AHP requires exact or crisp judgments (numbers). However, due to the complexity and uncertainty involved in real world decision problems, decision makers might be more reluctant to provide crisp judgments than fuzzy ones. Furthermore, even when people use the same words, individual judgments of events are invariably subjective, and the interpretations that they attach to the same words may differ. Moreover, even if the meaning of a word is well defined (e.g., the linguistic comparison labels in the standard AHP questionnaire responses), the boundary criterion that determines whether an object does or does not belong to the set defined by that word is often fuzzy or vague. This is why fuzzy numbers and fuzzy sets have been introduced to characterize linguistic variables. A linguistic variable is a variable whose values are not numbers but words or sentences from a natural or artificial language. Linguistic variables are used to represent the imprecise nature of human cognition when we try to translate people’s opinions into spatial data. The preferences in AHP are essentially human judgments based on human perceptions (this is especially true for intangibles), so fuzzy approaches allow for a more accurate description of the decision-making process (Chen, Tzeng & Ding, 2008; Tiryaki & Ahlatcioglu, 2009). A number of methods have been developed to handle fuzzy AHP.