Abstract
Analytic hierarchy process (AHP) is a widely used multi-attribute decision-making (MADM) approach. Due to the complexity and uncertainty involved in real world problems, decision makers might be prefer to make fuzzy judgments instead of crisp 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. This is why fuzzy numbers has been introduced to characterize linguistic variables. Fuzzy AHP methods have recently been extended by using type-2 fuzzy sets. Type-2 fuzzy set theory incorporates the uncertainty of membership functions into the fuzzy set theory. In this chapter, the authors firstly provide a short review on applications of interval type-2 fuzzy AHP on MADM problems. Then, they present a very efficient MADM technique, interval type-2 fuzzy AHP, to solve the portfolio selection problem that is to decide which stocks are to be chosen for investment and in what proportions they will be bought. And finally, they provided a case study on BIST.
TopIntroduction
Decision-making is a very important part of our lives, which often involves many and contradictory criteria that we face at any time in our daily lives. Multi-criteria decision making (MCDM) problems can be examined in two categories: multi-attribute decision making (MADM) and multi-objective decision making (MODM).
AHP is a MCDM method that has a wide range of applications and can be easily applied to real-life problems that allow weighting alternatives when choosing from existing alternatives. The AHP, which many researchers often use to address selection problems, is criticized for whether it reflects the uncertainty of the problems addressed in the solution process sufficiently because decision makers express their evaluations in exact or crisp judgments (numbers). However, decision-makers may not be willing to make crisp and precise evaluations when making their decisions due to uncertainty in real-life problems. Moreover, even if decision makers use the same words for their evaluation, the meanings they add to these words may be different from each other. Furthermore, even if an evaluation is well defined, the limit criterion that determines whether this evaluation belongs to the set is often not clear or ambiguous. Therefore, fuzzy numbers and fuzzy sets have been proposed to define linguistic variables which cannot be expressed by numbers. A linguistic variable is a variable expressed in words or sentences. The evaluations in AHP can be more accurately reflected in the process with fuzzy decision-making approaches because they are based on human judgment. (Chen et al. (2008), Tiryaki and Ahlatcioglu (2009), Ozkok and Pappalardo (2013)).
Key Terms in this Chapter
Type-2 Fuzzy Set: A set which is the extension of type-1 fuzzy sets has three-dimensional membership functions that provide additional degrees of freedom to make it possible to directly model uncertainties.
Fuzzy Decision Making: Decision making process involves taking decisions under uncertain environments where information can be handled by fuzzy sets and systems.
Analytical Hierarcy Process: A multi-criteria decision-making technique that results with the relative evaluation of alternatives based on the specified criteria.
Type-1 Fuzzy Set: A set addressing uncertainty by assigning a membership function value among [0,1] to each element.
Portfolio Selection Problem: The problem that is to decide which stocks are to be chosen for investment and in what proportions they will be bought considering the specific criteria.