# Preference Matrices with Fuzzy Elements in Decision Making

Chapter
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 677)

## Abstract

This chapter is aimed on pairwise comparison matrices with fuzzy elements. Fuzzy elements of the pairwise comparison matrix are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We particularly deal with pairwise comparison matrices with fuzzy number elements and investigate some properties of such matrices. In comparison with pairwise comparison matrices with crisp elements investigated in the previous chapter, here we investigate pairwise comparison matrices with elements from alo-group over a real interval. In some sense, this chapter is a continuation of the second part of the previous chapter. Such an approach allows for a generalization dealing with additive, multiplicative and fuzzy pairwise comparison matrices with fuzzy elements. Moreover, we deal with the problem of measuring the inconsistency of fuzzy pairwise comparison matrices by defining corresponding inconsistency indexes. Numerical examples are presented to illustrate the concepts and derived properties.

## Keywords

Fuzzy Elements Pairwise Comparison Matrices Inconsistency Index Priority Vector Interval Fuzzy Preference Relations
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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