# Pairwise Comparison Matrices and their Fuzzy Extension

## Multi-criteria Decision Making with a New Fuzzy Approach

• Jana Krejčí
Book

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 366)

1. Front Matter
Pages i-xviii
2. Jana Krejčí
Pages 1-15
3. Jana Krejčí
Pages 17-56
4. Jana Krejčí
Pages 57-84
5. Jana Krejčí
Pages 85-232
6. Jana Krejčí
Pages 233-260
7. Jana Krejčí
Pages 261-266
8. Back Matter
Pages 267-273

### Introduction

This book offers the first comprehensive and critical literature review of fuzzy pairwise comparison methods derived from methods originally developed for crisp pairwise comparison matrices. It proposes new fuzzy extensions of these methods and provides a detailed study of the differences and analogies between all the reviewed methods, as well as a detailed description of their drawbacks, with the help of many numerical examples. In order to prevent the drawbacks related to the reviewed fuzzy pairwise comparison methods, the book introduces constrained fuzzy arithmetic in fuzzy extension of the pairwise comparison methods. It proposes new fuzzy pairwise comparison methods based on constrained fuzzy arithmetic and critically compares them with the reviewed methods. It describes the application of the newly developed methods to incomplete large-dimensional pairwise comparison matrices showcased in a real-life case study. Written for researchers, graduate and PhD students interested in multi-criteria decision making methods based on both crisp and fuzzy pairwise comparison matrices, this self-contained book offers an overview of cutting-edge research and all necessary information to understand the described tools and use them in real-world applications.

### Keywords

Fuzzy Pairwise Comparison Matrices Crisp PCMs Multiplicative PCMs Additive PCMs Reciprocity of PCMs Invariance of PCMs Constrained Fuzzy Arithmetic Standard Fuzzy Arithmetic Two-Phase Pairwise Comparison Method Large-Dimensional Pairwise Comparison Problems Fuzzy Priorities of Objects Incomplete PCMs Multiplicative Fuzzy Priorities Weak Consistency Additive Transitivity Additive Reciprocity Triangular Fuzzy Numbers

#### Authors and affiliations

• Jana Krejčí
• 1
1. 1.Department of Industrial EngineeringUniversity of TrentoTrentoItaly

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-77715-3
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Engineering
• Print ISBN 978-3-319-77714-6
• Online ISBN 978-3-319-77715-3
• Series Print ISSN 1434-9922
• Series Online ISSN 1860-0808
• Buy this book on publisher's site