Jana Siebert

• Doctor of Philosophy
• MCI Management Center Innsbruck

Multiple-criteria decision making (MCDM) and evaluation problems dealing with a large number of objects are very demanding. Particularly when the use of pairwise-comparison (PC) techniques is required. A major drawback arises when it is not possible to obtain all the PCs, due to time or cost limitations, or to split the given problem into smaller s...

The aim of the paper is to highlight the necessity of applying the concept of constrained fuzzy arithmetic instead of the concept of standard fuzzy arithmetic in a fuzzy extension of Analytic Hierarchy Process (AHP). Emphasis is put on preserving the reciprocity of pairwise comparisons during the computations. For deriving fuzzy weights from a fuzz...

Proper formulas for obtaining the fuzzy maximal eigenvalue and the corresponding fuzzy maximal eigenvector of a fuzzy pairwise comparison matrix are proposed in this paper. First, the formulas for obtaining the fuzzy maximal eigenvalue of a fuzzy pairwise comparison matrix proposed by Csutora & Buckley (2001) and by Ishizaka (2014) are reviewed, an...

In the last 30 years, several distinguished researchers have proposed and discussed different fuzzy versions of well-known Saaty's Analytic Hierarchy Process (AHP). The paper recently published by K. Zhü in the European Journal of Operational Research heavily criticizes the fuzzy approaches to AHP, claiming the fallacy of all of them. Therefore, it...

Deriving accurate fuzzy priorities is very important in multi-criteria decision making with vague information. In this paper, appropriate formulas for obtaining fuzzy priorities from additive fuzzy pairwise comparison matrices are introduced. The formulas are based on the proper fuzzy extension of the formulas for obtaining priorities from additive...

Belief perseverance bias refers to individuals’ tendency to persevere in biased opinions even after the misinformation that initially shaped those opinions has been retracted. This study contributes to research on reducing the negative impact of misinformation by mitigating the belief perseverance bias. The study explores the previously proposed aw...

The spread and influence of misinformation have become a matter of concern in society as misinformation can negatively impact individuals’ beliefs, opinions and, consequently, decisions. Research has shown that individuals persevere in their biased beliefs and opinions even after the retraction of misinformation. This phenomenon is known as the bel...

In order to deal with the Covid-19 pandemic, many companies face numerous strategic decisions of utmost importance for their future. Being aware of one's objectives is a prerequisite for sound decision making. However, decision and policy makers are often not aware of their objectives when facing important decisions in “normal” times. In addition,...

Various definitions of consistency for interval fuzzy preference relations have been proposed in the literature. The aim of this paper is to review the definitions of multiplicative consistency based on the extension of Tanino’s multiplicative-transitivity property and to point out their drawbacks. In particular, some of the definitions proposed in...

The eigenvector method is one of the most used methods for deriving priorities of objects from multiplicative pairwise comparison matrices in Analytic Hierarchy Process (AHP). Fuzzy extension of AHP has been of much attention in order to capture uncertainty stemming from subjectivity of human thinking and from incompleteness of information that are...

While formal and rigorous procedures are adopted to ensure the reliability of measurement results, the decision-making activities based on the information returned by measurement are often poorly structured and based on vague assumptions and reasoning, thus negatively impacting the reliability of the achieved conclusion. To overcome this problem, a...

Measurement is often performed to acquire information useful to support decisions. Although decision making is more and more frequently based on information related to various heterogeneous properties, rigorous decision methods have not been properly analyzed yet. Decision makers attain conclusions by subjectively aggregating measurement results, o...

The main focus of this paper is the aggregation of local priorities into global priorities in the Analytic Hierarchy Process (AHP) method. We study two most frequently used aggregation approaches - the weighted arithmetic and weighted geometric means - and identify their strengths and weaknesses. We investigate the focus of the aggregation, the ass...

This chapter provides an introduction to multi-criteria decision making methods and specifies the focus of the book. It identifies critical issues related to multi-criteria decision making methods based on fuzzy pairwise comparison matrices and large-dimensional pairwise comparison matrices and derives the key research questions of the book. It pro...

Analytic Hierarchy process (AHP) is a powerful method belonging to the full aggregation family of multi-criteria decision-making methods based on pairwise comparisons of objects. Since the information about the problem is usually not complete in real decision-making problems, it is difficult to express precisely the preferences on pairs of compared...

This chapter is concerned with large-dimensional pairwise comparison problems and answers the following research question: “How can the amount of preference information required from the decision maker in a large-dimensional pairwise comparison matrix be reduced while still obtaining comparable priorities of objects?” The chapter reviews a real-lif...

This chapter is concerned with the fuzzy extension of the multi-criteria decision making methods based on pairwise comparison and answers the following research question: “Based on a fuzzy pairwise comparison matrix of objects, how should fuzzy priorities of these objects be determined so that they reflect properly all preference information availa...

This chapter reviews concepts from fuzzy set theory indispensable for the fuzzy extension of th e multi-criteria decision making methods based on pairwise comparison matrices. Trapezoidal and triangular fuzzy numbers and intervals, which are most often used for the fuzzy extension of pairwise comparison methods, are introduced here, and normalizati...

This chapter answers the research questions posed at the beginning of the book, summarizes the research results obtained in the book, and provides directions for future research in the field of fuzzy multi-criteria decision making methods based on pairwise comparisons.

This chapter provides a critical review of well-known and in real-life multi-criteria decision making problems most often applied pairwise comparison methods. Three types of pairwise comparison matrices are studied in this chapter—multiplicative pairwise comparison matrices, additive pairwise comparison matrices with additive representation, and ad...

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...

Research on multi-criteria decision making (MCDM) methods based on pairwise comparison matrices (PCM) has been emerging rapidly since the introduction of the first well-known pairwise comparison (PC) methods in 1970s. Moreover, since the original PC methods were not designed to cope with large-dimensional PC problems and with uncertainty present in...

Measurement is customarily performed to acquire information useful to support decisions. More and more frequently, the complexity of analyzed systems and problems requires to measure various heterogeneous properties and to process the returned results in order to obtain information directly exploitable to support decision-making activities. However...

Extension of Saaty’s definition of consistency to interval and fuzzy reciprocal preference relations is studied in the paper. The extensions of the definition to interval and triangular reciprocal preference relations proposed by Wang (2005), Liu (2009), Liu et al. (2014) and Wang (2015) are reviewed and some shortcomings in the definitions are poi...

The transformations between multiplicatively and additively reciprocal fuzzy pairwise comparison matrices are dealt with, and formulas for obtaining multiplicative fuzzy priorities from additively reciprocal fuzzy pairwise comparison matrices are proposed in this paper. The formulas are based on the concept of constrained fuzzy arithmetic and prese...

Methods based on pairwise comparison matrices (PCMs) form a significant part of multicriteria decision making (MCDM) methods. These methods are based on structuring pairwise comparisons (PCs) of objects from a finite set of objects into a PCM and deriving priorities of objects that represent the relative importance of each object with respect to al...

Various definitions of consistent interval fuzzy preference relations have been proposed in the literature. This paper aims to review the definitions of additive consistency based on the interval extension of Tanino’s additive-transitivity property. It is demonstrated that some of the definitions are not invariant under permutation of objects in in...

Multiple-criteria decision making (MCDM) and evaluation problems dealing with a large number of objects are very demanding. Particularly when the use of pairwise comparison (PC) techniques is required. A major drawback arises when it is not possible to obtain all the PCs, due to time or cost limitations, or to split the given problem into smaller s...

Fuzzification of the analytic hierarchy process (AHP) is of great interest to researchers since it is a frequently used method for coping with complex decision making problems. There have been many attempts to fuzzify the AHP. We focus particularly on the construction of fuzzy pairwise comparison matrices and on obtaining fuzzy weights of objects f...

In the Analytic Hierarchy Process (AHP), the maximal eigenvalue of a pairwise comparison matrix is used to verify its consistency using the Consistency index and to obtain the weights of objects from the pairwise comparison matrix. There have been many attempts to fuzzy the AHP, among which also the fuzzification of the maximal eigenvalue of a fuzz...

Fuzzification of the Analytic Hierarchy Process (AHP) has become very popular among researchers since fuzzy elements allow us to handle the vagueness of the meaning of linguistic terms expressing the intensities of decision makers' preferences. During the fuzzification, all properties valid for the AHP have to be preserved. However, standard approa...

In this paper we present a method developed at the Faculty of Science, Palacky University in Olomouc for the assessment of scientific quality of books (for the purposes of funds distribution among departments). The method is based on the fuzzified AHP used to determine fuzzy weights of predefined categories of publishers prior to the evaluation pro...

A modi�cation to the fuzzi�ed Saaty's scale for designing a multiplicative fuzzy pairwise comparison matrix and an improved method for computing fuzzy weights of elements from a multiplicative fuzzy pairwise comparison matrix will be proposed. For simplicity of explanation triangular fuzzy numbers will be used in this paper. In many cases of the fu...