Jan Stoklasa

Fuzzified AHP in the evaluation of scientific monographs

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 from them subsequently. We review the fuzzification of the geometric mean method for obtaining fuzzy weights of objects from fuzzy pairwise comparison matrices. We illustrate here the usefulness of the fuzzified AHP on a real-life problem of the evaluation of quality of scientific monographs in university environment. The benefits of the presented evaluation methodology and its suitability for quality assessment of R&D results in general are discussed. When the task of quality assessment in R&D is considered, an important role is played by peer-review evaluation. Evaluations provided by experts in the peer-review process have a high level of subjectivity and can be expected in a linguistic form. New decision-support methods (or adaptations of classic methods) well suited to deal with such inputs, to capture the consistency of experts’ preferences and to restrict the subjectivity to an acceptable level are necessary. A new consistency condition is therefore defined here to be used for expertly defined fuzzy pairwise comparison matrices.

Weak consistency in Saaty's AHP - evaluating creative work outcomes of Czech Art Colleges

The full consistency of Saaty’s matrix of preference intensities used in AHP is practically unachievable for a large number of objects being compared. There are many procedures and methods published in the literature that describe how to assess whether Saaty’s matrix is “consistent enough”. Consistency is in these cases measured for an already defined matrix (i.e. ex-post). In this paper we present a procedure that guarantees that an acceptable level of consistency of expert information concerning preferences will be achieved. The proposed method is based on dividing the process of inputting Saaty’s matrix into two steps. First, the ordering of the compared objects with respect to their significance is determined using the pairwise comparison method. Second, the intensities of preferences are defined for the objects numbered in accordance with their ordering (resulting from the first step). In this paper the weak consistency of Saaty’s matrix is defined, which is easy to check during the process of inputting the preference intensities. Several propositions concerning the properties of weakly consistent Saaty’s matrices are proven in the paper. We show on an example that the weak consistency, which represents a very natural requirement on Saaty’s matrix of preference intensities, is not achieved for some matrices, which are considered “consistent enough” according to the criteria published in the literature. The proposed method of setting Saaty’s matrix of preference intensities was used in the model for determining scores for particular categories of artistic production, which is an integral part of the Registry of Artistic Results (RUV) currently being developed in the Czech Republic. The Registry contains data on works of art originating from creative activities of Czech art colleges and faculties. Based on the total scores achieved by these institutions, a part of the state budget subsidy is being allocated among them.

Fuzzy approach - a new chapter in the methodology of psychology?

This paper aims to briefly introduce the main idea behind the fuzzy approach and to identify the areas and problems encountered in the humanities that might profit from using this approach. Based on a short overview of selected applications of fuzzy in psychology we identify key areas in which the fuzzy approach has already been applied, and propose a list of general types of problems that the fuzzy approach may provide solutions for in psychology and the humanities in general. These types of problems are illustrated using practical examples. The benefits and possible shortcomings of using the fuzzy approach compared to classical approaches in use today are discussed.The goal of this paper is to indicate areas in research and practice in the humanities, where modern mathematical tools—in this case linguistic fuzzy modeling—have already been used or might prove promising.

Computing Interval Weights for Incomplete Pairwise-Comparison Matrices of Large Dimension—A Weak-Consistency-Based Approach

Multiple-criteria decision making 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 subproblems. In such cases, two tools are needed to find acceptable weights of objects: an efficient method for partially filling a pairwise-comparison matrix (PCM) and a suitable method for deriving weights from this incomplete PCM. This paper presents a novel interactive algorithm for large-dimensional problems guided by two main ideas: the sequential optimal choice of the PCs to be performed and the concept of weak consistency. The proposed solution significantly reduces the number of needed PCs by adding information implied by the weak consistency after the input of each PC (providing sets of feasible values for all missing PCs). Interval weights of objects are computed from the resulting incomplete weakly consistent PCM adapting the methodology for calculating fuzzy weights from fuzzy PCMs. The computed weight intervals, thus, cover all possible weakly consistent completions of the incomplete PCM. The algorithm works both with Saatys PCMs and fuzzy preference relations. The performance of the algorithm is illustrated by a numerical example and a real-life case study. The performed simulation demonstrates that the proposed algorithm is capable of reducing the number of PCs required in PCMs of dimension 15 and greater by more than 60% on average.

Set-theoretic methodology using fuzzy sets in rule extraction and validation - consistency and coverage revisited

Abstract The use of set-theoretic concepts of consistency and coverage and their fuzzified versions needs to be accompanied with an extension of the general (non-fuzzy) methodology. In the fuzzy context, the same piece of data can provide partial evidence in favour of the existence of a given relationship, and at the same time contribute to its disproof, which constitutes a significant interpretation and methodological issue. We point out the possible problems of the use of these measures fuzzified in direct analogy to their non-fuzzy counterparts in the investigation of relationships and causality. We propose two alternative fuzzifications of these measures to be used in the set-theoretic framework and fuzzy set qualitative comparative analysis (fsQCA). We also introduce novel degree-of-support and degree-of-disproof measures to handle simultaneous subset relations. In this way, simultaneous partial support for- and disproof of a given rule by the given set of data can be analyzed in detail. The suggested measures can enhance the insights needed in theory building and be widely used in research using fuzzified set-theoretic methods for the assessment of the plausibility of the rules. We compare the newly suggested consistency and coverage measures with standard ones and discuss their properties in practical examples.

On academic faculty evaluation systems – more than just simple benchmarking

Academic faculty evaluation is a yearly recurring part of the management process at most universities and it is an issue that is getting more and more attention, as universities all over the world are required to become increasingly accountable for their performance and efficiency to their stakeholders. Designing good academic faculty evaluation systems is not a simple problem because multiple issues and a large number of criteria should be considered and aggregate in a sensible way. To highlight the diversity of existing academic evaluation systems, we present and shortly compare real world systems from four universities in three different countries. We argue that as there are no best practices or guidelines available for academic faculty evaluation systems the topic requires more research attention from both the human resources management side and from the systems design side.

Multiple-Criteria Evaluation in the Fuzzy Environment Using the FuzzME Software

This chapter describes a software tool for fuzzy multiple-criteria evaluation called FuzzME. The chapter will show the reader in an easy-to-read style how to apply the software for solving a broad range of fuzzy MCDM problems. The mathematical foundation on which the FuzzME software is built will be described and demonstrated on an example. The FuzzME implements a complete system of fuzzy methods. A common feature of all these methods is the type of evaluation that is well-suited to the paradigm of fuzzy set theory. All evaluations in the presented models are in the form of fuzzy numbers expressing the extent to which goals of evaluation have been fulfilled. The system of fuzzy methods can deal with different types of interaction among criteria of evaluation. If there is no interaction among criteria, then either fuzzy weighted average, fuzzy OWA operator, or fuzzified WOWA operator is used to aggregate partial evaluations (depending on evaluator’s requirements on the type of evaluation). If interactions among criteria are in the form of redundancy or complementarity, then fuzzified discrete Choquet integral is an appropriate aggregation operator. In case of more complex interactions, the aggregation function is described by an expertly defined base of fuzzy rules. The FuzzME also contains additional tools which make it possible to perform analysis of the designed evaluation model and to adjust it easily.

Fuzzified Likert Scales in Group Multiple-Criteria Evaluation

Likert scales have been in use since 1930s as tool for attitude expression in many fields of social science. Recently there have even been several attempts for the fuzzification of this instrument. In this chapter we explore the possibility of their use in multiple-criteria multi-expert evaluation. We focus on discrete fuzzy Likert scales, that are a generalization of the standard Likert scales. We propose a methodology that deals with the non-uniformity of the distribution of linguistic labels along the underlying ordinal evaluation scale and also with possible response bias. We also consider the analogy of Likert scales (crisp and fuzzy) on continuous universes. Likert-type evaluations of an alternative with respect to various criteria are represented using histograms. Histograms are also used to aggregate the Likert-type evaluations. A transformation of the multi-expert multiple-criteria evaluation represented by a histogram into a 3-bin histogram to control for the response bias is performed and an ideal-evaluation 3-bin histogram is defined. We propose a distance measure to assess the closeness of the overall evaluation to the ideal and suggest the use of the proposed methodology in multiple-criteria multi-expert evaluation.

Aggregation in the analytic hierarchy process: Why weighted geometric mean should be used instead of weighted arithmetic mean

Abstract 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 assumptions made on the way, and the effect of different normalizations of local priorities on the resulting global priorities and their ratios. We clearly show the superiority of the weighted geometric mean aggregation over the weighted arithmetic mean aggregation in AHP for the purpose of deriving global priorities of alternatives. We also contribute to the literature on rank reversal in AHP. In particular, we show that a change of the normalization condition for the local priorities of alternatives may result in different ranking when the weighted arithmetic mean aggregation is used for deriving global priorities of alternatives, and we demonstrate that the ranking obtained by the weighted geometric mean aggregation is not normalization dependent. Moreover, we prove that the ratios of global priorities of alternatives obtained by the weighted geometric mean aggregation are invariant under the normalization of local priorities of alternatives and weights of criteria. We also propose three alternative approaches to aggregating preference information contained in local pairwise comparison matrices of alternatives into a global consistent pairwise comparison matrix of alternatives and prove their equivalence.

Uncertain outcome presentations bias decisions: experimental evidence from Finland and Italy

Even in their everyday lives people are expected to make difficult decisions objectively and rationally, no matter how complex or uncertain the situation. In this research, we study how the format of presentation and the amount of presented information concerning risky events influence the decision-making process, and the propensity to take risk in decision makers. The results of an exploratory survey conducted in Finland and in Italy suggest that decision-making behavior changes according to the way the information is presented. We provide experimental evidence that different representations of expected outcomes create distinct cognitive biases and as a result affect the decisions made. This identified change in the perception of risk has, to the best of our knowledge, not been identified nor directly studied previously in the scientific literature. The paper thus presents novel insights into managerial decision-making that are potentially relevant for decision support theory, with implications to decision-makers and for information providers. Understanding the impact of various forms of presentation of risk is crucial in being able to convey information clearly and in a way that avoids misunderstandings. The implications of the results on being able to avoid opportunistic manipulation of decisions, are also of great concern in many application areas. Social networks are more and more frequently being used as a source of information and in this context it is crucial to acknowledge the effect that different ways of presenting and communicating risky outcomes may have on the behavior of the target group. Here presented results may, for example, be highly relevant for marketing and advertising that is conducted by using social media or social networks.