Konrad Kułakowski

• Associate Professor, PhD.
• Professor (Associate) at AGH University of Krakow

Decision-making methods very often use the technique of comparing alternatives in pairs. In this approach, experts are asked to compare different options, and then a quantitative ranking is created from the results obtained. It is commonly believed that experts (decision-makers) are honest in their judgments. In our work, we consider a scenario in...

Most decision-making models, including the pairwise comparison method, assume the honesty of the decision-maker. However, it is easy to imagine a situation where the decision-maker tries to manipulate the ranking results. This problem applies to many decision-making methods, including the pairwise comparison method. This article proposes three simp...

A project (e.g. writing a collaborative research paper) is often a group effort. At the end, each contributor identifies his or her contribution, often verbally. The reward, however, is quite often financial in nature. This leads to the question of what (percentage) share in the creation of the paper is due to individual authors. Different authors...

Most decision-making models, including the pairwise comparison method, assume the decision-makers honesty. However, it is easy to imagine a situation where a decision-maker tries to manipulate the ranking results. This paper presents three simple manipulation methods in the pairwise comparison method. We then try to detect these methods using appro...

The role of an expert in the decision-making process is crucial. If we ask an expert to help us to make a decision we assume their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is for an expert to provide manipulated data in a given case of decision-making process becomes essential. In the presented work, we con...

One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be d...

The role of an expert in the decision-making process is crucial, as the final recommendation depends on his disposition, clarity of mind, experience, and knowledge of the problem. However, the recommendation also depends on their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is to manipulate in a given case beco...

In the decision making methods the common assumption is the honesty and professionalism of experts. However, this is not the case when one or more experts in the group decision making framework, such as the group analytic hierarchy process (GAHP), try to manipulate results in their favor. The aim of this paper is to introduce two heuristics in the...

Decision-making methods very often use the technique of comparing alternatives in pairs. In this approach, experts are asked to compare different options, and then a quantitative ranking is created from the results obtained. It is commonly believed that experts (decision-makers) are honest in their judgments. In our work, we consider a scenario in...

This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings concerning the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index. Further on,...

In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's confidence in a particular judgment. Then, from corresponding graph representations of a given PC matrix, all sp...

The Heuristic Rating Estimation Method enables decision-makers to decide based on existing ranking data and expert comparisons. In this approach, the ranking values of selected alternatives are known in advance, while these values have to be calculated for the remaining ones. Their calculation can be performed using either an additive or a multipli...

One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be d...

The aim of this paper is to examine the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. We introduce several propositions on the (dis)similarity of both rankings with respect to the matrix size and its inconsistency expressed by the Koczkodaj's inconsistency index...

In this paper, we propose a new method for the derivation of a priority vector from an incomplete pairwise comparisons (PC) matrix. We assume that each entry of a PC matrix provided by an expert is also evaluated in terms of the expert's confidence in a particular judgment. Then, from corresponding graph representations of a given PC matrix, all sp...

The conceptual framework of bioeconomy advances sustainability by ensuring that environmental, social, and economic goals are met. Although numerous authors perceive bioeconomy as a key sector to achieve sustainable transformation, there is a lack of a comprehensive set of factors determining sustainable entrepreneurship in the bioeconomy sector. T...

There are many priority deriving methods for pairwise comparison (PC) matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary. The presented work formulates an estimation of the difference between priority vectors in the two most po...

One of the best-known methods of multi-criteria decision-making is the Analytic Hierarchy Process (AHP). This method provides a convenient and versatile framework for modeling multi-criteria decision problems, evaluating alternatives, and deriving final priorities. Rather than imposing a "correct" decision, AHP allows the user to create a ranking o...

One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are don...

There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary. The presented work formulates an estimation of the difference between priority vectors in the two most popular...

We introduce two new inconsistency measures for the incomplete pairwise comparisons matrices and show several examples of their calculation. We also carry out a comparative analysis of the new inconsistency indices with the existing ones based on the Monte Carlo simulation.

Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking depends on the inconsistency of the data from which it was created. There are many indices used for determining the level of inconsistency among compared alternatives. Unfortunately, most of them assume that the set...

The paper presents the results of the second stage of research on business models of language schools. It was assumed that there is a significant difference in the value propositions of schools and the expectations of their clients. An examination procedure was planned with the use of a questionnaire and statistical analysis such as factor analysis...

We introduce two new inconsistency measures for the incomplete pairwise comparisons matrices and show several examples of their calculation. We also carry out a comparative analysis of the new inconsistency indices with the existing ones based on the Monte Carlo simulation.

We examine satisfaction of the condition of order preservation (COP) with respect to different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order n = {3,4,...,9}, where a priority vector is derived both by the eigenvalue method (EV) and the geometric mean (GM) method. Our results suggest...

Apart from consistency, the completeness of information is one of the key factors influencing data quality. In the case of the pairwise comparisons (PC) method, much space in the literature is devoted to the quantitative analysis of this first idea, while the second issue has not been properly studied. The presented article is an attempt to bridge...

When creating the ranking based on the pairwise comparisons very often, we face difficulties in completing all the results of direct comparisons. In this case, the solution is to use the ranking method based on the incomplete PC matrix. The article presents the extension of the well known geometric mean method for incomplete PC matrices. The descri...

Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for determining the level of inconsistency among compared alternatives. Unfortunately, most of them assume that the...

We propose parametrized families of algorithms for approximating inconsistent matrices with consistent ones. We present experimental results, and optimize distance versus performance.

Alongside consistency, completeness of information is one of the key factors influencing data quality. The objective of this paper is to define ways of treating missing entries in pairwise comparisons (PC) method with respect to inconsistency and sensitivity. Two important factors related to the incompleteness of PC matrices have been identified, n...

Significance: The data about proteins identified by different proteomics studies of molecular changes caused by morphine administration (29 published articles) were gathered in the Morphinome Database. Unification of those data allowed for the identification of proteins that were indicated several times by distinct proteomics studies, which means...

Comparing alternatives in pairs is a well-known method used to create ranking. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is constructed. Experts conduct a series of single assessments, however, they may not always be consistent. The level of inconsistency among individual ass...

The article shows a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from alo-group is investigated. This approach allows for generalization of the previous results. Sufficient conditions for order preservation based on the properties of elements...

This article explores a relationship between inconsistency in the pairwise comparisons method and conditions of order preservation. A pairwise comparisons matrix with elements from an alo-group is investigated. This approach allows for a generalization of previous results. Sufficient conditions for order preservation based on the properties of elem...

Comparing alternatives in pairs are the well-known method of ranking creation. The experts are asked to perform a series of binary comparisons then using the mathematical methods the final ranking is prepared. As experts do the individual assessments, they may not always be consistent. The level of inconsistency among individual assessments is wide...

EVM (eigenvector method) and GMM (geometric mean method) are probably the two most popular priority deriving techniques for AHP (Analytic Hierarchy Process). Although much has already been discussed about these methods, one frequently repeated question is: what do they have in common? In this paper we show that both these methods can be constructed...

Having a reliable sales forecasting method is the Holy Grail of man- agement decision making. Such a method would make possible min- imization of operating costs and maximize revenues. The presented work includes the proposal of using the Heuristic Rating Estimation (HRE) method to sales forecasting. The HRE method unlike AHP uses both: pairwise co...

The growing popularity of shared-memory multiprocessor machines has caused significant changes in the design of concurrent software. In this approach, the concurrently running threads communicate and synchronize with each other through data structures in shared memory. Hence, the efficiency of these structures is essential for the performance of co...

The growing popularity of shared-memory multiprocessor machines has caused significant changes in the design of concurrent software. In this approach, the concurrently running threads communicate and synchronize with each other through data structures in shared memory. Hence, the efficiency of these structures is essential for the performance of co...

The AHP/ANP are multicriteria decision making theories that deal with both hierarchic structures when the criteria are independent of the alternatives and with networks when there is any dependence within and between elements of the decision. The essential aspect of these theories is the measurement of intangibles. They use numbers from an absolute...

The growing popularity of shared-memory multiprocessor machines has caused significant changes in the design of concurrent software. In this approach, the concurrently running threads communicate and synchronize with each other through data structures in shared memory. Hence, the efficiency of these structures is essential for the performance of co...

Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This does not take into account the actual values of preference. The Heuristic Rating Estimation (HRE) approach is...

The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. There are several popular implementations of the method including Eigenvector Method, Least Squares Method, Chi Squares Method and others. Each of the above methods comes with one or more inconsistency in...

This is the presentation shown at the EURO 2015 conference. It provides explanation of relationships between Condition of Order Preservation as defined by Bana e Costa & Vansninck and the inconsistency of a pairwise comparisons matrix.

This is the presentation shown at the EURO 2015 conference. It provides explanation of relationships between Condition of Order Preservation as defined by Bana e Costa & Vansninck and the inconsistency of a pairwise comparisons matrix.

This paper presents a concurrent algorithm for computing a consistent approximation to a generalized pairwise comparisons matrix (i.e. it is assumed that the reciprocity property is not required). Like its sequential counterpart, it is based on the iterative strategy “find the worst case and fix it”. The conducted experiments confirmed that a signi...

Presentation given during 23rd International Conference on Multiple Criteria Decision Making MCDM 2015, August 2nd–7th, 2015, Hamburg, Germany

Unfortunately, in the original publication, the conditions Q1, Q2 and Q3 given in Sect. 7 intended as convergence criteria for the algorithm (Kułakowski, A heuristic rating estimation algorithm for the pairwise comparisons method, CEJOR, 2015, Listing 1) are incorrect. Their values calculated under the assumptions of the example are also erroneous....

The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the pairwise comparisons matrix. In such cases the ranking result for the principal eigenvector of the pairwise compa...

Posted by a mistake as a dataset but removing it would decrease my downloads :)

Heuristic Rating Estimation (HRE) is a newly proposed method supporting decisions analysis based on the use of pairwise comparisons. It allows that the ranking values of some alternatives (herein referred to as concepts) are initially known, whilst the ranks for the other concepts have yet to be estimated. To calculate the missing ranks it is assum...

Pairwise comparisons are widely recognized method supporting decision making process based on the subjective judgments. The key to this method is the notion of inconsistency that has a significant impact on the reliability of results. Inconsistency is expressed by means of inconsistency indices. Depending on their construction, such indices may pay...

Organization of a tender is not easy. Preparation of the relevant specification, taking into account the non-price criteria, implementation of the objective and fair assessment procedure, and last but not least, selecting a satisfactory offer are in practice a considerable challenge. In meeting this challenge appropriate multi-criteria assessment m...

Comparison, rating, and ranking of alternative solutions, in case of multicriteria evaluations, have been an eternal focus of operations research and optimization theory. There exist numerous approaches at practical solving the multicriteria ranking problem. The recent focus of interest in this domain was the event of parametric evaluation of resea...

This paper presents an attempt at an analysis of parametric evaluation of research units with machine learning toolkit. The main goal was to investigate if the rules of evaluation can be expressed in a readable, transparent, and easy to interpret way. A further attempt was made at investigating consistency of the applied procedure and presentation...

Today, energy efficiency is one of the top priorities in building design and construction. A significant share of energy usage is due to indoor lighting. Although methods exist for design and control of intelligent lighting systems, the task of real-world lighting assessment and verification remains only partly addressed. This paper describes found...

The pairwise comparisons method is a way to decide the relative order among different concepts (alternatives). The most popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. It does not take into account the actual values of preference (even if they are initially known). The Heuri...

Increasing demand for computationally efficient algorithms and processors has turned the attention of researchers toward parallel and concurrent solutions. Because the frequency of contemporary processors cannot be tweaked infinitely, the only hopes for squeezing more performance from computers are parallel processing and parallel computation. The...

The pairwise comparisons method is a convenient tool used when the relative order between different concepts (alternatives) need to be determined. One of the popular implementation of the method is based on solving eigenvalue problem for the pairwise comparisons matrix. In such a case as the ranking result the principal eigenvector of the pairwise...

The coarsest bisimulation-finding problem plays an important role in the formal analysis of concurrent systems. For example, solving this problem allows the behavior of different processes to be compared or specifications to be verified. Hence, in this paper an efficient concurrent bisimulation algorithm is presented. It is based on the sequential...

The article presents RobustPI - an extension of the Robust middleware library, which allows the widely recognized Pioneer 3-AT robot to be programmed as a Webots based virtual hardware. Like Lego Mindstorms NXT robots, the Pioneer 3-AT model and Webots simulator are very popular as experimental platforms in many places all over the world. For this...

The Heuristic Ratio Estimation (HRE) approach proposes a new way of using the pairwise comparisons matrix. It allows the assumption that some alternatives (herein referred to as concepts) are known and fixed, hence the weight vector needs to be estimated only for the other unknown values. The main purpose of this paper is to extend the previously p...

The pairwise comparisons method is a powerful tool used for establishing the relative order between different concepts in situations in which it is difficult (or sometimes even impossible) to provide explicit rating. Appropriate ratings are determined by solving eigenvalue problem for the pairwise comparisons matrix. This study presents a new itera...

This paper presents the use of a Concurrent Communicating Lists (CCL) library in robot behavior modeling. CCL provides several software components, which allow the model to be built, simulated and formally verified. Due to the integration with the Robust library the CCL models can be deployed and executed on the actual hardware platforms. Besides t...

One of the fundamental skills of an autonomous mobile robot is its ability to determine a collision-free path in a dynamically changing environment. To meet this challenge, robots often have their own world model - an internal representation of the environment. Such a representation allows them to predict future changes to the environment, and thus...

This review is a meta-analysis of data describing proteins regulated by morphine influence studied worldwide across last years administration. Up to date (July 2010), 15 studies concerning this subject have been published. Animal models, examined brain structures, the route of morphine administration and proteomic platforms used for identification...

This paper presents RobustHX - an extension of the Robust middleware library, which allows the six-legged Hexor robot to be programmed in Java. Like Lego Mindstorms NXT robots, Hexor has been adopted by many academic centers in Poland as a tool for teaching AI robotics. For this reason, the authors hope that RobustHX may also be found as an interes...

The article presents an agent-based approach to modeling of pedestrian evacuation. It includes some theoretical aspect of using the agents techniques as well as case study of evacuation tests realized by the authors. Results from real data gained from experiments are compared with data from designed simulations. The use of agent-based methods gives...

This paper presents the cljRobust - middleware library, which allows an intelligent control application to be written for Lego Mindstorms NXT. cljRobust is based on Clojure, which is a modern, concurrent dialect of the Lisp language. It shortens the distance between deliberative, symbolic processing and hardware. In this way, cljRobust facilitates...

Environments designed for microscopic simulations of crowd dynamics have to be efficient, easy to maintain and develop. Growing interest in exact simulations of complex pedestrian behavior entails the necessity of a systematic approach in constructing these systems. The authors' experiences in this field result in the proposition of the new agent o...

The article presents the use of Multi-agent system (MAS) in pedestrian dynamics modeling. Current trends in pedestrian dynamics are presented with particular focus on a short review of various agent-based models of pedestrian dynamics. The models are briefly discussed and compared.

Increasing demand for computational power in contemporary constructions has created the need to build faster CPUs and construct more efficient algorithms. In this context especially the concurrent algorithms seem to be very promising. Depending on the number of available CPUs they may offer significant reductions in computation time. In this artic...

Recently, in response to growing market demand, several different techniques of business rules representation have been created. Some of them try to present business rules in a visual manner. However, due to the complexity of the problem, the graphic representations that are proposed seem to be far from perfection. In this paper we would like to de...

The growing popularity and common usage of real-time reactive systems on various domains force activities that lead to the improvement of the development stage by applying several software engineering methods e.g.: MDA (model driven architecture) or executable modelling, which could provide a working prototype of a system in the early stage of deve...

From the very beginning, notions such as bisimulation and formal methods like temporal logic HML or mu-Calculs were closely connected with process algebra CCS. Another formal method that is widely used for similar purposes is Petri nets formalism. The presented paper shows how the model given in the form of a Petri net could be transformed into an...

Reliability (like recoverability and fault tolerance) has often been considered as a crucial quality aspect of the reactive system. In this way, the designer can put great attention and effort into increasing their reliability level. On the other hand, the growing popularity and massive usage these systems on various domains could be noticed. This...

A successful autonomous mobile robot construction is highly dependent on the ability to plan its own motion to find a collision-free path leading to a specified target. In such planning, an internal representation of the surrounding world (World Model) is very helpful. The world model formally defined in this paper is built upon the asynchronous no...