The date: Thursday, February 27, at 18:00 (CET)

The speaker: Dr. David Bartl (Silesian University in Opava, Czechia)

Abstract: We briefly recall several methods to find the priority vector of a pairwise comparison matrix (PCM), namely: arithmetic mean method (AMM), least squares method (LSM), chi-square method (CSM), logarithmic least squares method (LLSM) or geometric mean method (GMM), weighted least squares method (WLSM), and Saaty’s eigenvector method (EVM). In this paper, we allow the PCM entries to be elements of a divisible alo-group (Abelian linearly ordered group), cf. the “general unified framework for pairwise comparison matrices in multicriteria methods” by Cavallo and D’Apuzzo (2009). Then, while most of the aforementioned methods, including Saaty’s EVM, cannot be used in this setting due to their intrinsic properties, the GMM can easily be adapted to find the priority vector of the PCM with entries from a divisible alo-group (Cavallo & D’Apuzzo, 2012) and, to our best knowledge, is the only currently known method that can be used in this setting. We then recall the classical notion of a cooperative game with transferable utility, and also the classical solution concept of nucleolus (Schmeidler, 1969) of the TU-game. Inspired by the concept of nucleolus, we propose a new nucleolus-like method to compute the priority vector of a pairwise comparison matrix with entries from any divisible alo-group. The method utilizes the theory of linear programming in abstract spaces (Bartl, 2007).

Zoom link: https://us06web.zoom.us/j/86585849745

Invitation: Webinar_D_Bartl.pdf

The date: Friday, January 31, 2025, at 13:00 (CET)

The speaker: Dr. Kevin Kam Fung Yuen (The Hong Kong Polytechnic University)

Abstract: Analytic Hierarchy Process (AHP) is a popular evaluation method used in engineering, business and management. However, the knowledge representation of paired ratio scale in AHP is doubtful. To address the identified drawbacks, paired interval scale for comparison evaluation is recommended. Paired interval scale is the key foundation of Cognitive Network Process (CNP) firstly proposed by K.K.F. Yuen in 2009. This talk discusses the limitations of classical rating methods, indicates the motivations of pairwise comparisons, reviews the details of AHP, highlights its drawbacks, articulates the motivations of CNP, demonstrates the usability of how CNP can be applied to a selection problem, and compares the results between CNP and AHP and concludes the reasons why CNP is better than AHP for the competitive selection cases. The proposed CNP method can be applied to diverse selection problems in engineering, business, and management.

Zoom link: https://us06web.zoom.us/j/87419247211

Invitation: Webinar_K_K_F_Yuen.pdf

The date: Thursday, December 12, 2024, at 18:00 (CET)

The speaker: Dr. Jean-Pierre Magnot (University of Angers, France)

Abstract: We analyze inconsistency reduction and ranking from the viewpoint of a mathematician. We first describe the analogy between pairwise comparisons and gauge theories, both in deterministic and in stochastic aspects. Secondly, we analyze the ranking problem under the lights of the topology of the finite configuration space. All along the talk we try to make some link with selected works on pairwise comparisons.

Zoom link: https://us06web.zoom.us/j/81417380703

Presentation: beamer-PC-12-10-2024.pdf