New preference violation indices for the condition of order preservation

<p>Consistency of pairwise comparisons is one particular aspect that is studied thoroughly in the recent decades. However, since the introduction of the concept of the condition of the order preservation in 2008, there is no inconsistency measure based on the aforementioned condition. Therefore, the aim of this paper is to fill this gap and propose new preference violation indices for measuring violation of the condition of the order preservation. Further, an axiomatic system for the proposed measures is discussed, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariance under inversion of preferences and continuity axioms.</p> <p>&nbsp;</p>

Coarse ethics: how to ethically assess explainable artificial intelligence

The integration of artificial intelligence (AI) into human society mandates that their decision-making process is explicable to users, as exemplified in Asimov’s Three Laws of Robotics. Such human interpretability calls for explainable AI (XAI), of which this paper cites various models. However, the transaction between computable accuracy and human interpretability can be a trade-off, requiring answers to questions about the negotiable conditions and the degrees of AI prediction accuracy that may be sacrificed to enable user-interpretability. The extant research has focussed on technical issues, but it is also desirable to apply a branch of ethics to deal with the trade-off problem. This scholarly domain is labelled coarse ethics in this study, which discusses two issues vis-à-vis AI prediction as a type of evaluation. First, which formal conditions would allow trade-offs? The study posits two minimal requisites: adequately high coverage and order-preservation. The second issue concerns conditions that could justify the trade-off between computable accuracy and human interpretability, to which the study suggests two justification methods: impracticability and adjustment of perspective from machine-computable to human-interpretable. This study contributes by connecting ethics to autonomous systems for future regulation by formally assessing the adequacy of AI rationales.

On the axiomatic approach to sharing the revenues from broadcasting sports leagues

We take the axiomatic approach to uncover the structure of the revenue-sharing problem from broadcasting sports leagues. We formalize two notions of impartiality, depending on the stance one takes with respect to the revenue generated in the games involving each pair of teams. We show that the resulting two axioms lead towards two broad categories of rules, when combined with additivity and some other basic axioms. We complement those results strengthening the impartiality notions to consider axioms of order preservation.

The extention rank ordering criteria weighting methods in fuzzy enviroment

We examine the satisfaction of the condition of order preservation (COP) concerning different levels of inconsistency for randomly generated multiplicative pairwise comparison matrices (MPCMs) of the order from 3 to 9, where a priority vector is derived both by the eigenvalue (eigenvector) method (EV) and the geometric mean (GM) method. Our results suggest that the GM method and the EV method preserve the COP almost identically, both for the less inconsistent matrices (with Saaty’s consistency index below 0.10), and the more inconsistent matrices (Saaty’s consistency index equal to or greater than 0.10). Further, we find that the frequency of the COP violations grows (almost linearly) with the increasing inconsistency of MPCMs measured by Koczkodaj’s inconsistency index and Saaty’s consistency index, respectively, and we provide graphs to illustrate these relationships.

Some Impossibilities of Ranking in Generalized Tournaments

In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with lower and upper bounds. An axiomatic approach is applied to the problem of ranking the competitors. Self-consistency (SC) requires assigning the same rank for players with equivalent results, while a player showing an obviously better performance than another should be ranked strictly higher. According to order preservation (OP), if two players have the same pairwise ranking in two tournaments where the same players have played the same number of matches, then their pairwise ranking is not allowed to change in the aggregated tournament. We reveal that these two properties cannot be satisfied simultaneously on this universal domain.