Type-reduction of type-2 fuzzy sets is considered to be a defuzzification bottleneck because of the computational complexity involved in the process of type-reduction. In this paper, we prove that the closed-form Nie-Tan operator, which outputs the average of the upper and lower bounds of the footprint of uncertainty, is actually an accurate method for defuzzifying interval type-2 fuzzy sets.

Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper, we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner's dilemma, are analyzed by means of the proposed methodology.

In this paper, we investigate winning strategies for round-robin iterated Prisoner's Dilemma (IPD) competitions and evolutionary IPD competitions. Since the outcome of a single competition depends on the composition of the population of participants, we propose a statistical evaluation methodology that takes into account outcomes across varying compositions. We run several series of competitions in which the strategies of the participants are randomly chosen from a set of representative strategies. Statistics are gathered to evaluate the performance of each strategy. With this approach, the conditions for some well-known strategies to win a round-robin IPD competition are analyzed. We show that a strategy that uses simple rule-based identification mechanisms to explore and exploit the opponent outperforms well-known strategies such as tit-for-tat (TFT) in most round-robin competitions. Group strategies have an advantage over nongroup strategies in evolutionary IPD competitions. Group strategies adopt different strategies in interacting with kin members and nonkin members. A simple group strategy, Clique, which cooperates only with kin members, performs well in competing against well-known IPD strategies. We introduce several group strategies developed by combining Clique with winning strategies from round-robin competitions and evaluate their performance by adapting three parameters: sole survivor rate, extinction rate, and survival time. Simulation results show that these group strategies outperform well-known IPD strategies in evolutionary IPD competitions.

Credit risk prediction heavily relies on historical data provided by financial institutions. The goal is to identify commonalities among defaulting users based on existing information. However, data on defaulters is often limited, leading to a concentration of credit data where positive samples (defaults) are significantly fewer than negative samples (nondefaults). It poses a serious challenge known as the class imbalance problem, which can substantially impact data quality and predictive model effectiveness. To address the problem, various resampling techniques have been proposed and studied extensively. However, despite ongoing research, there is no consensus on the most effective technique. The choice of resampling technique is closely related to the dataset size and imbalance ratio, and its effectiveness varies across different classifiers. Moreover, there is a notable gap in research concerning suitable techniques for extremely imbalanced datasets. Therefore, this study aims to compare popular resampling techniques across different datasets and classifiers while also proposing a novel hybrid sampling method tailored for extremely imbalanced datasets. Our experimental results demonstrate that this new technique significantly enhances classifier predictive performance, shedding light on effective strategies for managing the class imbalance problem in credit risk prediction.