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Berge's notion of equilibrium represents a complementary alternative to the Nash equilibrium when modeling socioeconomic behavior and human interactions. While the notion of Nash equilibrium is based on self-interest, as players seek to maximize their own payoffs given the action of the other players, the idea behind Berge equilibrium is mutual support, as given the action of one of the players, all others select their actions looking for her best interest. However, because of the demanding conditions involved, the existence of Berge equilibria is rarely guaranteed. In this paper, we propose vector-valued normal-form games as a unified framework in which to study and extend the concept of Berge equilibrium. Based on the equilibria of the so-called altruistic game, we introduce new equilibrium concepts which constitute different relaxations of Berge's notion, although they still retain the underlying idea of mutual support. We establish the links between these new equilibria, Nash equilibrium, Berge equilibrium, and other related concepts already existing in the literature. Our approach has the advantage that it permits the incorporation of preference information to identify the equilibria which are consistent with different altruistic attitudes of the players. [ABSTRACT FROM AUTHOR]

In the context of the construction of new liberal arts, the integration and intersection of disciplines have become a new trend in the development of higher education. How to promote the teaching reform of big data technology and application courses in the new liberal arts construction scenario has become an important issue in enhancing students’ digital talent literacy and social adaptability. In this study, an extended probabilistic linguistic TODIM (an acronym in Portuguese for interactive multi-criteria decision making) with probabilistic linguistic entropy weight and Hamming distance is presented for teaching reform plan evaluation for the core course “big data technology and applications” in the digital economy major. Firstly, probabilistic linguistic entropy weight, based on the entropy of the additive linguistic term set, is applied to generate weight information. Secondly, parameter sensitivity analysis is carried out to prove the stabilization and effectiveness of the extended TODIM approach. Thirdly, this extended approach can integrate the psychological factors and cognitive behaviors of decision-makers for effectively responding to education management in the new liberal arts construction scenario. Finally, a case study on teaching reform plan evaluation is carried out, and a comparative analysis with different criteria weights and different methods is conducted to verify the extended approach. The results indicate that the extended approach can provide an effective technical tool for scientific decision-making, especially in the teaching reform plan evaluation scenario in order to promote high-quality development of education.

We develop a monetary model in which a private company issues digital currency and uses payment data to estimate consumers' preferences. Sellers purchase preference information to produce goods that better match consumers' preferences. A monopoly arises in the digital currency industry, and digital currency is not issued if the inflation rate is sufficiently high. Due to reinforcing interactions between the value of preference information and trade volume, multiple equilibria (with and without digital currency) can exist, depending on market structures for monetary exchanges. When left to market forces alone, socially efficient uses of payment data may not occur. [ABSTRACT FROM AUTHOR]

The transformation method between the linguistic judgement matrix and other four forms of preference information is researched in this paper. The four forms of preference information are preference ordering, utility value, reciprocal judgement matrices and complementary judgement matrices. First, based on the definition of preference information, the mutual transformation methods of linguistic judgement matrix and other four forms of preference information are given. Then new transformation equations are obtained. Next, it is proved that when the linguistic judgement matrix has complete consistency, the other four forms of preference information will have complete consistency too. Finally, a numerical analysis is offered to show that these methods are feasible and effective.

In this paper a ranking method using common weights methodology is presented. The goal of the method is enhancing the decision maker (DM)'s influence in the ranking procedure. Although DM's preference information is an important element in our method, the approach can also be modified to be used in the absence of it. Since we aim to implement the approach on an empirical instance, the model is modified to deal with the properties of the sample, so it is developed in the presence of the interval data and flexible measures. Finally, the results are discussed. [ABSTRACT FROM AUTHOR]

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We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles. [ABSTRACT FROM AUTHOR]

With the continuous advancement of science and technology, the decision-making environment faced by managers is increasingly complex, which puts forward higher requirements for managers. Due to the complexity of the multi-attribute decision-making problem, it is difficult for the decision-maker to make the correct choice. In addition, due to the influence of the educational background and limited knowledge of the managers, it is impossible to evaluate with simple statistical data. In essence, the location problem of lowcarbon logistics parks is a MADM problem. Therefore, this paper establishes an optimization model to solve the multiple-attribute decision-making (MADM) problem with alternative preference and single-valued neutrosophic (SVN) information. Considering that the information of weight is unknown, a scientific model is built based on the minimum deviation method deriving the criterion weight. Furthermore, the above models and methods are extended to interval neutrosophic sets (INs). To verify the validity of the modified model, a numerical case for low-carbon logistics park site selection is taken as an example. Through the case study, we found that the method has strong operability and can make the most of the available information. [ABSTRACT FROM AUTHOR]

Most studies in dynamic multi-objective optimization have predominantly focused on rapidly and accurately tracking changes in the Pareto optimal front (POF) and Pareto optimal set (POS) when the environment undergoes changes. However, there are real-world scenarios where it is necessary to simultaneously solve changing objective functions and satisfy the preference of Decision Makers (DMs). In particular, the DMs may be only interested in a partial region of the POF, known as the region of interest (ROI), rather than requiring the entire POF. To meet the challenge of simultaneously predicting a changing POF and/or POS and dynamic ROI, this paper proposes a new dynamic multi-objective evolutionary algorithm (DMOEAs) based on the preference. The proposed algorithm consists of three key components: an evolutionary direction adjustment strategy based on changing reference points to accommodate shifts in preferences, an angle-based search strategy for tracking the varying ROI, and a hybrid prediction strategy that combines linear prediction models and population manifold estimation within the ROI to ensure convergence and distribution in scenarios where preferences remain unchanged. Experimental studies conducted on 30 widely used benchmark problems in which it outperforms contrasting algorithms on 71% of test suits. Empirical results demonstrate the significant advantages of the proposed algorithm over existing state-of-the-art DMOEAs. [ABSTRACT FROM AUTHOR]

Interactive methods are useful decision-making tools for multiobjective optimization problems, because they allow a decision-maker to provide her/his preference information iteratively in a comfortable way at the same time as (s)he learns about all different aspects of the problem. A wide variety of interactive methods is nowadays available, and they differ from each other in both technical aspects and type of preference information employed. Therefore, assessing the performance of interactive methods can help users to choose the most appropriate one for a given problem. This is a challenging task, which has been tackled from different perspectives in the published literature. We present a bibliographic survey of papers where interactive multiobjective optimization methods have been assessed (either individually or compared to other methods). Besides other features, we collect information about the type of decision-maker involved (utility or value functions, artificial or human decision-maker), the type of preference information provided, and aspects of interactive methods that were somehow measured. Based on the survey and on our own experiences, we identify a series of desirable properties of interactive methods that we believe should be assessed. [ABSTRACT FROM AUTHOR]

The data are not always real numbers due to the complexity and uncertainty of the real-world decision environment. This requires us to use probability-based expressions to describe the complex decision-making data in reality. In order to understand the probability-based decision-making information more comprehensively, this paper reviews and summarizes the current development of probability-based decision-making information. First, the number and the distribution of publications related to the probability-based decision-making information are analyzed. Then, based on presenting literature related to different concepts, all the existing different concepts are reviewed and discussed. Considering different forms of decision-making information, this paper summarizes decision-making methods from two aspects: the decision-making methods based on decision matrix and the decision-making methods based on preference information. We also summarize the existing literature from the perspective of application. In addition, based on current developments and the discussions above, some challenges concerning probability-based expressions are listed, which can be regarded as future research directions. [ABSTRACT FROM AUTHOR]

In real life, some complex problems are multi-objective optimization problems. Most of the existing studies have focused on how to obtain the optimal solutions distributed on the whole Pareto-optimal frontier. However, in some fields such as industrial production, the decision-makers of enterprises usually care about what specific measures can maximize the comprehensive benefits of enterprises. Due to this kind of realistic demands, we prefer to find a small part of the optimal solutions according to the preference information suggested by the decision-makers rather than obtain all of the Pareto-optimal solutions. However, almost all of the existing methods only repeat calculation when they meet the scenario where the user-preferences change over time. To address the multi-objective optimization problem under the scenario with dynamic user-preferences information, we propose a MOEA/D-DPRE (multi-objective optimization algorithm based on dynamic preference information) algorithm in this paper, and its framework is inspired by the MOEA/D-PRE (decomposition user-preference multi-objective evolutionary) algorithm. We analyze the four position relations between the distribution region of the old preference weight vectors (old preference region), and we also present the distribution region of the new preference weight vectors (new preference region) and propose the different strategy to the different case respectively. When the preference information changes, the MOEA/D-DPRE can converge to the region of new interest by responding to the change of preference and the historical information. Experimental results show that the proposed method is better than the compared method in convergence speed and distribution under the scenario with dynamic user-preferences information. [ABSTRACT FROM AUTHOR]

Online tourist reviews are the real feeling of tourists after the journey, which have a strong reference value for potential tourists to make travel decisions. However, it is almost impossible for a potential tourist to look through the massive online reviews related to tourist attractions (TAs) so that he/she can make the most appropriate decision. To this end, this paper proposes a recommender system to rank the alternative TAs through online reviews based on aspect-level sentiment analysis and multi-criteria decision-making (MCDM) with intuitionistic and hesitant fuzzy information. In this methodology, the aspects that the experienced tourists concern are extracted from online reviews to construct a three-level evaluation system (including target layer, criteria layer and sub-criteria layer), which not only ensures the comprehensive evaluation of TAs as much as possible, but also reduces the complexity of the decision-making process. Then, the online reviews related to these sub-criteria are transformed into the corresponding intuitionistic and hesitant fuzzy performance scores through aspect-level sentiment analysis. Furthermore, in order to obtain the final ranking result that more in line with the expectations of the potential tourist, the preference information from the potential tourist and experienced tourists is integrated to determine the weights of criteria. Subsequently, the intuitionistic and hesitant fuzzy TOPSIS (IHF-TOPSIS) method is proposed to rank the alternative TAs. Finally, a case study is provided to verify the validity and applicability of the methodology. [ABSTRACT FROM AUTHOR]

To reduce the dimensionality of high-dimensional data and enhance its classification accuracy, feature selection can be regarded as a multiobjective optimization problem that can be addressed by evolutionary computation algorithms with promising results. However, balancing the convergence and diversity of nondominated solutions remains challenging. To address these issues, this paper proposes a multiobjective sparrow search feature selection approach with sparrow ranking and preference information and its applications for high-dimensional data. First, during the population updating process, the updating formula of observers is combined with the mutualism phase of the symbiotic organisms search algorithm to design a location updating formula of observers in the sparrow search algorithm, balancing the local development ability and global search ability of sparrow search algorithm and increasing the possibility of moving closer to the optimal solution. Second, based on the dominant and nondominated sparrow individuals of each sparrow, the dominant and nondominated distances are defined, and the sparrow ranking is proposed. The feature ranking is then designed by using the definition of sparrow ranking. Following the definition of sparrow ranking and feature ranking, the selection strategy and location updating formula of the producers in the sparrow search algorithm are proposed. Finally, a preference information-based mutation algorithm is designed to augment the diversity of the nondominated solutions and more effectively guide the whole sparrow population to a better solution. The experimental results on 14 high-dimensional datasets show that the proposed algorithm outperforms different single-objective and multiobjective optimization feature selection algorithms in terms of classification efficiency and diversity of solutions. • A new location updating formula of observers is designed for the mutualism phase of the symbiotic organisms search algorithm. • The dominant and nondominated distances are defined and the feature ranking is designed with the sparrow ranking. • The novel selection strategy and location updating formula of the producers in the sparrow search algorithm are improved. • A preference information-based mutation algorithm is designed to augment the diversity of the nondominated solutions. [ABSTRACT FROM AUTHOR]

In researching multi-objective evolutionary algorithms (MOEAs), the decision-maker (DM) may not need the entire Pareto optimal front searched and may only be interested in the region of interest (ROI). Most existing preference-based research focuses on determining the location of the ROI and controlling its size. Those research typically ignores the preference information provided by the DM when solving problems. Since the convergence region and diversity of the population are determined according to the DM's preference information, so we propose a preference-based MOEA that uses a normal distribution (ND) to generate a weight vector, called MOEA/D-ND. The generation of the weight vector uses the DM's preference information to guide the solution to converge to the vicinity of the preference information. Because the randomness of the normal distribution can lead to a loss of diversity, an angle-based niche selection strategy is adopted. This strategy prevents the population from falling into a local optimum during the search process. Although the reference vector generated by MOEA/D-ND using the normal distribution will make the final solution set no longer uniformly distributed in the ROI, still, the closer region to the reference point, the more solution sets are obtained. The experimental results show that this algorithm has advantages in various benchmark problems with 2 to 15 goals. [ABSTRACT FROM AUTHOR]

Feature selection (FS) is an NP-hard combinatorial optimization problem, which aims to select the most relevant features from a large number of candidates. Recently, the FS in classification has been handled as a bi-objective optimization problem, where both the classification error and the number of selected features are minimized simultaneously. Despite of the effectiveness of existing multi-objective optimization (MOO) algorithms on FS, the convergence toward the Pareto front and the distribution over the Pareto front still deserve to be improved. To this end, this paper proposes a new multi-objective chemical reaction optimization algorithm for FS, termed MOFSCRO. In the proposed MOFSCRO, the preference information related to the problem is firstly extracted from the population. Then, three evolutionary operators based on the preference information are suggested to guide the population evolution, with the purpose of enhancing the population convergence and diversity. Experimental results on 12 benchmark data sets demonstrate the superiority of the proposed MOFSCRO over seven state-of-the-art FS algorithms in terms of both the classification error and the number of selected features. In comparison to five MOO algorithms, MOFSCRO also shows better performance according to the metric of inverted generational distance. • A MOCRO algorithm is proposed for the feature selection problem. • The problem-related preference information is utilized for guiding the search. • The evolutionary operators are designed to enhance the convergence and the diversity. [ABSTRACT FROM AUTHOR]