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The concept of the hybrid structure, as an extension of both soft sets and fuzzy sets, has gained significant attention in various mathematical and decision-making domains. In this paper, we delve into the realm of hemirings and investigate the properties of hybrid h-bi-ideals, including prime, strongly prime, semiprime, irreducible, and strongly irreducible ones. By employing these hybrid h-bi-ideals, we provide insightful characterizations of h-hemiregular and h-intra-hemiregular hemirings, offering a deeper understanding of their algebraic structures. Beyond theoretical implications, we demonstrate the practical value of hybrid structures and decision-making theory in handling real-world problems under imprecise environments. Using the proposed decision-making algorithm based on hybrid structures, we have successfully addressed a significant real-world problem, showcasing the efficacy of this approach in providing robust solutions. [ABSTRACT FROM AUTHOR]

Concerning the development of computational tools and solutions as a decision-making aid, this paper presents the results of the waspasWEB project, which strives to provide decision-makers with a readily accessible mechanism to employ the weighted aggregated sum product assessment (WASPAS) method. The social contribution of the project encompasses the development of a user-friendly and publicly accessible internet tool, as well as a package launched on the Comprehensive R Archive Network (CRAN) to serve the community of users of the R language. The use of operational research methodologies is crucial to justify decisions, and this effort seeks to advance the adoption of such methodologies, offering managers, researchers, and the general public an intuitive and easily accessible multi-criteria decision-making tool. In this way, we present the technical specifications, usability, and interactivity of the user with the computational platform, being validated its viability through a hypothetical case study. At the end of the research, it exposes the limitations and feasibility of the proposed computational model along with future research. [ABSTRACT FROM AUTHOR]

As an important branch of modern decision-making theory, multi-attribute decision-making (MADM) plays an important role in various fields. Classic MADM methods can provide a ranking of alternatives, and decision-makers need to evaluate the level subjectively based on the ranking results. Because of the limitation of knowledge, this is likely to lead to potential individual losses. Three-way decision (3WD) theory has good classification ability. Therefore, this paper proposes a dynamic hybrid multi-attribute 3WD (MA3WD) model. First, a new scheme for constructing loss functions is proposed from the perspective of gray relational analysis (GRA), which is an accurate and objective way to describe the relationship between loss functions and attribute values. Then, conditional probabilities are determined by employing the gray relational analysis technique for order preference by similarity to the ideal solution (GRA-TOPSIS). With these discussions, a GRA-based hybrid MA3WD model for a single period is proposed by considering multi-source information. Furthermore, by extending the single-period scenario to a multi-period one, we construct a dynamic hybrid MA3WD model, which can obtain the final three-way decision rules as well as the results of each period and each attribute. Finally, the proposed method is applied to the case of performance evaluation of elderly-care services to demonstrate the effectiveness of the method, and comparative analyses are given to verify the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we study an independent Bernoulli two-armed bandit with unknown parameters ρ and λ , where ρ and λ have a pair of priori distributions such that d R (ρ) = C R ρ r 0 (1 − ρ) r 0 ′ d μ (ρ) , d L (λ) = C L λ l 0 (1 − λ) l 0 ′ d μ (λ) and μ is an arbitrary positive measure on [ 0 , 1 ] . Berry proposed the conjecture that, given a pair of priori distributions (R , L) of parameters ρ and λ , the arm with R is the current optimal choice if r 0 + r 0 ′ < l 0 + l 0 ′ and the expectation of ρ is not less than that of λ. We give an easily verifiable equivalent form of Berry's conjecture and use it to prove that Berry's conjecture holds when R and L are two-point distributions as well as when R and L are beta distributions and the number of trials N ≤ r 0 r 0 ′ + 1 . [ABSTRACT FROM AUTHOR]

Revealed preference is one of the most influential ideas in economics. It is, however, not clear how it can be generally applied in cases where agents' choices depend on arbitrary changes in the decision environment. In this paper, we propose a generalization of the classic rational choice theory that allows for such framing effects. Frames are modeled as different presentations (e.g., visual or conceptual) of the alternatives that may affect choice. Our main premise is that framing effects are neutral (i.e., independent of labeling the alternatives). An agent exhibiting these neutral framing effects who is otherwise rational, is called impressionable rational. We show that our theory encompasses many familiar behavioral models such as status-quo bias, satisficing, present bias, framing effects resulting from indecisiveness, certain forms of limited attention, categorization bias, and the salience theory of choice, as well as hybrid models. Moreover, in all these models, sufficiently rich choice data allow our theory to identify the "correct" underlying preferences without invoking each specific cognitive process. Additionally, we introduce a falsifiable axiom that completely characterizes the behavior of agents who are impressionable rational. [ABSTRACT FROM AUTHOR]

The point estimation problems that emerge in Bayesian predictive inference are concerned with random quantities which depend on both observable and non-observable variables. Intuition suggests splitting such problems into two phases, the former relying on estimation of the random parameter of the model, the latter concerning estimation of the original quantity from the distinguished element of the statistical model obtained by plug-in of the estimated parameter in the place of the random parameter. This paper discusses both phases within a decision theoretic framework. As a main result, a non-standard loss function on the space of parameters, given in terms of a Wasserstein distance, is proposed to carry out the first phase. Finally, the asymptotic efficiency of the entire procedure is discussed. [ABSTRACT FROM AUTHOR]

In a previous paper, the problem of how the preventive maintenance organization for the k-out-of-n: F system could be used, in order to maximize system availability, was considered. The current paper continues these investigations using a different optimization criterion. The proposed approach is based on decision making theory for regenerative processes. We propose a general procedure for comparing different preventive maintenance strategies based on the ordered statistics distributions, aiming to choose the best one with respect to cost-type criterion. The lifetime distributions of system units are usually unknown and only one or two of their moments are available. For this reason, we pay special attention to the sensitivity analysis of decision making about preventive maintenance, taking into account the shape of the system unit lifetime distributions. A numerical study of two examples based on a real-world system illustrates the results of the proposed approach. [ABSTRACT FROM AUTHOR]

The theory of three-way decision has been widely utilized across various disciplines and fields as an efficient method for both knowledge reasoning and decision making. However, the application of the three-way decision theory to partially labeled data has received relatively less attention. In this study, we propose a semi-supervised co-training model based on the three-way decision and pseudo labels. We first present a simple yet effective method for producing two views by assigning pseudo labels to unlabeled data, based on which a heuristic attribute reduction algorithm is developed. The three-way decision is then combined with the concept of entropy to form co-decision rules for classifying unlabeled data into useful, uncertain, or useless samples. Finally, some useful samples are iteratively selected to improve the performance of the co-decision model. The experimental results on UCI datasets demonstrate that the proposed model outperforms other semi-supervised models, exhibiting its potential for partially labeled data. [ABSTRACT FROM AUTHOR]

Digital education is very important and valuable because it is a subpart of artificial intelligence, which is used in many real-life problems. Digital education is the modern utilization of digital techniques and tools during online purchasing, teaching, research, and learning and is often referred to as technology-enhanced learning or e-learning programs. Further, similarity measures (SM) and complex fuzzy (CF) logic are two different ideas that play a very valuable and dominant role in the environment of fuzzy decision theory. In this manuscript, we concentrate on utilizing different types of dice SM (D-SM) and generalized dice SM (GD-SM) in the environment of a CF set (CFS), called CF dice SM (CFD-SM), CF weighted dice SM (CFWD-SM), CF generalized dice SM (CFGD-SM), and CF weighted generalized dice SM (CFWGD-SM), and also derived associated outcomes. Furthermore, to evaluate or state the supremacy and effectiveness of the derived measures, we aim to evaluate the application of artificial intelligence in digital education under the consideration of derived measures for CF information and try to verify them with the help of several examples. Finally, with the help of examples, we illustrate the comparison between the presented and existing measures to show the supremacy and feasibility of the derived measures. [ABSTRACT FROM AUTHOR]

The multinomial distribution is often used in modeling categorical data because it describes the probability of a random observation being assigned to one of several mutually exclusive categories. Given a finite or numerable multinomial model M | n , p whose decision is indexed by a parameter θ and having a cost c θ , p depending on θ and on p , we show that, under general conditions, the probability of taking the least cost decision tends to 1 when n tends to ∞, i.e., we showed that the cost decision is consistent, representing a Statistical Decision Theory approach to the concept of consistency, which is not much considered in the literature. Thus, under these conditions, we have consistency in the decision making. The key result is that the estimator p ˜ n with components p ˜ n , i = n i n , i = 1 , ⋯ , where n i is the number of times we obtain the ith result when we have a sample of size n, is a consistent estimator of p. This result holds both for finite and numerable models. By this result, we were able to incorporate a more general form for consistency for the cost function of a multinomial model. [ABSTRACT FROM AUTHOR]

Quantum decision theory has been successfully applied to multi-attribute group decision-making (MAGDM) to model decision-makers' interference and superposition effects in recent years. Existing quantum models assume that interference effects among decision-makers are symmetric. However, asymmetric interference effects have been ignored. We propose a VIKOR-based linguistic distribution assessments (LDAs) model considering asymmetric interference effects in a quantum decision scenario. Firstly, we combine VIKOR with LDAs to obtain a compromise solution in a fuzzy multi-attribute decision scenario with conflicting attributes. Secondly, an aggregation framework based on quantum probability theory is constructed to explore group preferences considering asymmetric interference effects among decision-makers. Finally, the model is compared with other methods to confirm its validity and stability. [ABSTRACT FROM AUTHOR]

Human decision-making does not conform to the independent decision-making hypothesis from classical decision-making theory. Thus, we introduce quantum decision-making theory into the Lotka–Volterra model (L–V model), to investigate player population dynamics while incorporating the initial strategy, game payoffs and interactive strategies in an open social system. Simulation results show that: (1) initial strategy, entanglement intensity of strategy interaction, and payoffs impact population dynamics; (2) In cooperative coexistence, game players mutually exceed the initial environmental capacity in an open system, but not in competitive coexistence; (3) In competitive coexistence, an initial strategy containing an entanglement intensity of strategies plays a vital role in game outcomes. Furthermore, our proposed model more realistically delineates the characteristics of population dynamics in competitive or cooperative coexistence scenarios. [ABSTRACT FROM AUTHOR]