Large Language Models (LLMs) and Evolutionary Computation (EC) are increasingly being combined to support automated optimization, algorithm design, and adaptive decision-making. This survey reviews the bidirectional interaction between these two paradigms and examines how their complementary strengths can be leveraged in hybrid intelligent systems. First, we analyze how EC can enhance LLM-based systems through prompt optimization, hyperparameter tuning, and architecture search. Second, we review how LLMs can improve EC by supporting metaheuristic design, surrogate reasoning, adaptive operator control, and heuristic generation. We further discuss emerging co-adaptive frameworks in which LLMs and EC interact through iterative feedback loops. Beyond summarizing recent developments, the survey provides a structured perspective on interaction mechanisms, application patterns, and methodological challenges, including computational cost, reproducibility, interpretability, benchmarking, and generalization. The paper concludes by outlining open research questions and future directions for developing more robust, transparent, and scalable LLM-EC systems.

Recently, non-associative aggregation functions (operators), namely the overlap and grouping functions, have gained significant attention among researchers. Overlap functions quantify the overlapping degree of an entity belonging to multiple classes, while grouping functions assess the degree of support or evidence for an entity belonging to any given class. This study introduces the conceptualization of k-restricted overlap and grouping operators, a generalized family of overlap and grouping operators that incorporates restrictions in the aggregation process based on the number of boundary elements. For k-restricted overlap functions, the restriction applies to the left boundary element of the interval, whereas for k-restricted grouping functions, it applies to the right boundary element. This approach ensures that the function's annihilation depends on a fixed count of boundary elements instead of the existence of a single boundary element. This generalization broadens the applicability of overlap and grouping functions, making them more versatile and effective for tackling complex real-world problems. Some existence theorems are proved to validate the essence of k-restricted functions for any positive integer k by utilizing an extended class of overlap and grouping functions with added dimensional constraints. Representation theorems further explore their analytical properties. Additionally, these functions are generalized to arbitrary closed intervals [a, b], enabling broader applicability in real-world systems. A notable application of grouping functions lies in Convolutional Neural Networks (CNNs), particularly within pooling layers. This study employs k-restricted grouping functions as pooling function replacements in CNN architectures, demonstrating their empirical efficiency. Results show improved performance on larger datasets with sparse training samples, faster processing on both CPUs and GPUs, and enhanced gradients for backpropagation compared to baseline pooling methods. Our code is available at https://github.com/smlab-niser/krestrictedCNN.

Fairness is widely recognized as a key dimension to oversee and manage in the context of responsible AI. While it has been extensively studied in traditional recommender systems, it remains a relatively underexplored topic in group recommender systems (GRSs). In this work, we introduce an optimization framework over social choice-based group recommendation approaches, that explicitly manages the accuracy-fairness recommendation trade-off, by learning personalized user–group weights that balance predictive accuracy and demographic fairness among group members. Our formulation incorporates a parameter that controls the trade-off, as well as a regularization term that mitigates overfitting to validation data. We evaluate the proposal over the well-known ML–100K and ML–1M datasets, where experimental results across multiple settings demonstrate in several scenarios a systematic fairness gains both in validation and, notably, in held-out test data, while maintaining competitive accuracy with respect to uniform aggregation baselines. These results highlight the potential of optimization-driven approaches for incorporating fairness constraints into group decision processes, creating a novel research path towards more equitable and responsible GRS, and highlighting our work as pioneering in the bridging of fairness and social choice-based group recommendation. To foster reproducibility, we provide access to source code that includes links to the used open datasets 1.

Emergency plans are an indispensable component of emergency management, designed to effectively handle critical situations when an emergency event occurs. Due to its significance and necessity, emergency planning has drawn increasing attention in recent years. A central focus in this area is how to generate emergency plans effectively and adaptively. Numerous studies have approached this challenge from various perspectives, obtaining valuable insights and outcomes. Dynamic evolution and uncertainty are two pivotal, practical factors that emerge during emergency events and must be carefully considered in the generation of effective emergency plans. However, existing studies have not sufficiently tackled these critical aspects. To bridge this gap, this study proposes a robust optimization-based emergency plan generation method, which accounts for dynamic evolution by incorporating timeline changes, shifts in emergency situations, and updates in available resources. Additionally, it systematically integrates uncertainty from both quantitative and qualitative perspectives. Finally, an illustrative example, along with related discussions and comparisons, is provided to demonstrate the feasibility, validity, and contributions of the proposed method.

The frequent emergencies often lead to significant human and material losses, creating urgent and complex logistical demands. One of the key tasks in emergency logistics is the selection of a suitable site for constructing an emergency logistics center to facilitate timely relief delivery. To support the complex decision-making process involved in emergency logistics center site selection, this study proposes a multi-criteria group decision-making method that effectively handles uncertainty and hesitation in expert evaluations. Specifically, we propose an extended ORESTE (organisation, rangement et Synth & egrave;se de donn & eacute;es relarionnelles, in French) method integrated with normal-type hesitant fuzzy sets (N-HFSs). While the traditional ORESTE method is valued for its simplicity and capability for conflict analysis, it suffers from information loss and lacks flexibility in representing hesitant preferences. To address these limitations, N-HFSs are employed to more accurately reflect expert hesitation, and a new position-based distance measure is introduced to compare N-HFSs without requiring normalization, thus avoiding computational bias and enhancing interpretability. Moreover, an improved version of the ORESTE method is proposed in this paper to address the drawback of information losses. The proposed approach is applied to a case study involving the selection of emergency logistics center sites in China. Finally, to validate the robustness and effectiveness of the proposed method, comparative and sensitivity analyses are conducted. This model provides actionable guidance for emergency-management authorities and demonstrates that the new decision framework is a reliable tool for high-stakes, uncertain group decisions.

In many decision-making systems, relationship among entities are best represented using directed graphs. They capture asymmetric connections among the entities where influence flows in one direction rather than being reciprocated. In such systems, decisions are significantly impacted by variations in the directed edges, as they determine how influence propagates through the entities of the considered network. This study focuses on developing fusion functions that incorporate these directional influences represented through directed edges into the aggregation process, ensuring that the final outcome reflects the structural dependencies and varying levels of influence within the system. The first step is to analyze how different entities in a network are connected and how influence flows through these directed links. Then, to model the aggregation framework, we propose a fusion function well adapted to incorporate the directional nature of influence. This function ensures that aggregation respects the asymmetric relationships in the network, effectively capturing the impact of influence propagation on the final decision. We also extend our approach by developing a pre-aggregation version of the directed graph-based fusion functions. The pre-aggregation function is designed to incorporate the non-symmetric relationships among entities, where aggregation increment is done in a particular direction. This generalization is adaptable for various decision-making systems with different types of relationships. In such aggregation systems, certain properties of fusion functions such as idempotency and averaging behavior, etc. are often desirable. These properties are incorporated into the proposed framework to ensure its usability across diverse decision-making contexts.

Decision-making under strict uncertainty involves evaluating a set of alternatives without knowledge of the probability of scenarios using crisp evaluations. Our work reformulates traditional decision rules to a fuzzy environment, retaining the interpretability of classical principles while incorporating imprecision. Our methodological proposal provides a unified, flexible, and mathematically consistent framework for decision-making under imprecise payoffs. We adapt a total ordering mechanism for trapezoidal fuzzy numbers and admissible interval orders. Our application case study to portfolio selection under fuzzy strict uncertainty demonstrates how the proposed fuzzy generalization can handle financial imprecision and investor risk attitudes through ranking functions.

Minimum cost consensus (MCC) models are widely used in group decision-making to achieve agreement with minimal opinion adjustment costs. Although recent studies have incorporated fairness into MCC frameworks, most existing approaches rely on aggregate social welfare or inequality-based axioms and remain insensitive to subgroup structures induced by protected attributes. As a result, consensus outcomes may still systematically favor certain subgroups despite being cost-optimal or globally fair. To address this limitation, this paper proposes a fairness-aware MCC framework that explicitly accounts for subgroup-level fairness. Fairness is defined through deviation-based measures that evaluate the parity between the final consensus outcome and the opinions of subgroups formed by protected attributes. Fairness is incorporated into MCC models via constraint-based formulations and a learning-inspired objective that interpolates between utilitarian and Rawlsian principles. The proposed models preserve convexity and computational tractability, while enabling a flexible balance between efficiency, consensus, and subgroup fairness in heterogeneous group decision-making environments.

Multi-criteria sorting methods are widely used to classify alternatives into ordinal categories based on multiple criteria, which frequently arise in various real-world scenarios. Most existing approaches, however, address compensatory, non-compensatory, or dependent effects separately, overlooking their potential coexistence and interaction in practice. To address this limitation, we propose MULTIMOORA-Sort, a novel multi-criteria sorting approach that unifies these effects using the principle of multiplicative multi-objective optimization by ratio analysis (MULTIMOORA). To reduce the decision-maker’s cognitive burden of parameter specification and subjective uncertainty, we develop preference disaggregation analysis (PDA) framework to infer model parameters from assignment examples. Additionally, to enhance trust and interpretability, we introduce a counterfactual explanation framework that illustrates how changes in performance across criteria affect category assignments. The effectiveness of the proposed MULTIMOORA-Sort is demonstrated through two applications: (i) classifying 180 countries by economic freedom using indirect elicitation via PDA, and (ii) assessing the global health security status of 195 countries using direct elicitation. Results show that MULTIMOORA-Sort successfully unifies diverse decision behaviors, supports parameter learning, and provides intuitive explanations of sorting outcomes, offering a robust framework for practical multi-criteria sorting decision-making.

The construction of the semantics of fuzzy linguistic scales is a crucial task in decision analysis, as it requires translating decision-makers’ qualitative perceptions into quantitative representations. While recent approaches such as the Deck of Cards Method for Membership Function construction (DoC-MF) have enhanced interpretability and cognitive transparency, they remain limited to individual elicitation. In many real-world settings, however, fuzzy linguistic models must reflect the shared semantic understanding among decision-makers, calling for mechanisms that reconcile heterogeneous judgments without compromising semantic meaning. This paper proposes a consensus-based extension of the Deck of Cards Method for group decision-making. The approach introduces an optimization-based consensus protocol, denoted (C–DoC), that guides experts toward agreement by making minimal adjustments to their individual assessments. The protocol is applied across four stages: (i) building an agreed value scale, (ii) defining the cores of fuzzy levels, (iii) determining their supports, and (iv) shaping the left and right-hand sides of the membership functions using a ratio-based version of the DoC. Each stage combines human interpretability with mathematical rigor, ensuring that the resulting fuzzy scales are both semantically coherent and collectively validated. The resulting framework bridges the gap between fuzzy linguistic modeling and agreed scales by embedding interpretability and fairness within an optimization-driven process.

Since its inception, fuzzy set theory has been widely used to model uncertainty and imprecision in decision-making. However, conventional fuzzy sets, often referred to as type-1 fuzzy sets (T1FSs), have limitations in capturing higher levels of uncertainty, particularly when decision-makers (DMs) express hesitation or ambiguity in membership degrees. To address this, interval type-2 fuzzy sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, enhancing flexibility in modeling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs, which limits the interpretability and effectiveness of decision models. This study proposes a novel socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and applies it to multicriteria decision-making (MCDM) problems. Our method is structured in two phases. The first phase involves an interactive process between the DM and the analyst, in which a modified version of the deck of cards (DoC) method is proposed to construct T1FS membership functions on a ratio scale. We then extend this method to incorporate ambiguity in subjective judgments, resulting in an IT2FS model that better captures uncertainty in DMs’ linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining a mathematical formalization of the fuzzy information, including aggregation rules and an admissible ordering principle. The proposed framework enhances both the reliability and effectiveness of fuzzy decision-making by capturing the personalized semantics of linguistic information. A numerical example and a practical case illustrate its real-world applicability.

Large-Scale Group Decision-Making (LSGDM) in social network context has emerged as a research focus in decision sciences. Social relationships implicated in the network influence Decision-Makers’ (DMs) preferences and group consensus. However, existing research often overlooks the potential impact of uncertain adjustment costs driven by social relationships among DMs on the Consensus-Reaching Process (CRP). To address this issue, this paper develops a new Extended Linguistic Expressions with Symbolic Translation (ELICIT) information-based robust large-scale minimum cost consensus model under social networks. Firstly, the ELICIT model is used to represent DMs’ preferences, enhancing preference elicitation under uncertain conditions. Secondly, DMs’ weights are objectively determined based on the following-follower network, and the social network cost function is integrated into the Comprehensive Minimum Cost Consensus (CMCC) model. Then, three robust consensus models are developed to manage the uncertain adjustment costs of DMs within the network. Afterward, an ELICIT-based PROMETHEE ranking method is designed. Finally, a case study on selecting Healthcare Waste (HCW) treatment technology is conducted. The implemented sensitivity and comparative analysis demonstrate the effectiveness and advantages of the proposed method.

This paper introduces the concept of mutual consensus as a novel non-compensatory consensus measure that accounts for the maximum disparity among opinions to ensure robust consensus evaluation. Incorporating this concept, several new Minimum Cost Consensus (MCC) models are proposed, and their properties are analyzed. To show their applicability, these mutual consensus-based MCC models are then considered in the context of the OWA-MCC model, which employs Ordered Weighted Averaging (OWA) operators for preference aggregation. Concretely, we include a linearized formulation under symmetry conditions as well as examples of the non-convexity of the feasible region in the general case. Finally, mutual consensus is utilized to obtain approximate solutions for the OWA-MCC model, demonstrating its practical effectiveness and advancing the theoretical and applied dimensions of consensus modeling in group decision-making.

Since its inception, Fuzzy Set has been widely used to handle uncertainty and imprecision in decision-making. However, conventional fuzzy sets, often referred to as type-1 fuzzy sets (T1FSs) have limitations in capturing higher levels of uncertainty, particularly when decision-makers (DMs) express hesitation or ambiguity in membership degree. To address this, Interval Type-2 Fuzzy Sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, which enhanced flexibility in modelling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs and that limits the interpretability and effectiveness of decision models. This study proposes a socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and its application in multicriteria decision-making (MCDM) problems. Our methodology is structured in two phases. The first phase involves an interactive process between the DM and the decision analyst, in which a modified version of Deck-of-Cards (DoC) method is proposed to construct T1FS membership functions on a ratio scale. We then extend this method to incorporate ambiguity in subjective judgment and that resulted in an IT2FS model that better captures uncertainty in DM's linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining an appropriate mathematical representation of such information, aggregation rules, and an admissible ordering principle. The proposed framework enhances the reliability and effectiveness of fuzzy decision-making not only by accurately representing DM's personalized semantics of linguistic information.

Swarm intelligence effectively optimizes complex systems across fields like engineering and healthcare, yet algorithm solutions often suffer from low reliability due to unclear configurations and hyperparameters. This study analyzes Particle Swarm Optimization (PSO), focusing on how different communication topologies Ring, Star, and Von Neumann affect convergence and search behaviors. Using an adapted IOHxplainer , an explainable benchmarking tool, we investigate how these topologies influence information flow, diversity, and convergence speed, clarifying the balance between exploration and exploitation. Through visualization and statistical analysis, the research enhances interpretability of PSO's decisions and provides practical guidelines for choosing suitable topologies for specific optimization tasks. Ultimately, this contributes to making swarm based optimization more transparent, robust, and trustworthy.

Even though the integration of sentiment analysis and decision-making techniques has become popular in recent years, most of the related studies only consider the obtained sentiment score, thus neglecting the numerical ratings that are usually attached to text reviews. This paper introduces STandR (Sentiment from Text and Ratings)-BUI (Basic Uncertain Information), a novel preference-modeling structure for data-driven decision-making using social media microblogging information. STandR-BUI combines both the numerical rating and the sentiment score of a product into a BUI value, which provides a more precise representation of users’ opinions. In addition, we propose a consensus framework to make decisions based on the STandR-BUI values which can manage thousands of user reviews. Finally, an illustrative example is provided to demonstrate its effectiveness.

Fairness is currently regarded as a relevant dimension towards the goal of reaching trustworthy artificial intelligence-based systems. In recommender systems, fairness is focused on addressing biases that may disproportionately benefit or harm certain classes of users and items. In this contribution we are interested on provider fairness, which aims at guaranteeing that the providers of the items would have the same chance for the exposure of their items in the final recommendation lists. Particularly, we will be focused on characterizing the provider fairness associated to intelligent content-based recommendation used for suggesting e-services in a marketplace environment in the region of Extremadura, Spain. Herein, the generalized cross-entropy has been used as metric for characterizing fairness associated to both basic and latent dirichlet allocation (LDA)-based content-based recommendation. As main findings, our study has indicated that the recommendation based on latent dirichlet allocation might lead to better fairness values for those providers with larger number of e-services. For the managerial viewpoint, it suggests that a higher presence in online platforms of the products, might guarantee better associated fairness values. As far as we know, this contribution presents one of the first efforts on evaluating provider fairness recommendation in a concrete e-service scenario.

Multi-instance learning (MIL) is a widely applied technique in practical applications that involve complex data structures. MIL can be broadly categorized into two types: traditional methods and those based on deep learning. These approaches have yielded significant results, especially regarding their problem-solving strategies and experiment validation, providing valuable insights for researchers in the MIL field. However, considerable knowledge is often trapped within the algorithm, leading to subsequent MIL algorithms that rely solely on the model's data fitting to predict unlabeled samples. This results in a significant loss of knowledge and impedes the development of more powerful models. In this article, we propose a novel data-driven knowledge fusion for deep MIL (DKMIL) algorithm. DKMIL adopts a completely different idea from existing deep MIL methods by analyzing the decision-making of key samples in the dataset (referred to as the data-driven) and using the knowledge fusion module designed to extract valuable information from these samples to assist the model's learning. In other words, this module serves as a new interface between data and the model, providing strong scalability and enabling prior knowledge from existing algorithms to enhance the model's learning ability. Furthermore, to adapt the downstream modules of the model to more knowledge-enriched features extracted from the data-driven knowledge fusion (DDKF) module, we propose a two-level attention (TLA) module that gradually learns shallow- and deep-level features of the samples to achieve more effective classification. We will prove the scalability of the knowledge fusion module and verify the efficiency of the proposed architecture by conducting experiments on 62 datasets across five categories.

Ordered Weighted Averaging (OWA) operators have been widely applied in Group Decision-Making (GDM) to fuse expert opinions. However, their effectiveness depends on the selection of an appropriate weighting vector, which remains a challenge due to limited research on its impact on Consensus Reaching Processes (CRPs). This paper addresses this gap by analysing the influence of different OWA weighting techniques on consensus formation, particularly in largescale GDM (LSGDM) scenarios. To do so, we propose a Comprehensive Minimum Cost Consensus (CMCC) model that integrates OWA operators with classical consensus measures to enhance the decision-making process. Since existing OWA-based Minimum Cost Consensus (MCC) models struggle with computational complexity, we introduce linearized versions of the OWA-based CMCC model tailored for LSGDM applications. Furthermore, we conduct a detailed comparison of various OWA weight allocation methods, assessing their impact on consensus quality under different levels of expert participation and opinion polarization. Additionally, our linearized formulations significantly reduce the computational cost for OWA-based CMCC models, improving their scalability.

Fuzzy logic has enhanced decision-making by enabling more effective modeling of uncertainty in human judgments through membership functions. However, current approaches to constructing membership functions often over-look active collaboration between decision-maker and decision analyst, leading to a lack of interpretability and personalization. This paper introduces a socio-technical methodology, the Deck of Cards Method, to co-construct trapezoidal fuzzy numbers tailored to decision-maker's semantics. We illustrate the method's working through the performance evaluation example in a corporate context.