A novel generalized orthopair fuzzy CURLI MCDM framework for smart art communication integrating emotional intelligence

Abstract

The capacity to identify, adjust to, and interact with human emotions has become a crucial component of effective art communication in digital and interactive environments. Measuring smart art communication through an Emotional Intelligence (EI) lens is not easy since human emotional reactions are unpredictable, biased, inexplicable, and hard to measure. To overcome this problem, this paper suggests a q-Rung Orthopair Fuzzy Collaborative Unbiased Rank List Integration (qROF-CURLI) multicriteria decision-making (MCDM) model where uncertainty in expert judgments is modelled by a q-rung orthopair fuzzy set (qROFS) and the CURLI mechanism combines the rankings of individuals to produce a final and unbiased overall ranking. Expert linguistic assessments are converted into qROF numbers and aggregated to construct the decision matrix, after which the CURLI procedure produces the final ranking of alternatives. The applicability of the proposed framework is demonstrated through a decision-making case study related to smart digital art communication platforms, involving fifteen alternatives evaluated across nine criteria by four decision-makers. The criteria of benefits include Emotional Recognition Capability, Emotional Adaptability, Audience Engagement, Empathy Enhancement, Technological Integration, and Cultural Relevance, whereas the costs criteria include Implementation Cost, Technical Complexity, and Ethical Risk. According to the results, the gamified and AI-adaptive communication platforms receive the best rankings. The sensitivity analysis and benchmarking on the existing qROF-MCDM approaches prove the stability and reliability of the model. The suggested framework offers a usable support to assess emotionally intelligent digital art communication systems and offers a unique combination of CURLI rank aggregation with the MCDM using qROF in order to enhance the reliability of collective decisions that are made under uncertainty.

Introduction

Smart Art Communication evaluation through an Emotional Intelligence (EI) framework is a scientific methodology of determining the effectiveness of artistic content, platforms, and interactions to communicate, interpret, and react to human emotions. In the context of contemporary digital and interactive art experience, communication is no longer confined to the visual attractiveness and aesthetic merit, but goes further to emotional appeal, cognitive interest, and responsiveness. Smart Art Communication is using technological tools, including AI-driven platforms, interactive installations, and immersive experiences, to make the communication more emotional. The EI view would guarantee the communication process to be aware, control, and adjust to audience emotions to enhance empathy, engagement with the audience, and meaningful interaction. In this way, the critique of Smart Art Communication within the framework of EI can give us information about the efficiency, flexibility, and responsiveness of the artistic practices to the audience, which is essential to curators, educators, and digital art professionals. The multidimensionality of the smart art communication process necessitates the structured and systematic approach of its evaluation. It includes various stakeholders and requirements, including the ability to recognize emotions, emotional flexibility, the ability to engage the audience, the ability to develop empathy, the ability to integrate technology, its relevance to the culture, cost of implementation, technical complexity, and ethical risk. Individual criteria play different roles in the effectiveness of communication; the relations between them tend to be contradictory or interdependent. Thus, it will require a multicriteria approach that will allow the synthesis of different views and offer the consistent ranking of options. Formalizing evaluation within an EI framework, decision-makers will be able to see what strategies are best suited to create a balance between the emotional and the factual, thus, eventually, making informed choices within complex artistic settings.

The MCDM techniques have been found to be useful in dealing with such complicated evaluation issues as they enable ranking of a number of alternatives in conflicting criteria. Traditional MCDM models, including TOPSIS, WASPAS, and MARCOS, provide a framework in which the decision-making process is organized; nevertheless, they are typically focused on some form of exact or sharp data. Within the framework of Smart Art Communication based on EI, expert appraisals are not only subjective but also uncertain, and sharp depictions are insufficient. To overcome this, the fuzzy set theory and its variants give a more realistic approach to the uncertainty, hesitation, and imprecision in human judgment. Fuzzy Sets (FS), first proposed by Zadeh¹, are a model of uncertainty, where elements can be partially a member of the interval [0,1], but which are only a model of membership degrees (MD), which might not be a complete measure of hesitation or duality of decision-making. Extending FS to Intuitionistic Fuzzy Sets (IFS) to include both membership (MD) and non-membership degrees (NMD) with their sum constrained in the intervals [0,1], Atanassov² improved the model of uncertainty. Yager³ came up with the Pythagorean Fuzzy Sets (PyFS), which gives additional flexibility so that the sum of squared MD and NMD is within [0,1], but extends the modeling capability further still. Subsequently, this idea was extended by Yager⁴ to q-Rung Orthopair Fuzzy Sets (qROFS), where the sum of the q-th power of MD and NMD can have a range of [0,1], which gives even more freedom in representing imprecision and hesitation. In the current research paper, qROFS is used to simulate the uncertainty existing in expert assessments of Smart Art Communication within the EI paradigm, which can be better used to represent the decisions made by decision-makers.

Out of the many MCDM techniques, the CURLI method is very appropriate when comparing the alternatives without the need for data normalization, which diminishes scale distortion. CURLI ranks the alternatives using pairwise comparisons of dominance based on various criteria, which can support both qualitative and quantitative information. It is very efficient in assessing Smart Art Communication on the basis of EI because it is quite flexible and comparative, allowing for the combination of uncertain, hesitant, and multidimensional appraisals with the generation of strong and interpretable rankings. The fact that the method can be updated with expert weights of variations and retain the uncertainty information adds additional strength to its use, especially when making a decision that deals with the subjective perception of humans and emotional considerations. It has been proven by sensitivity analysis and comparative benchmarking that CURLI offers more stable and reliable rankings in comparison to traditional techniques, which leads to the strengthening of confidence in decision results.

It is based on these advantages that this paper introduces the qROF-CURLI framework, an expansion of CURLI by use of q-ROFS to deal with vagueness, partial membership, and hesitation in expert ratings. The given approach is innovative in the sense that it can be used both to incorporate the state of the art in fuzzy uncertainty modeling and to employ a powerful comparative decision-making approach, which in this case is the Smart Art Communication corresponding to the Emotional Intelligence framework. In the process, it not only ranks alternatives effectively but also gathers subtle expert views, is stable when different weights are applied, and gives practical managerial insights for application. This incorporation is a solution to traditional MCDM as well as available fuzzy methods, and it provides a flexible and reliable as well as interpretable decision support tool in situations where performing an artistic and emotional assessment is complex.

Research objectives

The main aims of the research are:

• To formulate a systematic review of Smart Art Communication from an Emotional Intelligence point of view.

• To generalize the CURLI MCDM approach with q-ROFS to include uncertainty, hesitation, and partial membership in the expert judgments.

• Ranking smart art communication options based on various benefit and cost parameters, to deliver interpretable and actionable information.

• To carry out the sensitivity analysis and benchmarking to ensure the robustness and stability of the proposed qROF-CURLI method.

Motivation and key contributions

The rationale behind this study is that there has been a growing trend of the application of AI-driven and interactive art platforms, where emotional appeal and responsive communication are paramount to user satisfaction. The current assessment tools are based on either crisp data or conventional fuzzy solutions, and this does not sufficiently reflect the ambiguity and hesitation in emotional assessment. This paper overcomes these limitations and introduces a new methodology of decision-making by integrating q-ROFS and the CURLI MCDM model.

Key contributions include:

• Implementing a qROF-CURLI system of systematized review of Smart Art Communication within the EI.

• Better representation of uncertainty, indecisiveness, and expert heterogeneity than the current fuzzy MCDM techniques.

• Sensitivity analysis and benchmarking on the strength and trustworthiness of rankings.

• Providing viable suggestions to curators, educators, and managers to give more importance to emotionally intelligent art communication approaches.

Structure of the study

The other section of this paper will be structured in the following manner. Section 2 presents the literature review detailing the areas of MCDM, the CURLI method, and qROFS. Section 3 gives the background and the fundamentals required in the suggested framework. Section 4 introduces the formulation of the provided qROF-CURLI-MCDM approach. The fifth section gives the case study of appraisal of smart art communication within the framework of emotional intelligence. Section 6 discusses the sensitivity analysis, validation, and comparison with the existing qROF-MCDM approaches. Finally, the conclusion of the study and future research directions will be presented in the last section, which will be Sect. 7.

Literature review

Studies on smart art communication under the emotional intelligence framework

The most recent studies indicate that Emotional Intelligence (EI) plays a very important role in improving smart art communication, especially in digital, interactive, and public art settings. In their work, Ullah et al.⁵ designed an overall infrastructure based on the type-2 fractional fuzzy sets to evaluate the measures taken to enhance the communication of public art using EI and the modes of reducing communication limitations and increasing the interest of the audience. In the same line of thought, Li⁶ used a q-rung orthopair fuzzy information-based decision support system, and it is evident that active listening and similar techniques serve as a great way of enhancing the effectiveness of communication and creating a stronger bond between parties in an art-oriented situation. In addition to the technical solutions, Drigas et al.⁷ emphasized the importance of emotionally intelligent leadership in educational and organizational practices through the fact that EI frameworks help people to build effective interpersonal and communication skills and utilize the new technologies to facilitate the processes of dealing with art. Zhang and Zhi⁸ evaluated how the Internet of Things can fit into cultural and brand communication contexts in art design within the framework of the Maritime Silk Road, and found that art installations, smart and cultural exhibits can enhance the effect of audience interest and brand communication. Simultaneously, Alrahamneh et al.⁹ also highlighted the role of EI frameworks in leading and governing digital spheres, demonstrating organized methods of developing emotional and communicative skills in digital and art-oriented realms. Moreover, EI as a key to leadership training and professional development has been established in healthcare settings where Junious¹⁰ and Esteron et al.¹¹ found that EI improves communications, interpersonal awareness, and critical thinking, which become a basis of successful teamwork and decision-making.

In addition, some of the recent developments in the fuzzy-based MCDM frameworks also evidenced the development of the fuzzy theory into more adaptable and resolute models that can manage complex and uncertain conditions. As an example, Sarwar et al.¹² suggested a medical waste management method using a fractional fuzzy-based MCDM method; they showed a better capacity to deal with the uncertainty and complexity of decisions. Equally, Habiba et al.¹³ have come up with a strong fractional fuzzy decision support system of sustainable energy planning, which highlights the versatility of a contemporary fuzzy system when it comes to decision problems on a large scale. These works support the increasing role of sophisticated fuzzy extensions in the representation of the real-life situations of decision-making that are characterized by ambiguity and human-related considerations. Comprehended altogether, these papers contribute to underlining the necessity of implementing the concept of EI to smart art communication, in which both methodological innovations, such as fuzzy-based modeling and decision support systems, and real-world applications to the field of leadership, education, and digital art platforms are served. They provide a sufficient foundation to adopt more advanced MCDM models, such as the qROF-CURLI model that is recommended in the current paper to analyze and optimize communication methods on smart art-related problems, which are under the guidelines of emotional intelligence systems.

CURLI MCDM method

The CURLI approach has become a strong MCDM technique to rank alternatives without data normalization, which leads to the distortion of the scale and the maintenance of the relative significance of criteria. An enhanced CURLI technique was suggested by Nguyen¹⁴ to deal with intricate MCDM issues and proved its efficiency in the form of a variety of case studies, and its ability to accommodate both qualitative and quantitative data. The technique has been effectively used in other technical decision-making problems, such as the selection of air conditioners, washing machines, and unmanned aerial vehicles (UAVs), usually with weighting and other decision-support methods¹⁵. The CURLI versatility is shown in further applications of CURLI in sustainability and industrial applications. In their choice of the most sustainable energy development options, Van Dua et al.¹⁶ relied on CURLI as it can address several conflicting criteria without requiring decision-makers to apply specific weights to each of those. Ba and Tien^11,17 used CURLI in manufacturing processes to make multicriteria decisions in grinding processes and found that the system is an efficient way to rank alternatives in situations where expertise is incomplete or unpredictable. Also, Dudic et al.¹⁸ compared CURLI with other MCDM tools like PSI in material selection to make gears, which proved its reliability, strength, and interpretation capability in the complicated engineering process. The strengths of CURLI include a comparative ranking structure, less reliance on normalization, and flexibility of integrating the subjective and objective evaluations, which makes CURLI especially applicable when assessing Smart Art Communication in terms of Emotional Intelligence. CURLI will provide strong, interpretable, and workable rankings by enabling the possibility of pairwise dominance evaluation and uniting expert evaluations without stringent data limitations. These features make the CURLI a perfect starting point to be able to extend the approach with the help of the fuzzy logic tools, including the qROFS used in this paper, to cope with the uncertainty and vagueness of the evaluations of the emotional intelligence.

Moreover, the current fuzzy theory advancements have provided more sophisticated hybrid models, which involve the incorporation of fractional, spherical and quantum-inspired fuzzy spaces into MCDM models. To give an example, Sarwar et al.¹⁹ devised a quantum-driven spherical fuzzy TOPSIS model, which is able to exhibit a high level of decision accuracy in sophisticated security systems. Moreover, Sarwar et al.²⁰ proposed q-fractional fuzzy Frank aggregation operators, which enhance the fusion of information and representation of uncertainty during decision-making. The methodological topicality of the fuzzy-based methodologies of uncertainty-aware MCDM is further justified by the presence of fuzzy control²¹, adaptive artificial intelligence learning models²² and neuro-fuzzy studies^23,24, which justifies the reason behind the inclusion of qROFS in the CURLI framework suggested in this study. Moreover, recent reports have suggested sophisticated fuzzy-based models, which solve uncertainty, hesitation, and the confidence of the expert in a complicated decision-making process. As an illustration, Kamran et al.²⁵ have suggested a complex picture fuzzy soft set method of assessing sustainability and have shown that it is more effective in managing the uncertainty of alternatives and cost. Equally, Kamran et al.²⁶ used Fermatean fuzzy rough sets to improve levels of confidence in industrial decision making in dynamic and automated conditions. Moreover, the mathematical basis of Fermatean fuzzy soft linear spaces has been examined to be used in supply chain management²⁷, and fuzzy operators and quaternion numbers on intuitionistic fuzzy rough contexts are discussed in the sparse and uncertain data situations²⁸. These investigations give a good ground for incorporating qROFS and CURLI, emphasizing the novelty of the approach used to deal with hesitation, uncertainty and multiple experts by the qROF-CURLI framework.

Research gap analysis

Although there has been an increased interest in the incorporation of the Emotional Intelligence concept in smart art communication, the existing studies have a number of gaps. The majority of available research focuses on the conceptual frameworks or particular EI skills, including active listening, leadership growth, or interaction, and they do not include the systematic assessment tools that are able to manage a variety of criteria simultaneously. Even though fuzzy-driven methods have been used to model the uncertainty in art communication, in most studies, these research methods lacked the incorporation of rigorous fuzzy modeling with the structured multicriteria decision-making frameworks, which could reliably rank alternatives using the qualitative and quantitative criteria. Although the CURLI approach has been proven effective in the field of engineering, sustainability, and industry, the opportunities of assessing smart art communication within the framework of an EI have not been investigated. Overall, traditional MCDM tools, including TOPSIS, WASPAS, and MARCOS, are restricted in consideration of hesitation, partial membership, and non-membership levels, which are inherent in the evaluation of emotional and artistic qualities by experts. Past fuzzy MCDM models in art communication have either concentrated on aggregation on one Criterion or lacked means to combine the collective of expert ratings, and at the same time be able to interpret the results. The existing approaches also tend to overlook both benefit and cost factors in the same evaluation, which is crucial in the appraisal of practical and resource-limited approaches to smart art communication. Emotional flexibility and audience interactivity need to be put on the scale of cost of implementation, technicality, and moral issues. The lack of a systematic framework uniting advanced fuzzy sets and a powerful method of MCDM adjusted to the EI-based art communication is a major gap in the research. This paper tackles these shortcomings by combining them with a qROF-CURLI modeling approach, which is an expansion of the CURLI approach, incorporating q-rung orthopair fuzzy sets to deal with uncertainty and the lack of decisiveness in the evaluation of experts. The suggested methodology efficiently draws inaccurate or wavering judgments, incorporates a number of decision-makers with diverse influence, prioritizes alternatives in terms of value and cost, and gives solid, interpretable, and actionable outcomes. By sealing these gaps of methodology and application, the qROF-CURLI framework provides a new decision assistance tool to gauge Smart Art Communication in the context of Emotional Intelligence.

Theoretical foundations

In the real world, real-life decision-making does not provide the criteria of real-life evaluation due to ambiguity, subjectivity, and inaccurate expert judgment. Suggested by Zadeh, FS theory is concerned with this type of uncertainty, but expresses all aspects as a single MD in [0,1], which is not appropriate to describe hesitation. To overcome this deficiency, Atanassov proposed IFS, which expands MD, NMD, and the degree of hesitation (HD), and uses them to describe the uncertainty in greater detail. Then, Yager proposed PyFS. However, these models are still restricted by relatively strict conditions on MD and NMD, which limit their ability to capture higher levels of uncertainty and hesitation in complex human judgments, particularly in emotionally driven decision-making environments such as smart art communication. An official definition of qROFS is the following.

Definition 1:

⁴ A qROFS in the universe of discourse is defined in the form:

Where and denote the MD and NMD, respectively. The pair satisfying the given condition:

It is known as a q-rung orthopair fuzzy number fuzzy number (qROFN). Further, the HD of is given as:

Definition 2:

⁴ For any qROFN denoted by, then the score function is defined as follows:

1

where.

Also, the qROFSs provide the extension of a number of existing fuzzy models into their special cases, which proves the theoretical superiority and the increased applicability. This stratification would make sure that the suggested structure is not just adaptable, but also one that accommodates the previous fuzzy surroundings, and as such, offers more strength in modelling human judgment uncertainty.

Formulation of the qROF-CURLI decision-making method

The CURLI technique is an MCDM approach that employs ranking of alternatives which are not normalized and hence minimizes scale distortion. It compares options made on the pairwise dominance analysis as per various criteria, which enable the combination of both qualitative and quantitative data. To cope with this uncertainty and indecisiveness of expert judgments, the CURLI framework is generalized through the use of generalized orthopair fuzzy sets, and the structure is named qROF-CURLI. This extension is twofold, in particular, for MD and NMD, to allow natural and flexible modelling of imprecise and hesitant information. A major theoretical strength of the CURLI framework is its ability to incorporate qROFS into the representation of expert opinions that are more expressive than traditional fuzzy and intuitionistic models, particularly when it comes to the emotional and cognitive appraisals. The approach can ensure solid and successful rankings in the presence of a complicated decision-making environment since the information representation formulated through qROF is matched with the comparative scheme of CURLI. Thus, the suggested qROF-CURLI model increases the interpretability of the decision-making process and its reliability because it efficiently reflects the existing uncertainty, hesitation, and subjectivity of smart art communication reviews. The calculation is planned to follow a few steps, including constructing the decision matrix, integrating qROF-based assessments of experts, a pairwise evaluation of choices, and ranking the ultimate result. The overall process of the proposed qROF-CURLI procedure is illustrated in Fig. 1.

Fig. 1.

Workflow of the qROF-CURLI Method.

Step 1:

Define Decision Makers, Criteria, and Alternatives.

The initial stage will be used to determine all the decision makers (DMs), criteria, and alternatives applicable to the decision problem. Suppose the decision makers are , the alternatives are , and the criteria are . This is what the decision-making process is based on.

Step 2:

Define Linguistic Terms for Evaluating DMs and Criteria.

Each DM evaluates the significance of the criteria by means of linguistic words, i.e., in qROFN form, where is MD, is NMD, and h is HD. In Table 1, the list of linguistic terms for the assessment of criteria and DMs is provided.

Table 1.

Linguistic terms for criteria and DMs.

Linguistic Term
Extremely Poor (EP)
Poor (P)
Fair (F)
Good (G)
Excellent (EX)

Step 3:

Determine the Weights of Decision Makers.

The qROFN evaluations provided by the decision-makers are used to determine the relative importance of each decision-maker. The DMs with the higher membership values and less hesitation are more weighted. The DM weights are represented by: represents the decision set of decision makers, the weight of decision is represented by and .

2

Step 4:

Construct and Aggregate the Criteria Decision Matrix.

Each DM evaluates all criteria based on the linguistic terms. The appraisals will be added together into a single qROFN of each Criterion using operator qROFWA:

3

where .

The step will create a unitary qROFN using the opinion of all DMs on a criterion.

Step 5:

Find Criteria Weights Based on qROF-Score Values of Criteria.

The qROF score is determined by applying the following Eq. (1). The resulting weights are said to be computed with normalization, and the aggregate weights must add up to 1. criteria exist, and all the weights of are less than.

4

These qROF-scores show the overall support of each Criterion with MD and NMD.

Step 6:

Define Linguistic Terms for Alternative Evaluation.

Each Criterion involves an alternative with the help of linguistic terms that are unique to alternatives. Table 2 gives an example of these terms.

Table 2.

Linguistic Terms for Alternatives.

Linguistic Term
Extremely Low (EL)
Low (L)
Medium Low (ML)
Medium (M)
Medium High (MH)
High (H)
Extremely High (EH)

Step 7:

Construct and Aggregate Alternative Decision Matrix.

Each DM evaluates all alternatives in all aspects. The assessments are added up with the assistance of the operator qROFWA Eq. (3).

Step 8:

Find qROF-Score Values.

The aggregated qROFNs are then transformed to a crisp qROF-score by using the following Equation: (1).

Step 9:

Perform Pairwise Comparison.

Regarding each Criterion , each alternative will be compared to all other alternatives ​ () based on their qROF-scores by means of using Eq. (5):

5

These pairwise comparison matrices reflect the relative superiority of alternatives for each Criterion.

Step 10:

Compute the CURLI scores.

Finally, the CURLI score of each alternative has been calculated as a sum of weighted pairwise comparison of all criteria using Eq. (6):

6

Step 11: Rank the alternatives based on CURLI scores.

The alternatives are listed in ascending order, with the alternative with the lowest rating being the most desirable since it is the best in all the performance criteria. The combination of qROFS and CURLI ranking in one framework of evaluation of Smart Art Communication under the Emotional Intelligence paradigm is new, despite their independence. The suggested qROF-CURLI framework is structured into steps of transforming linguistic judgments into qROFNs, combining them with the qROFWA operator and inputting them into the CURLI ranking system. This integration enables the consideration of both benefit and cost conditions simultaneously, integration of various opinions of experts and accurate modeling of hesitation, uncertainty and subjectivity. The approach is not simply an application, but an integrated framework that builds the mathematical and procedural power of the available MCDM tools to handle complicated emotional and cognitive evaluation issues.

Evaluation of smart art communication under the emotional intelligence framework

Smart Art Communication within Emotional Intelligence Framework Evaluation is a multidimensional program that assesses the extent to which artistic material, platforms, and interactions express emotions, create empathy, and develop significant engagement with the viewers in digitally intelligent spaces. When AIs are used to create artistic systems, immersive exhibitions, and interactive media platforms, the art communication process will no longer be confined to the visual aesthetics but will be expanded to emotional appeals, cognitive processes, responsiveness, and adaptability. Emotional intelligence is a key variable in this transformation because it helps systems and communicators to be aware of, perceive, control, and react to human emotions. Thus, when considering Smart Art Communication within the scope of Emotional Intelligence, it is necessary to have a structured decision model that can process subjective judgments, ambiguity, and multicriteria complexity in a single decision model.

The necessity of assessing Smart Art Communication within an Emotional Intelligence framework can be explained by the increasing number of artificial intelligence, digital platforms, and human-centred design in artistic communication. In the absence of a systematic assessment model, institutions, digital curators, and creative technologists might not be able to distinguish between strategies that do and do not optimally contribute to emotional involvement, and those that are just functionaries of technology novelty. Misalignment of emotions may lead to a decrease in the trust, involvement, and interpretation of the audience. Therefore, a holistic assessment methodology will not only make smart art systems technologically adapted but also emotionally, ethically, and socially sensitive. The form of evaluation is one that facilitates sustainable artistic and creative development, enhances public gratification, and reinforces communicative effectiveness in the fields of education, culture, and business art.

As the assessment task includes several criteria that contradict each other, including emotional flexibility, audience interest, cost-effectiveness, and the complexity of the technology, the MCDM model is needed. MCDM techniques are extensively applied in the resolution of intricate decision challenges where there are numerous choices and attributes that are uncertain. Yet, the traditional MCDM methods might fail to sufficiently describe the ambiguity and indecisiveness of human judgments of feelings. Thus, despite the existing large number of MCDM methods, a qROF-CURLI approach to uncertainty is suggested in this paper to make it more flexible and efficient. The qROF setting has more latitude to model membership and non-membership degrees than intuitionistic and Pythagorean fuzzy sets, and the CURLI aggregation scheme offers consistency, logical interaction and reliability to group decision-making situations.

In order to demonstrate the computational procedure and applicability of the proposed model, an illustrative hypothetical scenario is considered where four decision-makers are involved in the evaluation process:

• 

• 

• 

• 

These scholars evaluate fifteen intelligent art communication strategies (alternatives):

• Immersive Virtual Reality Exhibition,

• AI-Based Emotion-Adaptive Art Platform,

• Interactive Digital Storytelling System,

• Augmented Reality Museum Guide,

• Emotion-Sensing Installation Art,

• Smart Art Education Application,

• Social Media Intelligent Art Campaign,

• AI-Generated Personalized Artwork Service,

• Digital Performance Analytics Dashboard,

• Blockchain-Based Art Engagement Platform,

• Multi-Sensory Projection Mapping System,

• Gamified Art Learning Environment,

• Virtual Community Art Forum,

• Real-Time Emotion Feedback Display System, and.

• Hybrid Physical-Digital Exhibition Model.

Nine criteria are used to perform the assessment.

• Emotional Recognition Capability (Benefit) is the capability of the system to identify and infer the emotions of the audience so that it can engage in adaptive communication.

• Emotional Adaptability (Benefit) examines the effectiveness with which the system adapts the artistic material to the emotional feedback to personal engagement.

• Audience Engagement Level (Benefit) represents the level of active engagement and interaction, which is supported through the platform.

• Empathy Enhancement Potential (Benefit) evaluates how the communication plan is able to create emotional connection and shared understanding among the audiences.

• Technological Intelligence Integration (Benefit) is a measurement of the level of sophistication and efficiency of AI-driven features incorporated in the system.

• Cultural and Social Relevance (Benefit) considers how it fits in the values of society, diversity, and inclusivity, which enhances communicative authenticity.

• Implementation Cost (Cost) takes into account the financial investment needs, such as hardware, software, and training costs.

• Technical Complexity (Cost) is an operational complexity, the cost of maintenance, and technical skill.

• Data Privacy and Ethical Risk (Cost) evaluates possible risks related to the collection of emotional data and algorithmic decisions that are of critical importance in emotionally intelligent systems.

Criterion through are benefit-type as the greater their values, the better the communication effectiveness and Criterion through is a cost-type since the greater the value it has, the less feasible and sustainable the situation is.

Step 1:

In the operationalization of the evaluation of these fifteen alternatives against the nine criteria, the step-wise outline has been used. To begin with, Tables 1 and 2 provide linguistic terms and gains and costs of qROFNs, respectively. Table 3 then brings out the four weights of the decision-makers by the relative weight of the decision-maker participating in the process of making the evaluation, with the assistance of the decision-maker. (2) of the weights.

Table 3.

Weights Assigned to Decision-Makers Based on qROF Evaluations.

DMs
LTs
qROFNs
Weights

Step 2:

The Table 4 that provides the linguistic rating of the decision-makers is then compiled with the ratings of the alternatives of the decision-makers to each of the criteria. Such linguistic words are translated to qROFNs in Table 5, hence creating the qROF decision matrix. Lastly, Table 6 illustrates how the process of group evaluation aggregation can be carried out by considering the use of the qROFWA operator, where the implementation of the qROFWA operator of the proposed qROF-CURLI technique is an input in the evaluation.

Table 4.

Linguistic Assessment of Criteria by Decision-Makers.

Table 5.

q-Rung Orthopair Fuzzy Decision Matrix for Criteria Across Decision-Makers.

Table 6.

Aggregated q-Rung Orthopair Fuzzy Matrix of Criteria Using qROFWA Operator.

Step 3:

The criteria weights are calculated using the aggregated qROFNs and their corresponding qROF-score values (Eq. 1). These computed weights are presented in Table 7 and illustrated graphically in Fig. 2.

Table 7.

Normalized Weights of Criteria Based on Aggregated qROF Scores.

	Scores	criteria weights

Fig. 2.

Visualization of criteria weights.

Step 4:

The DMs compare the options on the basis of the criteria through the use of linguistic terms, which are translated to qROFNs to constitute the qROF decision matrix (Tables 8 and 9). For consistency, the linguistic evaluations provided by decision-makers were carefully converted into qROFNs according to the predefined linguistic scale, and the labels of alternatives and criteria were standardized across Tables 8 and 9.

Table 8.

Evaluation of alternatives and criteria.

Table 9.

q-Rung Orthopair Fuzzy Decision Matrix for Alternatives.

Step 5:

The qROFWA operator is used to combine the qROFNs of the alternatives into a group consensus matrix (Table 10). The aggregation process strictly follows the qROFWA formulation, ensuring consistent calculation and accurate aggregation of individual expert evaluations into the group decision matrix presented in Table 10.

Table 10.

Aggregated q-Rung Orthopair Fuzzy Decision Matrix for Alternatives Using qROFWA Operator.

Step 6:

The qROF-score of both alternatives is computed using the formula (1) and presents the preliminary ranking using the qROF information (Table 11).

Table 11.

Computed qROF-Score Values of Alternatives.

Step 7:

In both criteria, the alternatives will be compared against each other in a pairwise manner in all the criteria to establish how they perform with respect to each other. The resulting comparisons are then added up to get the pairwise comparison matrix, as presented in Table 12. To clarify, Table 12 is derived from Table 11, which contains the computed qROF scores of all alternatives. Equation (5) is applied to compare each pair of alternatives for each of the 9 criteria, producing + 1, 0, or −1 values depending on whether an alternative is superior, equal, or inferior to another. These values are then summed across all criteria to generate the aggregated dominance scores shown in Table 12. Each entry in the table thus reflects the cumulative superiority or inferiority of an alternative relative to all others, providing a transparent basis for ranking.

Table 12.

Pairwise Comparison Matrix of Alternatives Based on qROF Scores.

Step 8:

The CURLI score of each alternative is finally determined as a composite between the pairwise comparison scores and the weight of the criteria. Ranking of the alternatives has been done in terms of the scores. Table 13 contains the final CURLI scores, and Fig. 3 contains a graphical display of the ranking.

Table 13.

CURLI Scores and Final Ranking of Alternatives.

	CURLI scores	Ranking

Fig. 3.

Visual ranking of alternatives derived from the qROF-CURLI method.

Result discussion

The findings of the given qROF-CURLI approach indicate that (Gamified Art Learning Environment) is ranked 1 st, then, (AI-Based Emotion-Adaptive Art Platform) and (Social Media Intelligent Art Campaign) are given 2nd and 3rd place, respectively. These options perform strongly across multiple benefit criteria—Emotional Recognition Capability, Emotional Adaptability, Audience Engagement, and Empathy Enhancement—while maintaining relatively lower Implementation Cost, Technical Complexity, and Ethical Risk, highlighting the trade-offs managed by the model. Options and receive 4th and 5th positions with high technology intelligence integration, but with a minor consideration of a higher cost-based parameter. Average-ranked ones like , , and hold equal emotional performance with average trade-offs in complexity and viability. Less preferable options, such as , , , and especially (15th rank), illustrate reduced emotional adaptability or increased operational and ethical constraints. Because the data used is hypothetical and the purpose of the data is to illustrate mathematically how the algorithm works, these rankings indicate the mathematical characteristics and subtleties of the qROF-CURLI system under a variety of criteria, and not the actual performance in the real world. Overall, the findings give a clue to the way the framework can be used to identify the strategies that can optimize emotional responsiveness, engagement, and adaptive interaction to consider the cost and practical limitations, demonstrating its usefulness in evaluating the smart art communication in the context of emotional intelligence.

Sensitivity analysis

A sensitivity analysis is performed to assess the integrity and the firmness of the suggested qROF-CURLI decision framework given different levels of significance of the decision-makers and criteria. Such analysis will provide that the resultant ranking of the smart art communication options will not rely overly on a particular weighting system and will be useful in various situations of preference.

Sensitivity of criteria weights to changes in decision makers’ weights

In the first stage, the sensitivity to the change in criteria weights to decision-maker weight variation is examined in ten different cases. Figure 4 (Decision Makers’ Weights across Ten Distinct Scenarios) is the systematic variation of the weights of - to exhibit the changes of dominance between experts. As an example, in Scenario 7, () has a great weight, whereas in Scenario 8, () has a comparatively greater impact. On the same note, both Scenario 2 and 10 have equal distributions of decision-makers. These ordered variations give the opportunity to examine the effect of expert influence on the aggregated weights of criteria.

Fig. 4.

Decision makers’ weights across ten distinct scenarios.

The effects on the criteria weights that correspond to changes in decision maker weights are shown in Fig. 5 (Sensitivity of Criteria Weights to Change in Decision Maker Weights). The outcomes show that benefit criteria like (Cultural and Social Relevance) and (Implementation Cost, cost-type) show significant variations in Scenario 7, with the highest values of with a significant dependence on the preferences structure of . On the other hand, most criteria, like (Emotional Adaptability) and - (Technical Complexity and Ethical Risk), do not change significantly in most situations, except when there are extreme dominance situations. The negative values in certain cases (e.g., and in Scenario 7, indicate directional changes in aggregated fuzzy influence and not instability in the model, which proves that the model is very sensitive to changes in expert preferences without loss of structural consistency.

Fig. 5.

Sensitivity of criteria weights to changes in decision makers’ weights.

Sensitivity analysis of alternative rankings with respect to criteria weights

The second step is the sensitivity analysis of the alternative rankings to the criteria weights and is illustrated in Fig. 6 (Sensitivity Analysis of Alternative Rankings with Respect to Criteria Weights). The findings prove that the leading-ranked options have comparatively fixed performance patterns in most cases. As an example, that was ranked 1 st in the beginning displays only negative values of deviations in Scenario 1–6 and 8–10, meaning that it is mostly superior with the moderate fluctuations. Likewise, both and maintain directional trends when changing the criteria weights. Nevertheless, Scenario 7, which is associated with the extreme dominance of leads to apparent deviations in multiple alternatives (e.g., with and with (), which underscores the effect that the extreme weighting structures can have a temporary effect on the ranking intensity, but not a permanent one that would alter the overall performance trends. Middle and low rank alternatives are moderately fluctuating, yet do not show chaotic and unsystematic ranking. Most of the substitutes exhibit regulated and explainable deviations, which proves the effectiveness of the qROF-CURLI framework in adopting uncertainty and weight variations. On the whole, the sensitivity analysis confirms the soundness of the suggested model by proving that it is strong, stable, and dependable when the decision-maker and criteria-weight settings are varied, supporting its appropriateness to assess Smart Art Communication within the context of an Emotional Intelligence framework in complicated and uncertain conditions.

Fig. 6.

Sensitivity analysis of alternative rankings with respect to criteria weights.

Benchmarking against existing qROF-MCDM methods

Benchmarking against some of the existing qROF-MCDM techniques, such as qROF-CoCoSo, qROF-MARCOS, qROF-CRADIS, and qROF-FUCA, was used to prove the effectiveness and strength of the proposed qROF-CURLI approach. Under these methods, Table 14 displays quantitative rankings of fifteen smart art communication alternatives. The suggested qROF-CURLI regularly has equalized rankings that are more or less in line with the expectations of the experts and well functioning with the uncertainty and emotional intelligence elements.

Table 14.

Quantitative benchmark comparison.

	qROF-CoCoSo	qROF-MARCOS	qROF-CRADIS	qROF-FUCA	qROF-CURLI (Proposed)

In an attempt to measure the extent of this resemblance between rankings produced by the various techniques, the rank correlation coefficient of Spearman was calculated against the suggested qROF-CURLI technique, which is presented in Table 15. A positive value above one suggests greater conformity to the model that is proposed.

Table 15.

Spearman’s Rank Correlation Coefficient Analysis.

MCDM	Spearman vs. qROF-CURLI
qROF-CoCoSo
qROF-MARCOS
qROF-CRADIS
qROF-FUCA

The quantitative comparison points out that the qROF-CURLI has a high degree of consistency with traditional techniques such as CoCoSo and gives more balanced results in situations in which there are extreme changes in the weight of decision-makers (such as sensitivity analysis). Techniques such as FUCA are negatively correlated, indicating that they can be unstable or have overemphasized specific criteria in emotionally complex situations. Qualitative benchmarking was also conducted to evaluate every approach concerning its applied relevance, the ability to withstand uncertainty, computational burdens, and adaptability to utilize Emotional Intelligence standards. Table 16 designates Ratings of High (H), Medium (M), and Low (L).

Table 16.

Qualitative comparative assessment.

Method	Applicability	Robustness under Uncertainty	Computational Complexity	EI Integration Flexibility
CoCoSo29	M	M	M	L
MARCOS30	M	M	M	M
CRADIS31	L	M	M	L
FUCA32	L	L	H	L
CURLI15	H	H	M	H
TOPSIS33	M	L	M	M
OPARA34	M	M	M	M
RANCOM35	L	L	H	L
WASPAS36	M	M	M	M

The qualitative analysis confirms that the proposed qROF-CURLI approach has the ethical capability of practical applicability, robustness, and flexibility to incorporate Emotional Intelligence, and the computational complexity is manageable. In comparison with other qROF-MCDM solutions and the classical ones, such as TOPSIS or WASPAS, qROF-CURLI offers a more balanced and reliable method of assessing Smart Art Communication in the conditions of the complex, multicriteria, and uncertain.

Practical and managerial implications

The results of this research have a number of implications for practitioners, curators, and managers in the fields of art communication and digital media. The Gamified Art Learning Environment () and AI-Based Emotion-Adaptive Platforms () as the best ranked alternatives demonstrate that emotionally adaptive and interactive systems are worth considering to increase audience engagement and empathy. These insights can assist managers in making investments in intelligent art forms that incorporate the emotional intelligence features, which will guarantee increased satisfaction among the audience and a sense of engagement. In addition, the suggested qROF-CURLI framework offers a systematic decision-making tool in the face of uncertainty that would allow evaluation of multiple alternative options, allowing the allocation of resources, choice of strategies, and risk analysis of digital and hybrid art communication projects.

Key advantages of the study

This research has a number of major strengths as compared to the current practices. First, the qROF-CURLI method is effective in terms of capturing vagueness and hesitation in human judgment, particularly in the circumstances of assessing the elements of emotional intelligence. Second, the approach is capable of group decision-making, which combines various expert views with weighting so that it is fair and flexible. Third, the model is robust to changes in weight and when the influence of decision-makers is extreme, and it is sensitive enough to provide reliable and interpretable rankings through sensitivity analysis and benchmarking. Finally, the framework is very flexible, which is why it can be applied in various situations of smart art communication, such as digital art exhibitions, educational practice, and interactivity.

Study limitations

Despite being a strong study, it has some limitations. The analysis is established on hypothetical data and a small sample of four decision-makers and may not be applicable to the overall environment. The decision of criteria and a weighting scheme, which is also well designed, is, however, subjective and may vary across cultures and institutions. In bigger problems, there may be additional options, standards, or decision-makers that can enhance the computational complexity, which may require maximization so as to allow real-time implementation. Also, linguistic terms turned into qROFNs can create bias because of subjectivity in interpreting and discretizing expert opinions, and expert aggregation can enhance personal inconsistencies or extreme views. These limitations could be overcome in future studies with the use of adaptive linguistic scales, strategies of consensus building or a combination of both qROFNs and probabilistic or interval-based representations of uncertainty. Finally, despite the fact that the qROF-CURLI model is a powerful one applying to uncertainty modeling, the model is yet to be used to dynamic developments of emotional responses over time, which could be relevant in changing the audience interaction in long-term projects.

Conclusion and future research directions

The new qROF-CURLI MCDM model represented in this paper can be applied to the evaluation of smart art communication through the prism of emotional intelligence in order to successfully solve multicriteria decision-making issues in both uncertain and dynamic conditions. The model proposed will include the application of qROFS and CURLI aggregation mechanism to ensure that vulnerability in expert judgment is prevented, balance benefit and cost criteria are achieved and give robust rankings of alternatives. According to the case study, the interactive, emotionally adaptive platforms, particularly gamified learning platforms, are more effective than other methods in terms of engaging the audience, empathy and integrating technologies. Sensitivity analysis and comparison with existing qROF-MCDM methods both support the stability, reliability and quality of the proposed approach.

To improve this framework in future studies, it can be supplemented with the sophisticated use of artificial intelligence to manage dynamic and real-time settings, hybrid learning models, real-time data streams, and intelligent control systems. Further extensions involve dynamic modeling of emotional reactions, involving more decision-makers to make a wider consensus, and extending it to fields like virtual cultural heritage, adaptive education and AI-mediated creative systems. Optimization of predictive assessment and real-time decision support can be further enhanced by hybridizing the qROF-CURLI model with machine learning, which will enhance its usage in intelligent art communication ecosystems.

Author contributions

Chengao Bao contributed fully.

Data availability

The computational framework and calculation workflow used to generate the results are provided as a structured Microsoft Excel file and are publicly available via Zenodo at [10.5281/zenodo.19369328](https:/doi.org/10.5281/zenodo.19369328). The file contains all intermediate steps, formula-based computations, and ranking procedures required to reproduce the analysis.

Declarations

Competing interests

The authors declare no competing interests.

Ethics statement

No human participants or external experts were involved in this study. The dataset used is entirely hypothetical and was constructed solely for methodological demonstration purposes. Therefore, informed consent was not required.