Uncertain Linguistic Sets Research Articles

Advanced CoCoSo method for uncertain MAGDM: Evaluating college students’ entrepreneurial skills

With the in-depth implementation of the innovative development-driven strategy of “mass innovation and entrepreneurship” put forward by the state, colleges and universities, as the main positions for cultivating innovative and entrepreneurial talents, have set up a multi-level and all-round training system for college students’ innovative and entrepreneurial ability according to the relevant policies and implementation opinions of the state for deepening innovation and entrepreneurship education in colleges and universities, and actively promoted the improvement of college students’ innovative and entrepreneurial ability. The college students’ innovation and entrepreneurship ability evaluation could be regarded as the classical multiple attribute group decision making (MAGDM) issue. The PULTSs could well depict uncertain information during the college students’ innovation and entrepreneurship ability evaluation and the combined compromise solution (CoCoSo) method is appropriate to stable the decision-making results. In this paper, the probabilistic uncertain linguistic combined compromise solution (PUL-CoCoSo) method based on the probabilistic uncertain linguistic sets (PULTSs) and combined compromise solution method is proposed for multiple attribute group decision making (MAGDM). The weights of attribute based on the CRITIC method are obtained under PULTSs. Finally, an application related to the college students’ innovation and entrepreneurship ability evaluation is utilized to demonstrate the usage of the developed algorithms.

Wearable sensor-based on exercise monitoring system for disabled the individuals using a multi-attribute fuzzy evaluation mode

Recently, there has been a lot of interest in using the wearable sensors for tracking the exercise progress because of the unbiased accuracy and precision they are provided throughout the continual monitoring. For those with physical impairments, the system’s non-intrusive, lightweight ways of the monitoring activity may ease their load and enhance the quality of their decision-making. As a different measuring unit measures the exercise activity levels recorded by the each wearable sensor, it is challenging to assess the monitoring system. Hence, this paper proposes a Hybridized Fuzzy Multi-Attribute for Exercise Monitoring System (HFMA-EMS) to address the uncertainty issues of the wearable sensors. The Triangular Fuzzy membership function is proposed to begin classifying the observed values. Pair-wise attribute comparison and evaluator weighting in a T-spherical uncertain linguistic set setting utilizing the Techniques for Ordering of Preferences by Similarities to Ideal Solutions (TOPSIS). In the suggested method, a utility function is used to assess the merits of a model in which attribute the weights are calculated, followed by an exercise in which the attributes are ordered employing the Measurements of the Alternative and Ranking Compromise Solutions model (MARCOS). The performance is performed to analyze the proposed method’s accuracy, precision, recall, f1-score, and correct and incorrect exercise assessment by an accelerometer, gyroscope, and magnetic field sensor unit. The application scenario of the HFMA-EMS can be used in the clinical applications, healthcare management, and sports injury detection.

A novel uncertain information modeling method based on cosine similarity and cross entropy under spherical uncertain linguistic fuzzy set

Multi-attribute group decision-making (MAGDM) is one of the research hotspots in human cognitive and decision-making theory. However, there are still challenges to the existing MAGDM methods in modeling uncertain linguistics of decision-makers’ (DMs’) cognitive information and objectively obtaining weights. Therefore, this paper aims to develop a new MAGDM method considering incomplete known weight information under spherical uncertain linguistic sets (SULSs) to model uncertain information in MAGDM problems. The method mainly includes the following aspects. Firstly, a new concept, which enables an intuitive evaluation of neutral membership and hesitancy degrees at the linguistic evaluation, has been is first developed for capturing the more uncertain information. Secondly, the cosine similarity measure (CSM) and cross-entropy measure (CEM) are widely used to measure ambiguous information because of their robustness of measurement results. The CSM and CEM are extended to SULSs to calculate the DMs’ and attributes weights quantitively, respectively. Thirdly, in terms of effective integration of fuzzy information to obtain more accurate decision results, the Hamy mean (HM) and dual Hamy mean (DHM) operators are valued due to their consideration of the interrelationships between inputs. Two extension operators, named spherical fuzzy uncertain linguistic weight HM and DHM, are proposed to integrate spherical fuzzy uncertain linguistic information in the third stage. In the experiment, a decision case is presented to illustrate the applicability of the proposed method, and results show the effectiveness, flexibility and advantages of the proposed method are demonstrated by numerical examples and comparative analysis.

A novel CE-PT-MABAC method for T-spherical uncertain linguistic multiple attribute group decision-making

A T-spherical uncertain linguistic set (TSULS) is not only an expanded form of the T-spherical fuzzy set and the uncertain linguistic set but can also integrate the quantitative judging ideas and qualitative assessing information of decision-makers. For the description of complex and uncertain assessment data, TSULS is a powerful tool for the precise description and reliable processing of information data. However, the existing multi-attribute border approximation area comparison (MABAC) method has not been studied in TSULS. Thus, the goal of this paper is to extend and improve the MABAC method to tackle group decision-making problems with completely unknown weight information in the TSUL context. First, the cross-entropy measure and the interactive operation laws for the TSUL numbers are defined, respectively. Then, the two interactive aggregation operators for TSUL numbers are developed, namely T-spherical uncertain linguistic interactive weighted averaging and T-spherical uncertain linguistic interactive weighted geometric operators. Their effective properties and some special cases are also investigated. Subsequently, a new TSULMAGDM model considering the DM’s behavioral preference and psychology is built by integrating the interactive aggregation operators, the cross-entropy measure, prospect theory, and the MABAC method. To explore the effectiveness and practicability of the proposed model, an illustrative example of Sustainable Waste Clothing Recycling Partner selection is presented, and the results show that the optimal solution is h3. Finally, the reliable, valid, and generalized nature of the method is further verified through sensitivity analysis and comparative studies with existing methods.

Hybrid Framework for Safety Design of Human–Rail Vehicle Transportation System Using Stochastic Approach and Optimization

The human–rail vehicle transportation system safety design is complicated given that the complexity of the multilevel system with parameter uncertainties propagating from the vehicle structure (primary collision) to the interior human compartment (secondary collision). This study establishes a hybrid framework incorporating a stochastic approach and an integrated optimization strategy to improve train crashworthiness and reduce passenger crash injuries. The stochastic approach utilizes adaptive sparse polynomial chaos expansion models and variance-based sensitivity indices to evaluate the statistic characteristics of system responses and quantify the contribution ranking of uncertain parameters to response variations. The optimization strategy integrating the evolutionary algorithm and the multi-criteria decision making (MCDM) is proposed to solve the non-uniqueness of Pareto optimal solutions. In the optimization process, the modified DEMATEL–ANP method with interval type-2 fuzzy sets is developed to deal with vague linguistic judgments for the importance sequence of human injury responses. The q-rung orthopair trapezoidal fuzzy uncertain linguistic sets–TOPSIS method is established to address hesitant linguistic evaluations for the Pareto front and select the final optimal solution. Compared with the initial design, the driver Abbreviated Injury Scale (AIS) 3+ joint injury probability is reduced from 67.08% to 14.17% after optimization. Results prove that the proposed framework is a practical tool for improving the passive safety of railway industry.

Linear diophantine uncertain linguistic-based prospect theory approach for performance evaluation of islanded microgrid-system scenarios

AbstractRenewable-energy-based hybrid microgrids can aid in achieving one of the United Nations Sustainable Development Goals, i.e. ‘Affordable and clean energy’. However, experts may be faced with the challenge of selecting the best one for the electrification of an area. To avoid the challenge and realize the ultimate goal of the United Nations, the present study, therefore, proposes a novel prospect theory-based decision-making approach to help experts in opting for the best microgrid scenario. The proposed decision-making framework considers the risk appetite of the decision-maker, a quintessential aspect of the process. Linear diophantine uncertain linguistic sets are used to model the linguistic evaluations from the experts. The information from different experts is aggregated using a linear diophantine uncertain linguistic power Einstein-weighted geometric operator. Finally, the prospect-theory-based TOmada de Decisao Interativa Multicriterio approach is employed to evaluate the performance of the available microgrid scenarios and hence opt for the best microgrid scenario. The proposed framework has been used to evaluate the performance of seven possible microgrid scenarios and hence select the best one that can be implemented for rural electrification of a remote village in Assam, India. The microgrid scenario consisting of a photovoltaic–wind turbine–fuel cell–battery converter (MG3) has been revealed to be the best scenario among the seven considered microgrid scenarios. The validity of the obtained ranking results has been adjudged through a comprehensive evaluation regarding the attenuation factor and the weights of the criteria. Moreover, previous case studies have also been solved using the proposed methodology and the results reveal a good correlation between the obtained ranking results.

Sustainable Supplier Selection using Neutrosophic Sets and MCDM Framework

Because of stricter rules from the government and growing awareness among the general public, sustainable supply chain management (SSCM) performs a significant role in the management of firm manufacturing operations. Companies that want to promote sustainable supply chain management (SSCM) must first choose the most suitable sustainable supplier, which is a MCDM dilemma, as highlighted in a number of research studies. In addition, because of their limited expertise, those who make decisions have a propensity to convey their opinions via the use of language phrases. The purpose of this work is to report on a unique MCDM model for the choice of sustainable suppliers. This approach integrates the MCDM MABAC method inside an uncertain language situation. With the assistance of uncertain linguistic sets, the neutrosophic sets used to overcome these uncertainty. When it comes to generating the ranking of possible suppliers, the MABAC is dependable and easy to understand. In conclusion, an iron maker is used as an example to illustrate the practicability and efficacy of the suggested strategy for the selection of sustainable suppliers.

A new situation assessment method for aerial targets based on linguistic fuzzy sets and trapezium clouds

Situation assessment has attracted much attention. The chief aim of this paper is to research the problem from the perspective of multicriteria group decision-making (MCGDM). First of all, this paper expresses the threat information with linguistic fuzzy sets, including Atanassov’s intuitionistic fuzzy sets (AIFSs), Atanassov’s interval-valued intuitionistic fuzzy sets (AIVIFSs), and interval intuitionistic uncertain linguistic sets (IIULSs). Then, some relevant concepts and aggregation operators of trapezium clouds are proposed, meanwhile, a new approach that calculates the weights considering subjectivity and objectivity is presented with multi-objective programming. Next, the conversion methods between AIFSs, AIVIFSs, IIULSs and trapezium clouds are derived. Finally, the algorithm process is presented and an illustrative example is employed to prove the validity. Also, the comparison analysis with other widely used methods is conducted to verify the feasibility of the proposed algorithm.

A study on the Heronian mean operators for managing complex picture fuzzy uncertain linguistic settings and their application in decision making

The major influence of this manuscript is to diagnose a valuable and considerable technique of Complex Picture Fuzzy Uncertain Linguistic setting and described its useful and valuable operational laws. The theory of Complex Picture Fuzzy Uncertain Linguistic information is massive modified and generalized than the Complex intuitionistic Fuzzy Uncertain Linguistic, Complex Fuzzy Uncertain Linguistic, Fuzzy Uncertain Linguistic and Uncertain Linguistic information. Keeping the supremacy and dominancy of the Complex Picture Fuzzy Uncertain Linguistic information, we investigated the Complex Picture Fuzzy Uncertain Linguistic Arithmetic Heronian Mean, Complex Picture Fuzzy Uncertain Linguistic Weighted Arithmetic Heronian Mean, Complex Picture Fuzzy Uncertain Linguistic Geometric Heronian Mean and Complex Picture Fuzzy Uncertain Linguistic Weighted Geometric Heronian Mean operators. The property of idempotency, boundedness, monotonicity, and various well-known results with certain specific cases of the invented work are also deliberated. Furthermore, in the availability of the above-proposed analysis, we constructed a multi-attribute decision-making technique by considering the diagnosed operators for complex picture fuzzy uncertain linguistic information to enhance the worth and rationality of the invented theory. Finally, we illustrated the merits and restrictions of the novel operators by comparing them with certain prevailing operators based on fuzzy generalization. Finally, in the presence of evaluated examples, we compared the pioneered operators with various existing operators to enhance the feasibility and worth of the invented operators.

Classification of the wind turbine components based on importance degrees: A three-way decision perspective

The bad working environment and various complex influencing factors lead to the high failure rate of a wind turbine. It is necessary to decide on a reasonable maintenance strategy for wind turbines. The classification of wind turbine components based on their importance degrees can identify the components which have an important impact on the reliability and maintenance of wind turbines. However, the traditional multi-criteria decision-making method can only provide the importance ranking of components, rather than the importance classification of components. The emergence of the three-way decision (TWD) method makes up for this deficiency. Then we classify the importance degrees of components by the TWD method. Firstly, the decision-theoretic rough sets are introduced into the uncertain linguistic setting to construct uncertain linguistic decision-theoretic rough sets. Secondly, the weights of experts are attained based on the consistency degree of loss functions. Thirdly, conditional probability is attained by the evaluation based on distance from the average solution method. And the classification of wind turbine components is derived based on the minimum-loss principle. Finally, a case study about the classification of the wind turbine components based on importance degrees is employed to certify the practicability of our designed method. The proposed model extends both the theory and practice of TWD and offers a classification helpful to make maintenance strategies for reducing the risk of component failure.

T-spherical uncertain linguistic MARCOS method based on generalized distance and Heronian mean for multi-attribute group decision-making with unknown weight information

The T-spherical uncertain linguistic (TSUL) sets (TSULSs) integrated by T-spherical fuzzy sets and uncertain linguistic variables are introduced in this article. This new concept is not only a generalized form but also can integrate decision-makers’ quantitative evaluation ideas and qualitative evaluation information. The TSULSs serve as a reliable and comprehensive tool for describing complex and uncertain decision information. This paper focuses on an extended MARCOS (Measurement of Alternatives and Ranking according to the Compromise Solution) method to handle the TSUL multi-attribute group decision-making problems where the weight information is completely unknown. First, we define, respectively, the operation rules and generalized distance measure of T-spherical uncertain linguistic numbers (TSULNs). Then, we develop two kinds of aggregation operators of TSULNs, one kind of operator with independent attributes is T-spherical uncertain linguistic weighted averaging and geometric (TSULWA and TSULWG) operators, and the other is T-spherical uncertain linguistic Heronian mean aggregation operators (TSULHM and TSULWHM) considering attributes interrelationship. Their related properties are discussed and a series of reduced forms are presented. Subsequently, a new TSUL-MARCOS-based multi-attribute group decision-making model combining the proposed aggregation operators and generalized distance is constructed. Finally, a real case of investment decision for a community group-buying platform is presented for illustration. We further test the rationality and superiorities of the proposed method through sensitivity analysis and comparative study.

Complex Pythagorean uncertain linguistic group decision-making model based on Heronian mean aggregation operator considering uncertainty, interaction and interrelationship

To effectively solve the mixed problem of considering the uncertainty of individuals and groups, the interaction between membership degree (MD) and non-membership (ND), and the interrelationship between attribute variables in complicated multiple attribute group decision-making (MAGDM) problems, in this paper, a concept of complex Pythagorean uncertain linguistic (CPUL) set (CPULS) is introduced, the interaction operational laws (IOLs) of CPUL variables (CPULVs) are defined. The CPUL interaction weighted averaging and geometric operators are presented. A new concept of CPUL rough number (CPULRN) is further constructed. The CPUL rough interaction weighted averaging and geometric aggregation operators (AOs) are extended. The ordering rules of any two CPULRNs are defined. The CPUL rough interaction Heronian mean (HM) (CPULRIHM) operator and its weighted form are advanced, related properties and special cases are explored. An MAGDM model based on CPUL rough interaction weighted HM (CPULRIWHM) operator is built. Lastly, we conduct a case study of location selection problem for logistics town project to show the applicability of the proposed methodology. The sensitivity and methods comparison are analyzed to verify the effectively and superiority.

A novel multi-criteria decision-making framework for selecting municipal solid waste management alternative with 2-dimensional uncertain linguistic sets.

Municipal solid waste management (MSWM) has been considered as a complicated multi-criteria decision-making problem for the uncertain context and related criteria. To select an optimal MSWM scenario, this paper provides a comprehensive MCDM framework for decision-makers under 2-dimensional uncertain linguistic (2-DUL) environment. Distinguished from traditional approaches, this framework not only guarantees the consistency of comparison matrix but improves effectiveness and efficiency in the decision process. Moreover, it accurately solves the cardinal and ordinal information of MSWM scenarios. Firstly, due to ambiguous and uncertain decision context, the 2-DUL set, characterized by I class of the linguistic evaluation information and II class of the reliability of the assessment results, is adopted to describe decision-makers' preference. An expectation reduced-dimension is developed to effectively handle 2-DUL set. Secondly, to guarantee consistency and reduce numerical pairwise comparisons, a best-worst-method (BWM)-based analytic network process (ANP) is utilized to form the local priority vectors of the main criteria and sub-criteria. Main criteria weights and sub-criteria weights are then obtained by aggregating all local priority vectors. Thirdly, an extended QUALIFLEX approach is employed to rank all alternative MSWM scenarios by comparing the weighted concordance/discordance index among overall possible permutations of all alternative scenarios. Finally, the developed framework is applied in a case study to determine an optimal MSWM scenario in Beijing. Additionally, a comparison analysis is complemented. The results demonstrate that the proposed framework is feasible, efficient, and superior in MSWM scenarios selection.

Knowledge Representation and Reasoning with an Extended Dynamic Uncertain Causality Graph under the Pythagorean Uncertain Linguistic Environment

A dynamic uncertain causality graph (DUCG) is a probabilistic graphical model for knowledge representation and reasoning, which has been widely used in many areas, such as probabilistic safety assessment, medical diagnosis, and fault diagnosis. However, the convention DUCG model fails to model experts’ knowledge precisely because knowledge parameters were crisp numbers or fuzzy numbers. In reality, domain experts tend to use linguistic terms to express their judgements due to professional limitations and information deficiency. To overcome the shortcomings of DUCGs, this article proposes a new type of DUCG model by integrating Pythagorean uncertain linguistic sets (PULSs) and the evaluation based on the distance from average solution (EDAS) method. In particular, experts express knowledge parameters in the form of the PULSs, which can depict the uncertainty and vagueness of expert knowledge. Furthermore, this model gathers the evaluations of experts on knowledge parameters and handles conflicting opinions among them. Moreover, a reasoning algorithm based on the EDAS method is proposed to improve the reliability and intelligence of expert systems. Lastly, an industrial example concerning the root cause analysis of abnormal aluminum electrolysis cell condition is provided to demonstrate the proposed DUCG model.

A method to multi-attribute decision making problems by using heronian mean operators based on linear diophantine uncertain linguistic settings

In the real decision process, an important problem is how to express the attribute value more efficiently and accurately. In the real world, because of the complexity of decision-making problems and the fuzziness of decision-making environments, it is not enough to express attribute values of alternatives by exact values. For this managing with such sorts of issues, the principle of Linear Diophantine uncertain linguistic set is a valuable and capable technique to manage awkward and inconsistent information in everyday life problems. In this manuscript, we propose the original idea of Linear Diophantine uncertain linguistic set and elaborated their essential laws. Additionally, to determine the association among any numbers of attributes, we elaborated the Linear Diophantine uncertain linguistic arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic weighted arithmetic Heronian mean operator, Linear Diophantine uncertain linguistic geometric Heronian mean operator, Linear Diophantine uncertain linguistic weighted geometric Heronian mean operator, and their properties are also discovered. By using these operators, we utilize the multi-attribute decision-making procedure by using elaborated operators. To determine the consistency and validity of the elaborated operators, we illustrate some examples by using explored operators. Finally, the superiority and comparative analysis of the elaborated operators with some existing operators are also determined and justified with the help of a graphical point of view.

Evaluation of Emergency Intelligence Capability of Major Public Health Events in Probabilistic Uncertain Language Environment

Emergency intelligence capability is an important index reflecting the intelligence level of emergency management. The accuracy of emergency intelligence capability evaluation is related to the scientific nature of emergency decision-making. By analyzing the operation process and mechanism of the emergency intelligence system for major public health events, this paper establishes the evaluation index system of the emergency intelligence capability. By using the decision method of VIKOR and considering the preference of experts in the evaluation process, this paper proposes the evaluation model based on the probabilistic uncertain language environment. The use of probabilistic uncertain linguistic term set (PULTS) to describe the uncertain information is helpful to improve the scientific and accuracy of emergency rescue decision-making of major public health events and then realize the organic unity of emergency information and scientific decision-making of public health events.

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved, neutrosophic sets are attracting more attention due to the greater power of the structure of neutrosophic sets. The ability to account for components that are true, false or neither true nor false is useful in the resolution of real-life problems. However, simultaneous variations render neutrosophic sets unsuitable in specific circumstances. To enable the management of these sorts of issues, we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multi-valued complex neutrosophic uncertain linguistic sets. Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth, abstinence, and falsity, and uncertain linguistic terms, which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval. Some important Dombi laws are elaborated along with Bonferroni mean operators, which offer a flexible general structure with modifiable factors. Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. To determine relationships among any number of attributes, we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases. By using these laws, we can deploy the multi-attribute decision-making (MADM) technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets. To determine the power and flexibility of the elaborated approach, we resolve some numerical examples based on the proposed operator. Finally, the work is validated with the help of comparative analysis, a discussion of its advantages, and geometric expressions of the elaborated theories.

A Multi-MOORA decision making method based on Muirhead mean operators and complex spherical fuzzy uncertain linguistic setting

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead’s general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed.

Some Single-Valued Neutrosophic Uncertain Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple-Attribute Decision Making

The Maclaurin symmetric mean (MSM) operator has a good aggregation effect. It can capture the relationships between multiple input parameters, and the neutrosophic uncertain linguistic numbers can well represent some indeterminate and incomplete information. In this paper, we combine the MSM operator with the singled-valued neutrosophic uncertain linguistic set and propose some MSM operators based on single-valued neutrosophic uncertain linguistic environment, such as single-valued neutrosophic uncertain linguistic Maclaurin symmetric mean(SVNULMSM) operator and single-valued neutrosophic uncertain linguistic generalized Maclaurin symmetric mean(SVNULGMSM) operator. First of all, according to the neutrosophic set and uncertain linguistic numbers, we propose the single-valued neutrosophic uncertain linguistic numbers and give some operating rules. Furthermore, considering the influence of attribute weight on the results, we introduce the weighted SVNULMSM operator and weighted SVNULGMSM operator. Then, we propose a method to deal with MSDM problems and give the specific steps to solve the problem. Finally, an investment example is used to verify the effectiveness of our method, and the superiority of the method is proved by comparing with other methods.

Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.