2-tuple Linguistic Variables Research Articles

A MAGDM model based on 2-tuple linguistic variables and power Hamacher aggregation operators for optimal selection of digital marketing strategies

A MAGDM model based on 2-tuple linguistic variables and power Hamacher aggregation operators for optimal selection of digital marketing strategies

Dependence assessment in human reliability analysis using the 2-tuple linguistic information and DEMATEL method

Human reliability analysis (HRA), which is to analyze human contribution to system risk, is an effective way to model and assess human errors. Dependence assessment among human errors is an essential part of HRA, which often depends on the judgments of experts. As real-world problems often involve many complex factors, the judgments provided by the experts are often linguistic terms, even under uncertainty. To this end, by integrating 2-tuple linguistic variables and DEMATEL method, this paper presents a novel way to assess the dependence among human actions in HRA. In the proposed method, the linguistic judgments of the experts are modeled using 2-tuple linguistic variables, and the weights of the influential factors are determined using DEMATEL method, furthermore, the conditional human error probability is calculated by aggregating the 2-tuples of different influential factors based on the 2-tuple weighted average operator, where a novel weight calculation method is developed to determine the weights of different experts. Finally, a case study is presented to demonstrate the effectiveness and reliability of the proposed method. By adopting 2-tuple linguistic variables and DEMATEL method, the proposed method could effectively address the uncertainty in the dependence assessment while capturing the relationship among the influential factors.

Three-way decisions with complex q-rung orthopair 2-tuple linguistic decision-theoretic rough sets based on generalized Maclaurin symmetric mean operators

<abstract> <p>In this manuscript, we generalized the notions of three-way decisions (3WD) and decision theoretic rough sets (DTRS) in the framework of Complex q-rung orthopair 2-tuple linguistic variables (CQRO2-TLV) and then deliberated some of its important properties. Moreover, we considered some very useful and prominent aggregation operators in the framework of CQRO2-TLV, while further observing the importance of the generalized Maclurin symmetric mean (GMSM) due to its applications in symmetry analysis, interpolation techniques, analyzing inequalities, measuring central tendency, mathematical analysis and many other real life problems. We initiated complex q-rung orthopair 2-tuple linguistic (CQRO2-TL) information and GMSM to introduce the CQRO2-TL GMSM (CQRO2-TLGMSM) operator and the weighted CQRO2-TL GMSM (WCQRO2-TLGMSM) operator, and then demonstrated their properties such as idempotency, commutativity, monotonicity and boundedness. We also investigated a CQRO2-TL DTRS model. In the end, a comparative study is given to prove the authenticity, supremacy, and effectiveness of our proposed notions.</p> </abstract>

An Integrative Decision-Making Mechanism for Consumers’ Brand Selection using 2-Tuple Fuzzy Linguistic Perceptions and Decision Heuristics

Consumers perform decision-making (DM) processes to select their preferred brands during their entire consumer journeys. These DM processes are based on the multiple perceptions they have about the products available in the market they are aware of. These consumers usually perform different DM strategies and employ diverse heuristics depending on the nature of the purchase, ranging from more pure optimal choices to faster decisions. Therefore, the design of realistic DM approaches for modeling these consumer behaviors requires a good representation of consumer perceptions and a reliable process for integrating their corresponding heuristics. In this work, we use fuzzy linguistic information to represent consumer perceptions and propose four consumer DM heuristics to model the qualitative linguistic information for the consumer buying decision. In particular, we use 2-tuple fuzzy linguistic variables, which is a substantially more natural and realistic representation without falling in a loss of information. The set of selected heuristics differ in the degree of involvement the consumers give to their decisions. Additionally, we propose a heuristic selection mechanism to integrate the four heuristics in a single DM procedure by using a regulation parameter. Our experimental analysis shows that the combination of these heuristics in a portfolio manner improves the performance of our model with a realistic representation of consumer perceptions. The model’s outcome matches the expected behavior of the consumers in several real market scenarios.

Advanced FMECA Method Based on Intuitionistic 2-Tuple Linguistic Variables and the Triangular Fuzzy Analytic Hierarchy Process

Failure mode effects and criticality analysis (FMECA) is a commonly adopted approach to defining, assessing, and reducing possible failures in designs, systems, processes, products, and services. Traditional FMECA ranks the failure modes of products based on a risk priority number (RPN), which is obtained by multiplying the risk elements. Conventional FMECA has the shortcomings of badly handling unknown information and unreasonably assessing RPNs. To deal with these issues, an advanced FMECA method based on intuitionistic 2-tuple linguistic variables (I2LVs) and the triangular fuzzy analytic hierarchy process (TFAHP) is proposed. In this method, the fuzzy evaluation of risk elements given by different FMECA members is represented by I2LVs, which can efficiently handle unknown information. The TFAHP method is adopted to assess the weights of risky elements and rank the risk priorities of different failure modes. Finally, an application case of an insulated-gate bipolar transistor is used to verify the effectiveness and robustness of the proposed method.

An interval 2-Tuple linguistic Fine-Kinney model for risk analysis based on extended ORESTE method with cumulative prospect theory

The risk assessment is one of the most significant procedures for identifying, preventing, and controlling Occupational Health and Safety (OHS) risks. One of many kinds of techniques for OHS risk assessment is based on the Fine-Kinney model. Most of the Fine-Kinney-based risk assessment approaches can consider the relative importance degree of risk parameters. Nevertheless, the current Fine-Kinney-based risk assessment approaches do not have abilities to capture the reference dependence effects and detailed relationships among hazards. In addition, these approaches overlook the influence of the deviation of risk evaluation information. To overcome these limitations, in this paper, an improved Fine-Kinney model is proposed for OHS risk assessment by integrating the weighted power average (WPA) operator, ORESTE (Organísation, rangement et Synthèse de données relarionnelles (in French)) method, and cumulative prospect theory. First, the interval 2-Tuple linguistic variables are adopted to transform linguistic risk information into quantitative risk rating information. Then, an extended WPA operator is proposed to fuse the risk evaluation information from decision-makers, in which an optimization model is constructed to determine the weights of decision-makers. Next, an extended ORESTE method based on cumulative prospect theory and interval 2-Tuple linguistic variables is incorporated into the Fine-Kinney model to prioritize OHS risk. After that, the OHS risk assessment of the automobile components manufacturing process is presented to test the applicability and rationality of the improved Fine-Kinney model. After that, a sensitivity analysis is conducted to further illustrate the proposed model. Finally, the comparative analyses between the proposed risk assessment approach and other Fine-Kinney models are led to illustrating its effectiveness and advantages.

A collaborative emergency decision making approach based on BWM and TODIM under interval 2-tuple linguistic environment.

Emergencies require various emergency departments to collaborate to achieve timely and effective emergency responses. Thus, the overall performance of emergency response is influenced not only by the efficiency of each department alternative but also by the coordination effect among different department alternatives. This paper proposes a collaborative emergency decision making (CEDM) approach considering the synergy among different department alternatives based on the best–worst method (BWM) and TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method within an interval 2-tuple linguistic environment. First, the evaluation information provided by decision makers (DMs) is represented by interval 2-tuple linguistic variables to reflect and model the underlying diversity and uncertainty. On the basis of the DMs’ evaluations, the individual and collaborative performance evaluations of multi-alternative combinations composed of different department alternatives are constructed. Then, the BWM is extended into interval 2-tuple linguistic environment to obtain the weights of evaluation criteria, where the group decision making is taken into account in an interval fuzzy mathematical programming model. Furthermore, to derive more practical and accurate decision results, an interval 2-tuple linguistic TODIM (ITL-TODIM) method is proposed by considering the DMs’ psychological behaviours. In the developed ITL-TODIM method, both the gain and loss degrees of one alternative relative to another are simultaneously computed. Finally, a numerical example is presented to illustrate the applicability of the proposed method. Sensitivity and comparative analyses are also provided to demonstrate the effectiveness and advantages of the proposed approach.

Three-Way Decisions Based on Q-Rung Orthopair Fuzzy 2-Tuple Linguistic Sets with Generalized Maclaurin Symmetric Mean Operators

As a typical model of three-way decisions (3WD), decision-theoretic rough sets (DTRS), have gained attention from scholars in decision-making problems. The q-rung orthopair fuzzy 2-tuple linguistic variable (QROF2-TLV) is a mixture of two different notions, q-rung orthopair fuzzy sets (QROFS) and 2-tuple linguistic variables (2-TLV), and is an extensive and proficient technique for coping with awkward and complicated information in realistic decision-making. In this paper, we first propose a DTRS model for 3WD based on QROF2-TLV that gives a new method for evaluating loss functions (LF) of DTRS. We further present the q-rung orthopair fuzzy 2-tuple linguistic generalized Maclaurin symmetric mean (QROF2-TLGMSM) and weighted QROF2-TLGMSM operators and then provide the LFs of DTRS based on QROF2-TLV with the values aggregated by the QROF2-TLGMSM operator. Thus, we propose the q-rung orthopair fuzzy 2-tuple linguistic variable DTRS (QROF2-TLV-DTRS) model. Subsequently, a technique for concluding another DTRS model, which can give the related semantic translation of the decision consequences of every other option, is presented. The model is applied to expound the proposed technique in detail, and the impacts of various conditional probabilities on decision outcomes are discussed. A comparative analysis of the proposed approach is also conducted to examine the proficiency of the proposed method.

Group operations and isomorphic relation with the 2-tuple linguistic variables

This paper aims to put forth the theory of 2-tuple linguistic groups concerning the binary operation in the conventional sense. For this, a formal methodology has been introduced to prove that a predefined nonempty linguistic term set, LT, and the interval, $$[\frac{-1}{2},\frac{1}{2}]$$ , forms a group. Further, we have proved that a set of all 2-tuple linguistic information, $$\overline{LT} \equiv LT \times [\frac{-1}{2},\frac{1}{2}]$$ , and numerical interval, $$[-n,n]$$ , where n is presumed to be a positive integer, also forms a group. Later on, we develop a one-to-one correspondence and homomorphic group relation between the set of all 2-tuple linguistic information and numerical interval, $$[-n,n]$$ . Henceforth, a similarity relation between the two groups is obtained. Finally, a practical application is defined by proposing the notion of a 2-tuple linguistic bipolar graph to illustrate the usefulness and practicality of the group isomorphic relation.

A Two-Phase Model for Personnel Selection Based on Multi-Type Fuzzy Information

From the viewpoint of human resource management, personnel selection is one of the more important issues for enterprises in a high-level competitive environment. In general, many influence factors, quantitative and qualitative, affect the decision-making process of personnel selection. For considering qualitative factors, decision-makers cannot always easily judge the suitable degree of each applicant. Under this situation, this research proposes a systematic decision-making method based on computing with linguistic variables. First, unsuitable applicants are filtered by considering the quantitative information of each applicant. At this stage, technique for order of preference by similarity to ideal solution (TOPSIS) and entropy methods are aggregated to eliminate unsuitable applicants in accordance with their closeness coefficient values. Second, experts (or decision-makers) use different types of 2-tuple linguistic variables to express their opinions of suitable candidates with respect to qualitative criteria. At this stage, we consider different preference functions in the preference ranking organization method for enrichment evaluation (PROMETHEE) method to calculate the outranking index of each suitable candidate. Next, we aggregate the closeness coefficient and outranking index of each suitable applicant to determine the ranking order. In order to illustrate the computational processes, an example demonstrates the practicability of the two-phase personnel selection method. The benefit of the proposed method is as follows. (1) It reduces the time for reviewing and evaluating the huge numbers of applicants. (2) It avoids subjective judgment by experts to determine the weights of all criteria. Finally, conclusions and contributions are discussed at the end of this paper.

Interval 2‐tuple Pythagorean fuzzy linguistic MULTIMOORA method with CIA and their application to MCGDM

The reliable evaluation of financial performance of universities plays an important role in sustainable development of universities, and it could be regarded as a multicriteria group decision making problem. Based on this, in this paper, with respect to the attribute evaluation values are expressed by interval 2-tuple Pythagorean fuzzy linguistic variables, we develop an extended MULTIMOORA method. First, we propose the interval 2-tuple Pythagorean fuzzy linguistic set based on Pythagorean fuzzy set and interval-valued 2-tuple linguistic variables, and further introduce the score and accuracy functions and Hamming distance of it. Then, considering that there are some deficiencies in the traditional MULTIMOORA method, such as exist the case of circular reasoning, and so forth. We improve it by proposing a comprehensive integration approach, which can not only consider both the utility values and sort results, but also reflect the preference attitude of decision makings simultaneously. Based on these research findings, an interval 2-tuple Pythagorean fuzzy linguistic MULTIMOORA method is presented and the calculation process of this method is described in detail. Finally, we give the numerical example concerning the evaluation of financial management performance in universities to illustrate practicability and reliability of the proposed approach and compare the proposed method with different methods to perform its flexibility.

Emergency medical center location problem with people evacuation solved by extended TODIM and objective programming

This study aims to decide the location of emergency medical centers and the evacuation of survivors after a disaster happened. An extended interactive multi-criteria decision making method (TODIM) with interval 2-tuple linguistic variables is proposed to evaluate the potential locations of the emergency medical centers. A bi-objective mixed-integer programming is then established to determine the final locations and the evacuation plan based on previous evaluations. A real case of an earthquake in Wenchuan, China in 2008 is analyzed to demonstrate the effectiveness of our method.

A Competitive Multiattribute Group Decision-Making Approach for the Game between Manufacturers.

Under the competitive market environment, the game between manufacturers comes down to the competitive multiattribute group decision-making problem. In this study, the evaluation information of experts is given in the form of 2-dimension 2-tuple linguistic variables, and an approach is proposed for the competitive multiattribute group decision-making problem based on game theory and evidence theory. Firstly, based on the evidence theory, the attribute values of each situation are obtained by aggregating the 2-dimension 2-tuple linguistic evaluation information given by experts. Secondly, according to the attribute values of every situation, the evidence theory is applied for the second aggregation to obtain the overall values of every situation, and then the game matrix of competitive multiattribute group decision problem is formed. Then, according to the bivariate game matrix, the Nash equilibrium point of competitive multiattribute group decision-making problem is determined based on game theory. Finally, a practical case about the alternative selections for a duopoly problem is used to illustrate the effectiveness and applicability of the proposed approach for the competitive multiattribute group decision-making problem.

Integrating interval-valued multi-granular 2-tuple linguistic BWM-CODAS approach with target-based attributes: Site selection for a construction project

The site selection procedure for mega-structure projects can be an effective tool that could considerably improve the amount of income generation potential. Evidently, selecting the optimal location to establish a shopping center in a metropolitan area of Tehran, Iran is challenging due to the complexity of several conflicting evaluation criteria as well as multiple alternatives. Moreover, the site selection process of a mega-structure project can be viewed as a multiple attribute decision making (MADM) problem. Additionally, in such complex environments decision-makers and policy-makers usually might utilize linguistic terms to evaluate different alternatives with respect to multiple evaluation criteria according to their experience, qualifications, and preferences. Moreover, in real-world decision-making assessment problems, decision-makers tend to assign specific target-values for the selection attributes to obtain their optimal choices. In response, this study solves a site selection problem using a hybrid multi-granular interval-valued 2-tuple linguistic variables and target-valued criteria with the Best-Worst Method (BWM) and COmbinative Distance-based ASsessment (CODAS). Using the suggested hybrid MADM approach can results in an optimal and comprehensive site selection process without information loss. Finally, the outcomes of the current study show that the proposed target-based method is an optimal technique for such decision-making problems.

Advanced FMEA method based on interval 2-tuple linguistic variables and TOPSIS

Failure mode and effects analysis (FMEA) is a widely used technique for identifying, evaluating, and eliminating potential failures in production, system, and process. The traditional FMEA ranks the failure modes according to risk priority numbers (RPN), which are obtained by the multiplications of the crisp values of risk factors, such as occurrence (O), severity (S), and detection (D). However, the traditional FMEA is criticized for mishandling uncertain information and calculating RPN unreasonably. To overcome the above deficiencies, this study presents an advanced FMEA method combined with interval 2-tuple linguistic variables (ITLV) and technique for order preference by similarity to ideal solution (TOPSIS). In the proposed method, the evaluations given by different FMEA members based on their different linguistic term sets are represented by ITLVs, which are feasible and valid variables to effectively deal with uncertain information. The TOPSIS method is used to rank the risk priorities of failure modes by comprehensively considering all of risk factors. Finally, an application case is provided to illustrate the validity and robustness of the proposed method.

Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Materials Selection Using a 2-tuple Linguistic Multi-criteria Method

The materials selection can affect the design component radically, with effect on the manufacturing systems efficiency, environmental impact issues, and customer satisfaction. There are different methods employed for materials selection; however, two steps are usual for most of these methods: screening and ranking. The ranking step identifies among materials candidates those that can perform the function the best as possible. Multi-criteria methods have been widely employed to materials selection, especially in the ranking step. Most of these methods take advantage of fuzzy numbers and linguistic variables to process qualitative information and information with uncertainties. One of the approaches that have been developed to solve issues related to make decisions in multi-criteria methods using linguistic information is the 2-tuple linguistic computational model. The main advantage of this approach is taking the “loss of information” away, which provides a higher precision on results. This paper aims to present a multi-criteria method for materials selection ranking step based on 2-tuple linguistic variables. The steps and several equations needed to apply the proposed method are described. Two case studies are presented and compare results with other methods to demonstrate the proposed method potential.

Application of a FMEA method combining interval 2-tuple linguistic variables and grey relational analysis in preoperative medical service process

In general, the patients must pass through a series of preoperative hospital services before being operated in the operating theatre. Since the low efficiency of the services involved in the pre-operative procedures may have significant impact on the operating theatre, the hospital management should not only focus on the optimal allocation of the resources at the operating theatre, but also take actions to improve the service quality of key resources involved in the pre-operative procedures. In this study, a failure mode and effect analysis model (FMEA) is developed in combination with interval 2-tuple linguistic and gray relational analysis to evaluate the possible risks for medical services involved in the pre-operative process of a special hospital. The purpose of this study is to unveil the possible factors that may lead to the low efficiency and low quality of such medical service so as to provide corresponding recommendations to improve their service quality, and indirectly improve the efficiency of the operating theatre of the targeted hospital.

A large group decision making approach for dependence assessment in human reliability analysis

Human reliability analysis (HRA) is a systematic technique to assess human contribution to system risk and has been widely used in diverse complex systems. Dependence assessment among human errors is an important activity in HRA, which depends heavily on domain experts’ knowledge and experience. Normally, it is common for experts to give their judgments using linguistic labels and different types of uncertainties may exist in the dependence assessments. Additionally, the existing dependence assessment methods are limited to small-scale expert groups, which reduce the accuracy of dependence analysis with the increasing complexity of high risky systems. In this article, we develop a large group dependence assessment (LGDA) model based on interval 2-tuple linguistic variables and cluster analysis method to manage the dependence in HRA. Further, we propose an extended Muirhead mean operator to determine the dependence levels between consecutive operator actions. Finally, an empirical healthcare dependence analysis is taken as an example to illustrate the effectiveness and practicality of our proposed LGDA approach.

Prioritized Aggregation Operators and Correlated Aggregation Operators for Hesitant 2-Tuple Linguistic Variables

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness.