2-tuple Linguistic Preference Relations Research Articles

2-tuple linguistic decision-making with consistency adjustment strategy and data envelopment analysis

2-tuple linguistic preference relations (2-TLPRs) are useful tools for addressing decision-making issues where the decision makers (DMs) are inclined to apply linguistic variables to express evaluation information. To retain the DM’s initial preference information as much as possible, this paper provides a 2-tuple linguistic decision-making method that incorporates a consistency adjustment algorithm and a 2-tuple linguistic data envelopment analysis (DEA) model. As two important aspects of decision-making, it is worthy to further study the improvements in consistency and weight generation for alternatives with 2-TLPRs. In this paper, in order to adjust the consistency of an original 2-TLPR to a predetermined level, a convergent consistency-improving algorithm is first presented, and we employ a minimum adjustment strategy to preserve the DM’s initial evaluation information. A 2-tuple linguistic DEA model is then developed to generate a vector of weights for the alternatives and we can derive reliable decision-making results. Finally, we provide a numerical example that can identify the most influential factor in Fog–haze weather to indicate the applicability of the 2-tuple linguistic decision-making method. The comparative analysis highlights the advantages and effectiveness of the 2-tuple linguistic decision-making method.

A Fuzzy Evaluation Approach for Scientific Research Projects with 2-Tuple Linguistic Preference Relations

Science and technology project evaluation is an important means of science and technology management. Whether the evaluation of science and technology projects is fair or not directly affects the development of national economy and the allocation of science and technology resources. Due to the complexity of the project and the fuzziness of human thinking, the expert information is often difficult to quantify in the process of project evaluation. Generally, the better choice is to express it in qualitative language. In this paper, the 2-tuple linguistic preference relation is proposed to evaluate scientific research projects. The reasonableness of the concept of complete consistency for the 2-tuple linguistic preference relation is discussed. Priority of 2-tuple linguistic preference relation is set up based on the 2-tuple weighted geometric averaging operator. Finally, combined with Science and technology project evaluation problem, the effectiveness and feasibility of the method are verified.

On Consistency and Priority Weights for Uncertain 2-Tuple Linguistic Preference Relations

Consistency and priority weights of preference relations are two important phases of decision-making process since the decision-making solutions are determined by them. Therefore, it is meaningful to investigate consistency and priority weights for preference relations. In this paper, consistency and uncertain 2-tuple linguistic priority weights of uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First, based on the additive consistency, an additive consistency index is developed to measure the additive consistency level of U2TLPRs. Second, a goal programming model is proposed to adjust the unacceptable additive consistent U2TLPR until it satisfies acceptable additive consistency. Furthermore, an optimization model is developed to derive the uncertain 2-tuple linguistic priority weights from an U2TLPR. Meanwhile, in group decision-making (GDM) problems, similarities and confidence degrees of decision makers (DMs) are defined to determine DMs’ weights. Subsequently the properties of collective U2TLPR are discussed. Finally, the proposed methods are implemented in two examples including a GDM problem to verify the validity of the proposed methods.

Additive consistency-based approach for group decision making with hesitant 2-tuple linguistic preference relations

Additive consistency-based approach for group decision making with hesitant 2-tuple linguistic preference relations

An Interactive Consensus Model for Group Decision-Making with Incomplete Multi-Granular 2-Tuple Fuzzy Linguistic Preference Relations

As a result of the heterogeneity of decision-makers, it is more suitable to use multi-granular linguistic information to express assessing information over alternatives for decision-makers. Decision-makers may only provide partial preference information as the limitation of knowledge over the alternatives. Thus, the incomplete multi-granular 2-tuple fuzzy linguistic preference relations (IMGFLPRs) can be applied to manage the GDM problems in complex environments. In this paper, we propose a novel group decision-making (GDM) model based on mathematical programming with IMGFLPRs. It is more important that the proposed mathematical programming can directly deal with IMGFLPRs and does not need to be converted into a uniform form. By this means, we construct a consensus reaching process based on IMGFLPRs, considering simultaneously dynamic adjustment of experts’ weight. Finally, an emergency plan selection problem is solved by the proposed model, which shows the result of GDM is effectiveness.

A Multicriteria Decision-Making Approach Based on Fuzzy AHP with Intuitionistic 2-Tuple Linguistic Sets

In the modern literature related to linguistic decision-making, the 2-tuple linguistic representation model and its useful applications in various fields have been extensively studied and used during the last decade. Recently, some useful multicriteria decision-making (MCDM) methods have been introduced based on fuzzy analytic hierarchy process (AHP) for 2-tuple linguistic representation model. By keeping in mind the importance of this linguistic model, in this paper, we introduce a fuzzy AHP methodology for intuitionistic 2-tuple linguistic sets (I2TLSs) which is a useful extension of the 2-tuple linguistic representation model. This study is comprised of four stages. In the first stage, we define some operational laws for I2TL elements (I2TLEs) and prove some related important properties. In the second stage, intuitionistic 2-tuple linguistic preference relation (I2TLPR) and multiplicative I2TLPR are defined using I2TLSs. In the 3rd stage, a transformation mechanism is introduced which can transform an I2TLPR to a corresponding intuitionistic preference relation (IPR) and vice versa. In the fourth stage, an approach is proposed for checking the consistency of an I2TLPR and presented a method to repair the inconsistent one by using the proposed transformation mechanism. Finally, a numerical example is given and comparative analysis is carried out with the TOPSIS method to verify the validity of the proposed method.

A multi criteria comprehensive evaluation approach for emergency response capacity with interval 2-tuple linguistic information

Emergency response capacity evaluation (ERCE) is an important and challenging issue in emergency management with the frequent occurrence of emergency events. Because of their different backgrounds and preferences, decision makers (DMs) often prefer to use linguistic variables from different linguistic term sets to express their decision information about the importance and the ratings of multi criteria involved in ERCE issue, some of which may be imprecise and uncertain. Therefore, this paper proposes a multi criteria comprehensive evaluation (MCCE) approach for ERCE with interval 2-tuple linguistic information. First, a new method for comparison between interval 2-tuples is proposed. Then, the classic analytical hierarchy process is extended into the ITL-AHP, in which the interval 2-tuple linguistic preference relation (ITLPR) and its multiplicative consistency are defined. An iterative algorithm to improve the consistency level of an ITLPR is proposed. Based on improved ITLPRs, the priority weights of criteria are derived by the normalizing rank summation method. In individual decision information collecting processes, both subjective weights and objective weights of DMs are considered. Furthermore, some interval 2-tuple interval weighted aggregation operators in which the weight vectors take the form of interval 2-tuple linguistic information are developed. Finally, a numerical illustration and comparison analyses are provided to elucidate the feasibility and superiority of the proposed method. The proposed method can provide a flexible way to perceive and appraise the emergency response capacity (REC) and an effective tool to handle the emergency management performance evaluation and decision making under fuzzy and uncertain information environment.

A minimum deviation approach for improving the consistency of uncertain 2-tuple linguistic preference relations

Abstract This paper proposes a novel approach for improving the consistency of uncertain 2-tuple linguistic preference relations (U2TLPRs). In particular, we introduce a new definition of consistency for U2TLPRs and show that the degree of consistency of a given U2TLPR can be measured explicitly by minimizing its deviation from a consistent U2TLPR. Based on this finding, we provide an iterative algorithm for repeatedly adjusting the consistency of a U2TLPR to a desired level while taking into account the initial preferences of decision makers. In addition, by analyzing the structural properties of the algorithm, we further present an improved version of the procedure for directly obtaining an acceptable U2TLPR without any iteration. Numerical results indicate that the proposed method is not only simple and efficient in calculation but also effective in preserving the original preference information provided by decision makers.

Discussing incomplete 2-tuple fuzzy linguistic preference relations in multi-granular linguistic MCGDM with unknown weight information

Owing to the vagueness of real-world environments and limited knowledge of human beings, it is natural for decision makers to express their preferences by means of incomplete 2-tuple fuzzy linguistic preference relations (FLPRs). Besides, since different decision makers possess distinctive educational and academic background, they may select linguistic term sets with different granularities to represent their opinions. This study primarily focuses on multi-granular linguistic multi-criteria group decision-making (MCGDM) based on incomplete 2-tuple FLPRs. First, we introduce an extended four-way procedure for estimating unknown elements from an acceptable incomplete 2-tuple FLPR as well as a completion method for obtaining unknown linguistic 2-tuples in an unacceptable incomplete 2-tuple FLPR. Based on the four ways for estimating unknown values, a formula is then established to calculate the consistency index of an incomplete 2-tuple FLPR. Second, a 2-tuple linguistic induced generalized ordered weighted averaging operator is introduced and further analyzed from different aspects. Subsequently, by systematically fusing the aforementioned contributions, a novel approach is developed to address MCGDM problems with multi-granular incomplete 2-tuple FLPRs and unknown weight information. Specifically, the importance weights of decision makers with respect to different criteria are decided by the corresponding consistency indices. Finally, an investment problem is furnished to illustrate the application of our proposed approach.

Completing 2-tuple linguistic preference relations based on upper bound condition

The purpose of this paper is to propose a method to estimate missing preference values when handling incomplete linguistic preference relations assessed by using 2-tuple linguistic preference values. We assert that additive transitivity alone may result in estimated values that do not qualify as 2-tuple linguistic preference values. Therefore, an upper bound condition based on additive transitivity is proposed to deal with incomplete 2-tuple linguistic preference relations (2TLPRs). We prove that if experts with incomplete information abide by this property, then the missing preference values can be estimated such that they are expressible. Additionally, because of this property, the resultant complete 2TLPR is proved to be consistent. Based on additive transitivity and the upper bound condition, an interactive completing algorithm is developed to estimate the missing entries in incomplete 2TLPR. When the upper bound condition is not satisfied or there exist entries that do not coincide with the real opinions of the experts, the proposed algorithm can automatically adjust the known entries by interacting with the experts. By using the proposed algorithm, the completed 2TLPR is not only additively consistent, but also can accurately reflect the actual preference of the experts.

A group consensus decision support model for hesitant 2-tuple fuzzy linguistic preference relations with additive consistency

Hesitant fuzzy linguistic term sets suit the modelling of qualitative setting so that experts provide several possible linguistic values than a single term for an indicator, alternative, variable, etc. This paper proposes a consistency and consensus based decision support model for group decision m aking with hesitant 2-tuple fuzzy linguistic preference relations (H2TFLPRs). A revised definition of hesitant fuzzy linguistic preference relation (HFLPR) is presented. In order to measure the consensus degrees, two indexes, an individual to group consensus index (ICI) and a group consensus index (GCI) are introduced, respectively. A consistency control process is developed to transform an unacceptable consistency H2TFLPR to an acceptable one. Then, an iterative group consensus reaching process is designed to conduct the decision makers (DMs) to achieve the predefined consensus level. In the consistency and consensus improving process, both the feedback mechanism and no-feedback mechanism are devised to conduct the DMs how to modify their original judgments, and both mechanisms can retain the DMs’ original information as much as possible. Finally, a numerical example is illustrated to demonstrate the effectiveness of the proposed method.

A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms

As a result of uncertainty and complexity for environments of decision-making, it is more suitable for decision makers to use hesitant fuzzy linguistic information. In this paper, a novel group decision making (GDM) model based on fuzzy linear programming is proposed for incomplete comparative expressions with hesitant fuzzy linguistic term set (HFLTSs). We establish an equivalence theorem of additive consistency between 2-tuple fuzzy linguistic preference relation (FLPR) and corresponding fuzzy preference relation. Based on this framework, a fuzzy linear programming is established to address incomplete comparative expressions with HFLTSs. It is more important that the proposed fuzzy linear programming has a double action, finding the highest consistent incomplete 2-tuple FLPR and increasing inconsistent 2-tuple FLPR to the additive consistent 2-tuple FLPR based on given incomplete comparative expressions with HFLTSs. By this means, a novel GDM model is constructed based on importance induced ordered weighted averaging operator. Finally, an investment decision-making in real-world is solved by the proposed model, which shows the result of GDM is effectiveness.

Supplier selection using ANP and ELECTRE II in interval 2-tuple linguistic environment

In supply chain management, supplier selection can be treated as a type of hierarchical multi-criteria decision-making (MCDM) problems since it involves various criteria and hierarchical structure among criteria often exists. This paper investigates a kind of MCDM problems with two-level criteria and develops a novel hybrid method integrating TL-ANP (2-tuple linguistic analytic network process) and IT-ELECTRE II (interval 2-tuple Elimination and Choice Translating Reality II). Considering interactions among criteria, a TL-ANP approach, in which comparison matrices are consistent 2-tuple linguistic preference relations, is put forward to determine weights of criteria and sub-criteria. To deal with the case of criteria being not compensated, an IT-ELECTRE II approach is proposed. In this approach, ratings of alternatives on sub-criteria are represented as interval 2-tuple linguistic variables. A possible degree and a likelihood-based preference degree are respectively defined, followed by concordance, discordance and indifferent sets. Afterwards, concordance and discordance indices are identified and applied to establish net concordance and net discordance indices. Further, comprehensive dominant values of alternatives are obtained to rank alternatives. Thereby, a novel hybrid method is presented for MCDM with two-level criteria under interval 2-tuple linguistic environment. At length, a real case of supplier selection is examined and comparison analyses are conducted to illustrate the application and superiority of the proposed method.

Consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations

Due to the uncertainty of the decision environment and the lack of knowledge, decision-makers may use uncertain linguistic preference relations to express their preferences over alternatives and criteria. For group decision-making problems with preference relations, it is important to consider the individual consistency and the group consensus before aggregating the preference information. In this paper, consistency and consensus models for group decision-making with uncertain 2-tuple linguistic preference relations (U2TLPRs) are investigated. First of all, a formula which can construct a consistent U2TLPR from the original preference relation is presented. Based on the consistent preference relation, the individual consistency index for a U2TLPR is defined. An iterative algorithm is then developed to improve the individual consistency of a U2TLPR. To help decision-makers reach consensus in group decision-making under uncertain linguistic environment, the individual consensus and group consensus indices for group decision-making with U2TLPRs are defined. Based on the two indices, an algorithm for consensus reaching in group decision-making with U2TLPRs is also developed. Finally, two examples are provided to illustrate the effectiveness of the proposed algorithms.

Consensus-Based Group Decision Making Under Multi-granular Unbalanced 2-Tuple Linguistic Preference Relations

In group decision making (GDM) situations, it is quite natural that the decision makers who may have different background and knowledge will provide their preferences by means of different linguistic term sets. Specifically, multi-granular linguistic term sets that are not uniformly and symmetrically distributed will be employed. To deal with this type of GDM problems, this paper proposes a consensus-based GDM model by using two existing 2-tuple linguistic representation models (i.e., the Herrera and Martinez model and the Wang and Hao model), which we called the GDM model based on multi-granular unbalanced 2-tuple linguistic preference relations. First, the framework of the GDM model with multi-granular unbalanced 2-tuple linguistic preference relations is proposed. Then, the transformation function is obtained to relate multi-granular unbalanced linguistic preference relations with uniform balanced linguistic preference relations. Further, a consensus model is presented to help the decision makers reach a consensus. This consensus model not only provides a new way to simultaneously manage individual consistency and group consensus in a linear programming model, but also minimizes information loss (or consensus cost) when reaching the established consensus level. Finally, an example is given to illustrate the feasibility and validity of the proposed model.

Consistency-based algorithms to estimate missing elements for uncertain 2-tuple linguistic preference relations

AbstractFor actual decision making problems, decision makers sometimes may have difficulty to provide all the preference information over alternatives through pairwise comparisons. In this paper, we focus on estimating missing elements for an incomplete uncertain 2-tuple linguistic preference relation. First, the additive consistency of an uncertain 2-tuple linguistic preference relation is defined. Based on the defined additive consistency, we define acceptable incomplete uncertain 2-tuple linguistic preference relation and propose two new algorithms, including an iterative algorithm and an optimization-based algorithm to estimate the missing elements for an uncertain 2-tuple linguistic preference relation. Finally, some numerical examples are presented to illustrate the applicability of the two algorithms.

Some methods to deal with unacceptable incomplete 2-tuple fuzzy linguistic preference relations in group decision making

In this paper, we first propose a four-way procedure to estimate missing preference values when dealing with acceptable incomplete 2-tuple fuzzy linguistic preference relations (FLPRs). The proposed revised procedure can estimate more missing elements in the first iteration and also has more advantages than the existing methods. Then, we address situations in which an expert do not provide any comparison information for a particular alternative with other alternatives, and thus provides an unacceptable incomplete 2-tuple FLPR. We propose some methods to deal with the unacceptable situations. The main idea of these methods is to set some seed values for the unknown alternative and then to complete the unacceptable incomplete 2-tuple FLPRs by the revised procedure. We also give a simple algorithm to select the best alternative for the group decision making (GDM) problem with incomplete 2-tuple FLPRs. The analysis of advantages and drawbacks for each method are also presented.

The optimal group consensus models for 2-tuple linguistic preference relations

We establish in this paper the optimization model of group consensus of 2-tuple linguistic preferential relations (LPRGCO Model), put forward three kinds of solutions to this model, and discover in it the convergence of group consensus. To detect the LPRGCO Model, we first build two kinds of optimal matrices as standards to measure the group consensus of 2-tuple linguistic preference relations (LPRs). And to analyze consensus deviations, we then adopt three types of measures, namely, the individual degree of consistency regarding alternative decision pairs, the deviational degree of the group consensus regarding alternative decision pairs, and the degree of group consensus regarding the original 2-tuple LPRs. On the basis of the previous analysis we not only construct an optimization model to probe into the deviation of the group consensus of 2-tuple LPRs by minimizing the weighted arithmetic average of deviation degrees of individual consistency, but also point out three feasible solutions to this optimization model: the optimal solution, satisfactory solutions, and non-inferior solutions. Accordingly, we discover different conditions in terms of the three solutions. And hence, we can from the aforementioned discussion draw a conclusion that the deviation of group consensus either decreases or stays invariant as the number of decision makers (DM) increases. To expatiate on the practical value of the model proposed, we will display in this paper numerical examples.

Group decision making with 2-tuple intuitionistic fuzzy linguistic preference relations

The aim of this paper is to propose a new type of preference relation, the intuitionistic fuzzy linguistic preference relation (IFLPR). Taking as base the 2-tuple fuzzy linguistic representation model, we introduce the definition of the IFLPR, and its transitivity properties. We present an approach to group decision making based on IFLPRs and incomplete-IFLPRs, respectively. The score function and accuracy function are applied to the ranking and selection of alternatives. Finally, we give an example of IFLPRs in group decision making, and a comparative of the exploitation of the IFLPR with the exploitation of the traditional fuzzy linguistic preference relations.