AN EXTENDED HIERARCHICAL LINGUISTIC MODEL FOR DECISION‐MAKING PROBLEMS

In multi‐expert decision making (MEDM) problems the experts provide their preferences about the alternatives according to their knowledge. Because they can have different knowledge, educational backgrounds, or experiences, it seems logical that they might use different evaluation scales to express their opinions. In the present article, we focus on decision problems defined in uncertain contexts where such uncertainty is modeled by means of linguistic information, therefore the decision makers would use different linguistic scales to express their evaluations on the alternatives, i.e., multigranular linguistic scales. Several computational approaches have been presented to manage multigranular linguistic scales in decision problems. Although they provide good results in some cases, still present limitations. A new approach, so‐called extended linguistic hierarchies, is presented here for managing multigranular linguistic scales to overcome those limitations, an MEDM case study is given to illustrate the proposed method.     

Consensus reaching for group decision making with multi-granular unbalanced linguistic information: A bounded confidence and minimum adjustment-based approach

In group decision making problems, there exist the situations that decision makers may use unbalanced linguistic term sets that are not uniformly and symmetrically distributed to provide their linguistic assessments over alternatives. Moreover, due to the difference in knowledge and culture backgrounds, it is also possible that multi-granular linguistic term sets may also be used by decision makers. How to manage multi-granular unbalanced linguistic information in consensus-based group decision making has becoming an important topic in linguistic decision making. In this paper, we first revise Herrera’s unbalanced linguistic term sets and propose a simplified linguistic computational model to fuse multi-granular unbalanced linguistic terms. Afterwards, for multi-criteria group decision making problems with multi-granular unbalanced linguistic information, we develop two optimization models to generate adjustment advice for decision makers who have to change his/her opinions in consensus reaching process, which consider both the bounded confidence levels and minimum adjustment of decision makers’ linguistic assessments. Moreover, an algorithm is further proposed to help decision makers reach consensus in group decision making. Eventually, an application example for ERP system supplier selection and some simulation results are presented to illustrate and justify the consensus reaching algorithm.     

Group decision making model and approach based on interval preference orderings

In group decision making under uncertainty, interval preference orderings as a type of simple uncertain preference structure, can be easily and conveniently used to express the experts’ evaluations over the considered alternatives. In this paper, we investigate group decision making problems with interval preference orderings on alternatives. We start by fusing all individual interval preference orderings given by the experts into the collective interval preference orderings through the uncertain additive weighted averaging operator. Then we establish a nonlinear programming model by minimizing the divergences between the individual uncertain preferences and the group’s opinions, from which we derive an exact formula to determine the experts’ relative importance weights. After that, we calculate the distances of the collective interval preference orderings to the positive and negative ideal solutions, respectively, based on which we use a TOPSIS based approach to rank and select the alternatives. All these results are also reduced to solve group decision making problems where the experts’ evaluations over the alternatives are expressed in exact preference orderings. A numerical analysis of our model and approach is finally carried out using two illustrative examples.     

Adaptive consensus support model for group decision making systems

In this paper, we present an adaptive consensus support model for group decision making systems based on intervals of linguistic 2-tuples. The proposed method has the following advantages: (1) the evaluating values can either be represented by linguistic terms or intervals of linguistic terms, (2) if the required consensus degree is too high, then the proposed adaptive consensus support model can modify experts’ preferences to improve convergence toward a higher consensus degree or a sufficient agreement for group decision making and (3) the proposed method is an interactive method, where each expert can modify the adjustments made by the system during the consensus reaching process if he/she does not agree with the adjustments made by the system. The proposed adaptive consensus support model can overcome the drawback of Mata et al.’s method (2009). It provides us with a useful way for adaptive consensus support for group decision making based on intervals of linguistic 2-tuples.     

Group decision making with fuzzy linguistic preference relations via cooperative games method

When we consider the weighting approach for group decision making with fuzzy linguistic preference relations, the groupment of experts has merely been studied. In this paper, a novel weighting approach on the basis of cooperative games method is developed. The group decision error matrix is built to reflect the deviations of all experts with given initial weighting vector. An iterative algorithm is designed to lower the sum of the decision error so that a final convergence result can be obtained. The advantage of the weighting algorithm is that it can consider the contribution of each expert and reduce the sum of decision error with increasing iteration numbers. Then an optimization model using triangular fuzzy numbers as alternatives’ weights is constructed, whose results are used to rank the alternatives. Finally, a numerical example of subjective evaluation of vehicle sound quality is considered to illustrate the feasibility and validity of the proposed weighting approach in the group decision making problem.     

An Intuitionistic 2‐Tuple Linguistic Information Model and Aggregation Operators

Dealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. Fuzzy sets was presented to manage situations in which experts have some membership value to assess an alternative. The fuzzy linguistic approach has been applied successfully to many problems. The linguistic information expressed by means of 2‐tuples, which were composed by a linguistic term and a numeric value assessed in [ ? 0.5, 0.5). Linguistic values was used to assess an alternative and variable in qualitative settings. Intuitionistic fuzzy sets were presented to manage situations in which experts have some membership and nonmembership value to assess an alternative. In this paper, the concept of an I2LI model is developed to provide a linguistic and computational basis to manage the situations in which experts assess an alternative in possible and impossible linguistic variable and their translation parameter. A method to solve the group decision making problem based on intuitionistic 2‐tuple linguistic information (I2LI) by the group of experts is formulated. Some operational laws on I2LI are introduced. Based on these laws, new aggregation operators are introduced to aggregate the collective opinion of decision makers. An illustrative example is given to show the practicality and feasibility of our proposed aggregation operators and group decision making method.     

Weighted‐selective aggregated majority‐OWA operator and its application in linguistic group decision making

This paper focuses on the aggregation operations in the group decision‐making model based on the concept of majority opinion. The weighted‐selective aggregated majority‐OWA (WSAM‐OWA) operator is proposed as an extension of the SAM‐OWA operator, where the reliability of information sources is considered in the formulation. The WSAM‐OWA operator is generalized to the quantified WSAM‐OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM‐IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision‐making model under the linguistic domain, which consists of two‐stage aggregation processes, is developed in order to fuse the experts’ judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model.     

A novel approach for combination of individual and group decisions based on fuzzy best-worst method

The process of decision-making in an enterprise may either keep the business on track or derail it. Thus, a senior decision maker often use a group of experts as the supportive team to ensure appropriate decisions. The experts often have different expertise level regarding their knowledge, talent, proficiency, and experience. In this study, we first extend the best-worst method based on the linguistic preferences of decision-makers about importance of attributes. These preferences are converted into triangular fuzzy numbers to be utilized in the linear programming model. That is, in contrast with the original best-worst method in which the preferences towards the attributes are crisp, fuzzy preferences are considered in the proposed method to reflect the imprecise comments of experts. Second, we propose a novel group decision making approach based on the fuzzy best-worst method to combine the opinion of senior decision-maker and the opinions of the experts. Indeed, our model helps the senior decision-maker to make a significant trade-off between democratic and autocratic decision-making styles. From sensitivity analyses on two numerical examples, we show that, when there is conflict between senior decision-maker and group of decision-makers, the consistency of group decision-making (democracy) will increase as it tends to individual decision-making (autocracy).     

A consensus model for group decision making under interval type-2 fuzzy environment

We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situations. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute comparable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.     

Multiplicative consistency-based decision support system for incomplete linguistic preference relations

The experts may have difficulty in expressing all their preferences over alternatives or criteria, and produce the incomplete linguistic preference relation. Consistency plays an important role in estimating unknown values from an incomplete linguistic preference relation. Many methods have been developed to obtain a complete linguistic preference relation based on additive consistency, but some unreasonable values may be produced in the estimation process. To overcome this issue, we propose a new characterisation about multiplicative consistency of the linguistic preference relation, present an algorithm to estimate missing values from an incomplete linguistic preference relation, and establish a decision support system for aiding the experts to complete their linguistic preference relations in a more consistent way. Some examples are also given to illustrate the proposed methods.     

Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation

A large number of stakeholders take part in the process of decision making, namely, large-scale group decision making (LGDM) problems. Every stakeholder utilises a linguistic preference relation (LPR) to represent her/his preference information for alternatives. Then, a probabilistic LPR (PLPR) is established to represent the group preference. However, some stakeholders may only provide partial preference information about the alternatives. Thus, a PLPR with incomplete probabilities can be used to manage LGDM problems in complex environments. Based on the defined expected multiplicative consistency of PLPR, a probability computation model is established by mathematical programming to derive the missing probabilities of PLPR. In addition, an iterative algorithm to improve the consistency is proposed to obtain the PLPR with satisfactory consistency. Finally, a real-world investment decision-making problem with multiple stakeholders is solved to demonstrate the effectiveness of the proposed method.     

A consensus model for group decision making problems with linguistic interval fuzzy preference relations

Sometimes, we find decision situations in which it is difficult to express some preferences by means of concrete preference degrees. In this paper, we present a consensus model for group decision making problems in which the experts use linguistic interval fuzzy preference relations to represent their preferences. This model is based on two consensus criteria, a consensus measure and a proximity measure, and on the concept of coincidence among preferences. We compute both consensus criteria in the three representation levels of a preference relation and design an automatic feedback mechanism to guide experts in the consensus reaching process.     

On compatibility of uncertain additive linguistic preference relations and its application in the group decision making

We develop a new compatibility for the uncertain additive linguistic preference relations and utilize it to determine the optimal weights of experts in the group decision making (GDM). Based on some operational laws for the uncertain additive linguistic preference labels, we propose some new concepts of the compatibility degree and acceptable compatibility index for the two uncertain additive linguistic preference relations. We also prove the properties that the synthetic preference relation is also of acceptable compatibility under the condition that additive linguistic preference relations provided by experts are all of acceptable compatibility with the specific linguistic preference relation, which provides a theoretic basis for the application of the uncertain additive linguistic preference relations in the GDM. Furthermore, we establish a mathematical model to obtain the weights of experts based on the criterion of minimizing the compatibility in the GDM, and we discuss the solution to the model. Finally, we give a numerical example to make comparative analysis on compatibility index using the optimal experts’ weights approach and the equal experts’ weights approach, which indicates that the model is feasible and effective.     

A satisfactory-oriented approach to multiexpert decision-making with linguistic assessments.

This paper proposes a multiexpert decision-making (MEDM) method with linguistic assessments, making use of the notion of random preferences and a so-called satisfactory principle. It is well known that decision-making problems that manage preferences from different experts follow a common resolution scheme composed of two phases: an aggregation phase that combines the individual preferences to obtain a collective preference value for each alternative; and an exploitation phase that orders the collective preferences according to a given criterion, to select the best alternative/s. For our method, instead of using an aggregation operator to obtain a collective preference value, a random preference is defined for each alternative in the aggregation phase. Then, based on a satisfactory principle defined in this paper, that says that it is perfectly satisfactory to select an alternative as the best if its performance is as at least "good" as all the others under the same evaluation scheme, we propose a linguistic choice function to establish a rank ordering among the alternatives. Moreover, we also discuss how this linguistic decision rule can be applied to the MEDM problem in multigranular linguistic contexts. Two application examples taken from the literature are used to illuminate the proposed techniques.     

Trust based consensus model for social network in an incomplete linguistic information context

A theoretical framework to consensus building within a networked social group is put forward. This article investigates a trust based estimation and aggregation methods as part of a visual consensus model for multiple criteria group decision making with incomplete linguistic information. A novel trust propagation method is proposed to derive trust relationship from an incomplete connected trust network and the trust score induced order weighted averaging operator is presented to aggregate the orthopairs of trust/distrust values obtained from different trust paths. Then, the concept of relative trust score is defined, whose use is twofold: (1) to estimate the unknown preference values and (2) as a reliable source to determine experts’ weights. A visual feedback process is developed to provide experts with graphical representations of their consensus status within the group as well as to identify the alternatives and preference values that should be reconsidered for changing in the subsequent consensus round. The feedback process also includes a recommendation mechanism to provide advice to those experts that are identified as contributing less to consensus on how to change their identified preference values. It is proved that the implementation of the visual feedback mechanism guarantees the convergence of the consensus reaching process.     

Novel intuitionistic fuzzy decision making models in the framework of decision field theory

The intuitionistic fuzzy decision making problems have gained great popularity recently. Most of the current methods depend on various aggregation operators that provide collective intuitionistic fuzzy values of alternatives to be ranked. Such collective information only depicts the overall characteristics of the alternatives but ignores the detailed contrasts among them. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers (DMs) think about the decision making problems. In this paper, we develop a novel intuitionistic fuzzy decision making model in the framework of decision field theory. The decision making model emphasizes the contrasts among alternatives with respect to each attribute that competes and influences each other, and thus, the preferences for alternatives can dynamically evolve and provide the final optimal result. After that, we develop an intuitionistic fuzzy group decision making model based on decision field theory, and then make a practical case study on the application of the developed models to the “one belt, one road” investment decision making problems. Finally, we point out the characteristics and the limitations of our models in detail.     

Social Network Decision Making with Linguistic Trustworthiness–Based Induced OWA Operators

Classic aggregation operators in group decision making such as the ordered weighted averaging (OWA), induced ordered weighted averaging (IOWA), C‐IOWA, P‐IOWA, and I‐IOWA have shown to be successful tools to provide flexibility in the aggregation of preferences. However, these operators do not take advantage of information related to the interaction between experts. Experts involved in a group decision‐making problem may have developed opinions about the reliability of other experts' judgments, either because they have previous history of interaction with each other or because they have knowledge that informs them on the reliability of other colleagues in the group in solving decision‐making problems in the past. In this paper, and within the framework of social network decision making, we present three new social network analysis based IOWA operators that take advantage of the linguistic trustworthiness information gathered from the experts' social network to aggregate the social group preferences. Their use is analysed with simple but illustrative examples.     

Partitioned Bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making

In this study, a multi-attribute group decision making (MAGDM) problem is investigated, in which decision makers provide their preferences over alternatives by using linguistic 2-tuple. In the process of decision making, we introduce the idea of a specific structure in the attribute set. We assume that attributes are partitioned into several classes and members of intra-partition are interrelated while no interrelationship exists among inter partition. We emphasize the importance of having an aggregation operator, to capture the expressed inter-relationship structure among the attributes, which we will refer to as partition Bonferroni mean (PBM). We also investigate the behavior of the proposed PBM operator. Further to aggregate the given linguistic information to get overall performance value of each alternative in MAGDM, we analyze PBM operator in linguistic 2-tuple environment and develop three new linguistic aggregation operators: 2-tuple linguistic PBM (2TLPBM), weighted 2-tuple linguistic PBM (W2TLPBM) and linguistic weighted 2-tuple linguistic PBM (LW-2TLPBM). Based on the idea that total linguistic deviation between individual decision maker's opinions and group opinion should be minimized, we develop an approach to determine weight of the decision makers. Finally, a practical example is presented to illustrate the proposed method and comparison analysis demonstrates applicability of the proposed method.     

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and fusion: Taxonomy and future directions

The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed.     

Using a multi-criteria decision making approach to evaluate mobile phone alternatives

The arrival of the mobile phone and its rapid and widespread growth may well be seen as one of the most significant developments in the fields of communication and information technology over the past two decades. The aim of this study is to propose a multi-criteria decision making (MCDM) approach to evaluate the mobile phone options in respect to the users' preferences order. Firstly, the most desirable features influencing the choice of a mobile phone are identified. This is realized through a survey conducted among the target group, the experiences of the telecommunication sector experts and the studies in the literature. Two MCDM methods are then used in the evaluation procedure. More precisely, Analytic Hierarchy Process (AHP) is applied to determine the relative weights of evaluation criteria and the extension of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied to rank the mobile phone alternatives. A case study illustrates the effectiveness of the proposed approach.