Linguistic Distribution Assessments Research Articles

Prospect theory-based group decision-making with stochastic uncertainty and 2-tuple aspirations under linguistic assessments

Linguistic distribution assessments with probabilistic information are a flexible means to express the opinions of decision makers (DMs) with importance degree of each linguistic term. Therefore, research on multi-attribute group decision making (MAGDM) problems with linguistic distribution assessments is increasing. However, the probability distribution is usually only partially known. In order to obtain the complete probability distribution information, we propose the concept of stochastic linguistic term (SLT) with the aid of stochastic analysis. The SLT is an extension of general linguistic terms. Linguistic assessments with different models can be expressed as SLTs with complete probability distributions. Then the weighted averaging operator and score function of SLTs are presented. Considering the psychological behavior of DMs in decision making, we combine prospect theory and SLTs to handle uncertainty in MAGDM problems. Considering 2-tuple aspirations on attributes, a new MAGDM method with stochastic uncertainty based on prospect theory under linguistic assessments is proposed. Finally, a numeric example and comparative analysis illustrate the effectiveness and feasibility of the proposed method.

Integrating a consensus-reaching mechanism with bounded confidences into failure mode and effect analysis under incomplete context

Failure mode and effect analysis (FMEA) is one of the most powerful pre-accident risk management techniques and has been extensively used in various fields. Nevertheless, consensus issues and incomplete assessment information are rarely investigated in the current FMEA method. This paper integrates a consensus-reaching mechanism into the FMEA framework and adopts incomplete linguistic distribution assessments to represent risk assessment information. In the constructed FMEA framework, a deviation minimum-based optimization model is presented to manage incomplete assessment information, and this model aims to minimize the opinion deviation among FMEA members. Then, a consensus-reaching model with a novel feedback adjustment mechanism is proposed to assist FMEA members to gain a consensus. The novel feedback adjustment mechanism is based on a natural assumption that individuals have bounded confidences when updating opinions and that they only take into account the adjustment suggestions that are similar to their own. A two-stage optimization model with bounded confidences is built to support the novel feedback adjustment mechanism. In the first stage, a consensus maximum-based optimization model is proposed to judge whether the consensus among the FMEA members can be achieved under the specific bounded confidences. If it can be achieved, then in the second stage, an adjustment minimum-based optimization model with bounded confidences is designed to generate feedback adjustment suggestions; otherwise, the feedback adjustment suggestions generated from the first stage are used for supporting modifying opinions. Two case studies show that the proposal has a good application value, and the simulation experiment shows that our proposal can effectively improve the consensus success ratio and accelerate the speed to achieve a consensus compared with the existing baseline approach.

Group multigranular linguistic QFD for prioritizing service designs with combined weighting method

AbstractQualification for the importance degree of service designs (SDs) is an essential stage in promoting accommodation performances to satisfy customers and gain market shares. Although various methods have been applied to derive the priorities of SDs, they do not effectively deal with the vagueness of information and the heterogeneity of decision makers (DMs). This study presents an improved quality function deployment (QFD) for prioritizing SDs. Multigranular unbalanced linguistic term sets are used to capture evaluators' ratings to cope with vague information. The multigranular linguistic information is unified by using a novel uniform method. This kind of information then is represented as linguistic distribution assessments using the concept of random preferences based on possibility interpretations of weight information. A consensus‐based mathematical programming model is established to determine the weights of DMs. Moreover, a combined structure that combines maximizing deviation and best worst methods is used to derive basic weights of SDs. Finally, an illustrative example of island accommodation management in Weizhou Island is provided to demonstrate the applicability and advantages of the proposed QFD framework.

Managing personalized individual semantics and consensus in linguistic distribution large-scale group decision making

A linguistic distribution assessment is an effective approach to represent uncertain preferences in large-scale group decision making (LSGDM). The same word often signifies different things for different decision makers in linguistic distribution assessments, which is called personalized individual semantics (PIS). Moreover, preference conflicts widely exist in LSGDM. This paper develops a new framework to address PIS and consensus in LSGDM using linguistic distribution preference relations (LDPRs). In the proposed LSGDM framework, a consistency-driven optimization model is put forward to produce the numerical scales with the PIS by maximizing the consistency of the additive preference relation that is transformed from its LDPR. Then, a preference clustering technique is employed to decompose decision makers into different clusters for managing their preferences. Next, the paper devises a two-stage-based consensus reaching model to manage the individual consistency and group consensus, which seeks to minimize the preference information loss. The first stage aims to assist decision makers in achieving a consensus within each obtained cluster, and the second stage is devoted to facilitating the consensus building among the different clusters. Finally, a case study that evaluates water management plans and a comparative analysis with the existing baseline approach are conducted to assess the feasibility and validity of the proposed LSGDM framework.

Linguistic Distribution-Based Optimization Approach for Large-Scale GDM With Comparative Linguistic Information: An Application on the Selection of Wastewater Disinfection Technology

Managing comparative linguistic expressions (CLEs) information is a key issue in group decision-making (GDM). A transformation approach has been previously defined to convert CLEs into hesitant fuzzy linguistic terms sets (HFLTSs). However, it is noted that the occurring possibilities of the linguistic terms in the HFLTSs are assumed equal. This assumption might sometimes not capture the real opinions of the decision makers. Linguistic distribution assessments (LDAs) are an effective way to deal with this issue. This paper develops a linguistic distribution-based optimization approach for converting CLEs into LDAs, in which we assume that decision makers provide their opinions using preference relations with CLEs. Particularly, the proposed optimization approach is based on the use of a consistency-driven methodology, which seeks to minimize the inconsistency level of LDA preference relations obtained by transforming the original CLE preference relations elicited from decision makers. The linguistic distribution-based optimization approach is further developed to transform CLEs into interval LDAs to increase their flexibility. Moreover, society and technology trends make it possible to involve and manage large groups of decision makers in GDM environment. Therefore, a large-scale GDM framework with CLE information is designed based on the linguistic distribution-based optimization approach. To justify the effectiveness and applicability of the proposed methodology, it is applied to solve a real large-scale GDM problem, pertaining the selection of the best sustainable disinfection technique for wastewater reuse projects. A comparison against a baseline method is likewise provided to highlight the advantages and innovations of our proposal.

Water security sustainability evaluation: Applying a multistage decision support framework in industrial region

Abstract Faced with risks aroused by the ever-increasing expansion of industrialization and urbanization, water security sustainability takes more and more effect on balancing regional sustainability and development, especially for industrial regions. Introducing sustainability into the indicator framework of water security is an indispensable issue should be addressed. The indicators of water security sustainability in practice are measured by observation data obtained from a monitoring period. These data are commonly expressed in various forms, such as ratio and qualitative linguistic, which makes them hard to be quantified and evaluated. As multiply influential criteria are involved the water security sustainability evaluation process, it can be treated as a multi-criteria decision making problem. An appropriate evaluation framework with scientific and strategic multi-criteria decision making techniques is supposed to be constructed. This paper incorporates the dimensions related to sustainability into the indicator framework of water security sustainability. Another contribution of this paper is that it establishes an observation data conversion standard and adopts linguistic distribution assessments as information representation. Linguistic distribution assessments can capture the natural characteristics of the observation data of water security sustainability indicators. More importantly, a multistage decision support framework integrated with multi-criteria decision making techniques, such as best-worst method (BWM), decision making trial and evaluation laboratory (DEMATEL) and technique for order performance by similarity to ideal solution (TOPSIS), is constructed for water security sustainability evaluation. Then, deep analyzes about the evaluation results and influential factors are provided, thereby certifying the reliability of evaluation results and facilitating the enhancement of water security sustainability.

The optimization-based aggregation and consensus with minimum-cost in group decision making under incomplete linguistic distribution context

In real decision making, due to the limitation of knowledge, problem complexity and time pressure, it is natural that decision makers express their opinions with incomplete linguistic information. This paper developed a novel consensus model for group decision making (GDM) with incomplete linguistic distribution assessments (ILDAs). Firstly, we defined the concept of ILDAs and the consensus measure for GDM with ILDAs. Then, we presented a consensus-oriented aggregation model, which can obtain a collective opinion with maximum consensus, and further developed a minimum-cost consensus model with variable unit consensus cost. Following this, based on the proposed aggregation and consensus models, we proposed a novel consensus reaching process for GDM with ILDAs. Finally, a numerical example is conducted to demonstrate the validity of the proposed consensus reaching process.

Risk evaluation by FMEA of supercritical water gasification system using multi-granular linguistic distribution assessment

The sustainability challenge is increasingly driving the adoption of supercritical water gasification (SCWG) technology to ensure the elimination and recovery of pollution produced by sewage sludge treatment (SST). Risk evaluation by failure mode and effects analysis (FMEA) plays a crucial role in guaranteeing the reliability and safety of SCWG systems. However, some limitations in existing FMEA methods need to be ameliorated. Multiple risk factors are involved in prioritizing risk levels for failure modes in SCWG systems, it is essential a multiple criteria decision making (MCDM) process, in which overall assessments of failure modes should be provided according to their performances from several points during a system operation period. Due to differences in knowledge backgrounds and experiences, FMEA team members prefer to utilize multi-granular linguistic term sets to express their assessments of system risk. A hybrid risk evaluation model by FMEA is exploited with multi-granular linguistic distribution assessments to suit practical case. Best-worst and maximizing derivation methods are adopted to determine subjective and objective combined weights for distinguishing the importance of risk factors. Complex proportional assessment method is used to prioritize failure modes for explicitly and effectively reflecting the risk level of each failure mode. The proposed model is applied in a practical case of an SCWG system used in SST. Results derived from comparative and sensitivity analyses fully demonstrate the reliability and validity of the model.

A New Distance-Based Consensus Reaching Model for Multi-Attribute Group Decision-Making with Linguistic Distribution Assessments

This paper proposes a novel consensus reaching model for multi-attribute group decision making (MAGDM) with information represented by means of linguistic distribution assessments. Firstly, some drawbacks of the existing distance measures for linguistic distribution assessments are analyzed by using numerical counterexamples, and a new distance measure is proposed for linguistic distribution assessments in order to alleviate the limitations. Then, a novel consensus reaching model is developed for MAGDM with linguistic distribution assessment, in which a feedback mechanism is devised by combining an identification rule and an optimization-based model. In this consensus framework, the model allows experts who are identified to modify their preferences to provide additional preference information about linguistic distribution assessments in each iteration. Meanwhile, by solving an optimization model, the consensus reaching model can automatically generate preference adjustment suggestions for experts. Moreover, the optimization model solved in each iteration minimizes the deviation between the adjusted values and initial preferences, which in turn leads to the good performance of the proposed consensus reaching model in preserving the initial preference information. Finally, an illustrative example shows that the proposed consensus reaching model is feasible and effective, and a comparative analysis highlights the advantages and characteristics of the model.

Managing Multigranular Linguistic Distribution Assessments in Large-Scale Multiattribute Group Decision Making

Linguistic large-scale group decision making (LGDM) problems are more and more common nowadays. In such problems a large group of decision makers are involved in the decision process and elicit linguistic information that are usually assessed in different linguistic scales with diverse granularity because of decision makers' distinct knowledge and background. To keep maximum information in initial stages of the linguistic LGDM problems, the use of multi-granular linguistic distribution assessments seems a suitable choice, however to manage such multigranular linguistic distribution assessments, it is necessary the development of a new linguistic computational approach. In this paper it is proposed a novel computational model based on the use of extended linguistic hierarchies, which not only can be used to operate with multi-granular linguistic distribution assessments, but also can provide interpretable linguistic results to decision makers. Based on this new linguistic computational model, an approach to linguistic large-scale multi-attribute group decision making is proposed and applied to a talent selection process in universities.

A multi-criteria decision-making model for hotel selection with linguistic distribution assessments

The effect of online reviews on resulting decisions attracted the interests of merchants and researchers in different fields. According to existing studies, the decisions of tourists are highly likely modified after browsing online reviews from other travelers on a tourism website. The manner in which online reviews on tourism websites are utilized to select hotels and support tourists is a noteworthy research problem. Online reviews of a hotel are provided by various tourists with respect to different criteria; thus, each tourist is regarded as a decision-maker. In this instance, the problem of hotel selection is based on online reviews in a tourism website and is expressed as a multi-criteria decision-making problem. In this study, a mathematical model was designed to select appropriate hotels on websites. First, a new comparison method for linguistic distribution assessments was proposed based on linguistic scale functions. Second, a novel distance measurement between linguistic distribution assessments with different numbers of linguistic terms was defined with an adjustable parameter. Third, a model for calculating weights and a mathematical model were constructed according to the idea of prioritized aggregation operator and distance measurement. Finally, a case study of TripAdvisor.com was conducted to select suitable hotels using online reviews of hotels. Data analysis was completed to prove the viability of the designed model.

New approach for failure mode and effect analysis using linguistic distribution assessments and TODIM method

As a proactive risk management instrument, failure mode and effect analysis (FMEA) has been broadly utilized to recognize, evaluate and eliminate failure modes of products, processes, systems and services. Nevertheless, the conventional FMEA method suffers from many important deficiencies when used in the real world. First, crisp numbers are adopted to describe the risk of failure modes; but, in many practical situations, it is difficult to obtain exact assessment values due to inherent vagueness in the human judgments. Second, the priority ranking of failure modes is determined based on the risk priority number (RPN), which is questionable and strongly sensitive to the variation of risk factor ratings. Therefore, this paper applies linguistic distribution assessments to represent FMEA team members’ risk evaluation information and employs an improved TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method to determine the risk priority of failure modes. Furthermore, both subjective weights and objective weights of risk factors are taken into account while conducting the risk analysis process. Finally, an empirical case concerning the risk evaluation of a grinding wheel system is presented to demonstrate the practicality and effectiveness of the proposed new FMEA model.

Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making

The theory of hesitant fuzzy linguistic term sets (HFLTSs) is a powerful technique used to describe hesitant situations, which are typically assessed by experts using several possible linguistic values or rich expressions instead of a single term. The union of HFLTSs with respect to each expert, that is, an extended HFLTS (EHFLTS), further facilitates the elicitation of linguistic assessments for addressing group decision-making problems because EHFLTSs can deal with generalized (either consecutive or non-consecutive) linguistic terms. In this study, we propose proportional HFLTSs (PHFLTSs), which include the proportional information of each generalized linguistic term. The mathematical form for a PHFLTS is consistent with that for a linguistic distribution assessment. However, the underlying meanings of the proportions associated with generalized linguistic terms are different. PHFLTSs can be viewed as a special method for performing linguistic distribution assessments. PHFLTSs are recognized as a useful extension of HFLTSs and a possibility distribution for HFLTSs under different assumptions. We define the basic operations with closed properties among PHFLTSs on the basis of t-norms and t-conorms. We then propose a probability theory-based outranking method for PHFLTSs by providing possibility degree formulas. We also study two fundamental aggregation operators for PHFLTSs, namely, the proportional hesitant fuzzy linguistic weighted averaging operator and the proportional hesitant fuzzy linguistic ordered weighted averaging operator. Several important properties of these aggregation operators are investigated. Finally, we use the proposed multiple criteria group decision-making model in practical applications.

Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions

Linguistic distribution assessments with exact symbolic proportions have been recently presented. Due to various subjective and objective conditions, it is often difficult for decision makers to provide exact symbolic proportions in linguistic distribution assessments. In some situations, decision makers will express their preferences in multi-granular unbalanced linguistic contexts. Therefore, in this study, we propose the concept of linguistic distribution assessments with interval symbolic proportions under multi-granular unbalanced linguistic contexts. First, the weighted averaging operator and the ordered weighted averaging operator for the linguistic distribution assessments with interval symbolic proportions are presented. Then, we develop the transformation functions among the multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions. Finally, we present the application of the proposed linguistic distribution assessments in multiple attribute group decision making.

Consistency and consensus measures for linguistic preference relations based on distribution assessments

In this paper, we propose the concept of distribution assessments in a linguistic term set, and study the operational laws of linguistic distribution assessments. The weighted averaging operator and the ordered weighted averaging operator for linguistic distribution assessments are presented. We also develop the concept of distribution linguistic preference relations, whose elements are linguistic distribution assessments. Further, we study the consistency and consensus measures for group decision making based on distribution linguistic preference relations. Two desirable properties of the proposed measures are shown. A consensus model also has been developed to help decision makers improve the consensus level among distribution linguistic preference relations. Finally, illustrative numerical examples are given. The results in this paper provide a theoretic basis for the application of linguistic distribution assessments in group decision making.