Probabilistic Linguistic Term Sets Research Articles

Research on Multi-Stage Post-Occupancy Evaluation Framework of Community Comprehensive Elderly Care Service Facilities under the Public-Private Partnership Mode—A Case Study of China

The key to whether elderly individuals in the community can enjoy their later years peacefully lies in the service capabilities of community comprehensive elderly care service facilities (CCECSF) under the Public-Private Partnership (PPP) mode. To maintain a high level of service capability in community comprehensive elderly care service facilities under PPP mode, scientific evaluation of the effectiveness of these facilities is equally crucial. This article first constructs a post-occupancy evaluation index system of community comprehensive elderly care service facilities under PPP mode that includes three evaluation attributes and fifteen evaluation criteria based on the Chinese culture and lifestyle habits. Regarding the issue of direct users being unable to directly participate in evaluations, the uncertainty in evaluation information, and the volatility of evaluation results, a multi-stage post-occupancy evaluation model is constructed based on probabilistic linguistic term set, TOPSIS model and multi-stage decision theory. The above post-occupancy evaluation index system and evaluation model together constitute a multi-stage post-occupancy evaluation framework for community comprehensive elderly care service facilities under PPP mode. The outcomes of the case study indicate that the post-occupancy evaluation index system can offer a scientifically guided approach for evaluating the service level of community comprehensive elderly care service facilities under the PPP mode; meanwhile, the multi-stage evaluation model can enable direct user participation in the post-evaluation of facility usage and improve the robustness and reduce the fluctuation of the evaluation results, so as to improve the scientificity of the evaluation results.

A Hybrid Multi-Attribute Decision-Making Approach Considering Correlations Among Indicators

Considering the fuzzy and uncertainty of the evaluation information of the evaluation object, the type of indicators are expanded into five types of mixed evaluation information, namely, exact number, interval number, triangular fuzzy number, hesitant fuzzy number, and probabilistic linguistic term sets, and different types of evaluation information are adopted according to the different characteristics and types of indicators, respectively. When the evaluation information is hybrid information, the generalized Shapley function based on fuzzy measurement is used to analyze the interaction between indicators and determine the weights of indicators, considering that the interaction between indicators is more complicated. In view of the fact that the conversion of mixed information into the same kind of information will lead to the problem of complicated calculation and missing information, the VIKOR method is used to comprehensively evaluate the evaluation objects and select the best ones. Finally, the validity and feasibility of the proposed method is verified by taking the assessment of data literacy level and competence of teachers in a university in a western province of China as an example.

Intelligent evaluation system for new energy vehicles based on sentiment analysis: An MG-PL-3WD method

As a critical strategic tool within the framework of the digital economy (DE), artificial intelligence (AI) plays a crucial role in realizing an AI-assisted economy. This novel paradigm has gained widespread acceptance from governments globally, positioning itself as a cornerstone in the practical implementation of the DE. The increasing reliance on digital means for economic transformation, the treatment of data as a critical resource, and the integration of information technologies highlight the synergy between AI and the DE. Against this backdrop, online reviews and SA play a pivotal role, offering rich data streams continually emerging on various platforms. Therefore, this article utilizes a probabilistic linguistic term set (PLTS) to establish a multi-granularity probabilistic linguistic (MG-PL) information system. This approach, through sentiment analysis (SA), enables quantitative analysis of user emotional expressions. The integration of these technological aspects holds the promise of enhancing decision-making processes, facilitating the intellectualization of economic activities, and addressing existing challenges in the application of AI within the DE domain. Initially, SA is conducted on text-based online comment data, forming a probabilistic linguistic incomplete information system. The maximum similarity method is employed to establish a probabilistic linguistic complete information system. Subsequently, an adjustable MG-PL decision-theoretic rough set (DTRS) is developed, followed by the establishment of a three-way group decision model using three-way decisions (3WD) and a directed graph. The model’s applicability, stability, and feasibility are demonstrated via a case study centered on the acquisition of new energy vehicles (NEVs).

Distortion risk measures for tail-risk multicriteria decision-making based on a probabilistic linguistic environment

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, and several multi-criteria decision models based on PLTSs have been recently developed. In this framework, distortion risk measures are extensively used in finance and insurance applications, but are rarely applied in fuzzy systems. In this paper, distortion risk measures are applied to fuzzy tail decisions. In particular, three tail risk measurement methods are put forward, referred to as probabilistic linguistic VaR (PLVaR), expected probability linguistic VaR (EPLVaR), and Wang tail risk measure and extensively study their properties. Our novel methods help to clarify the connections between distortion risk measure and fuzzy tail decision-making. In particular, the Wang tail risk measure is characterized by consistency and stability of decision results. The criteria and expert weights are unknown or only partially known during the decision making process, and the maximising PLTSs deviations are showed how to determine them. The theoretical results are showcased on an optimal stock fund selection problem, where the three tail risk measures are compared and analyzed.

Research on probabilistic language multi-attribute group decision-making method based on correlation coefficient and improved entropy

To address the issue of unknown expert and attribute weights in the comprehensive assessment of hospitals, as well as the potential challenges posed by distance measures, this paper presents a probabilistic language multi-attribute group decision-making (MAGDM) approach that utilizes correlation coefficients and improved entropy. First, the correlation function, called the probabilistic linguistic correlation coefficient, is introduced into the probabilistic linguistic term set(PLTS) to measure the consistency among experts, so as to obtain the weights of experts. Next, based on Shannon entropy, an improved probabilistic linguistic entropy is proposed to measure the uncertainty of PLTS considering the number of alternatives and information quantity. Then, based on the correlation coefficient and improved entropy, the attribute weights are obtained. In addition, in order to overcome the counter-intuitive problem of existing distance measurement, this paper proposes a probabilistic language distance measurement method based on the Bray-Curtis distance to measure the differences between PLTSs. On this basis, by applying the technique for order preference by similarity to ideal solution (TOPSIS) method and using PLTSs to construct the MAGDM method, the ranking of alternative schemes is generated. Finally, the improved MAGDM method is applied to an example of the comprehensive evaluation of the smart medical hospitals. The results show that compared with the existing methods, this method can determine the weight information more reasonably, and the decision-making results are not counter-intuitive, so it can evaluate the hospital more objectively.

A decision-support model through online reviews: Consumer preference analysis and product ranking

Online reviews have become an important reference for consumers when choosing and purchasing products (or services); however, previous research based on these reviews has overlooked consumer preferences at the attribute level, as well as product ranking at the regional level. Here, we propose a decision-support model through online reviews involving 4 modules: (i) data collection and preprocessing, (ii) transformation from star ratings into probabilistic linguistic term sets (PLTSs), (iii) consumer preference analysis, and (iv) product ranking. After data collection and preprocessing, star ratings are represented as probabilistic linguistic term sets. Then, the most satisfactory product attribute and the least satisfactory product attribute are extracted from text comments using the well-known term-frequency-inverse document frequency (TF-IDF) algorithm. Thereafter, a data-driven best-worst method, in which preferences are given by objectively quantifying multiple product attributes based on star ratings and the weightage score obtained from the TF-IDF results, is established to analyze consumer preferences. Furthermore, product ranking is investigated from two levels: a region-based ranking method to discuss product ranking over different regions and a ranking position aggregation method to discuss product overall ranking based on a 0-1 integer programming model. We verify the decision-support model with a dataset of 10987 reviews of 20 automobile models from the Autohome platform. Some comparisons, theoretical and practical implications are provided.

Blockchain service platform evaluation with probabilistic linguistic preference information based on Choquet integral and ExpTODIM

The application of Internet of Medical Things (IoMT) can improve the treatment efficiency of medical institutions, but it still has hidden dangers in security and privacy. The introduction of blockchain technology into IoMT is expected to prevent these hidden dangers. This study proposes a multiple criteria decision aiding model to select a suitable blockchain service platform for IoMT to enhance its safety and reliability. The proposed model combines the probabilistic linguistic term set (PLTS), multiple criteria hierarchy process (MCHP), 2-additive Choquet integral and ExpTODIM method to assist decision-makers (DMs) to obtain a reliable and low-risk decision result. The MCHP is employed to analyze decision-making problems by hierarchical criteria. The 2-additive Choquet integral is adopted to reflect interactions between criteria, and parameter values in the 2-additive Choquet integral are indirectly determined based on the preference information of DMs. PLTSs are used to represent the evaluation information of experts and the preference information of DMs. The ExpTODIM (Exponential TODIM) method is adopted to rank alternatives considering the psychological characteristics of DMs. An illustrative example demonstrates the applicability and merits of the proposed model with comparative analysis.

Probabilistic linguistic prospect outranking risk decision making method based on stochastic dominance and application in emergency plan evaluation

In the decision-making process, probabilistic linguistic term sets (PLTSs) could represent decision-makers’ uncertain evaluation information. The combination of probabilistic and linguistic information assists decision-makers to depict their evaluation information more flexibly. In this paper, a prospect outranking decision-making method based on stochastic dominance is proposed for solving the multi-attribute risk decision-making problem under the probabilistic linguistic information environment. Firstly, to fully preserve the original probabilistic linguistic information, we give the definitions of the generalized probability distribution and the corresponding generalized cumulative distribution function of a PLTS for defining the distance measure between PLTSs. Secondly, based on the positive and negative ideal cumulative distribution functions, we propose the probabilistic linguistic prospect value functions. After that, considering the uncertainty of the relationship between alternatives, several kinds of novel prospect stochastic dominance and almost stochastic dominance relations are defined, which consider the decision makers’ distinction between gains and losses to measure the subtle relationship between alternatives. The stochastic dominance approach and the almost stochastic dominance approach under the probabilistic linguistic decision-making environment are put forward. Besides, we use the superiority and inferiority ranking method to solve the dominance ranking problem of the uncertainty relationship between any two alternatives. Finally, the proposed method is applied in the evaluation of emergency plans to show the accuracy and reliability, and comparative analyses are made to illustrate its availability.

A group decision framework for core competitiveness evaluation of small and medium-sized foreign trade enterprises under probabilistic linguistic term sets

Since the reform and opening up, China’s foreign trade has developed rapidly. The import and export trade volume has doubled, and the team of foreign trade enterprises is constantly expanding. After China’s accession to the WTO and the liberalization of foreign trade management rights, a group of small and medium-sized foreign trade enterprises have grown up in recent years and are becoming a new force in the development of China’s foreign trade industry. So, how to make these enterprises grow and grow in the international market competition, and focus on cultivating the core competitiveness of small and medium-sized foreign trade enterprises, has become a strategic issue related to the overall development of foreign trade. Recently, COmbinative Distance-based ASsessment (CODAS) method computes the Euclidean distances as the primary measure and Hamming distances as the secondary measure to assess alternatives based on predetermined attribute. Moreover, the probabilistic linguistic term sets (PLTSs) are effective tool for depicting uncertainty of the multiple attribute group decision making (MAGDM) problems. The core competitiveness evaluation of small and medium-sized foreign trade enterprises is a classical MAGDM. In this paper, the CODAS method is extended to the MAGDM with PLTSs. Firstly, the definition of PLSs is introduced. Then, on the basis of the classical CODAS method, the PL-CODAS method is proposed to cope with MAGDM under PLTSs and its significant characteristic is that it can fully consider PLED and PLHD. Finally, a practical example for core competitiveness evaluation of small and medium-sized foreign trade enterprises is given to verify the developed approach and some comparative analysis was also given to verify the PL-CODAS approach.

Multi-attribute decision making based on VIKOR with probabilistic linguistic term sets: An application to the risk evaluation of foreign direct investment.

The multiple global environments have triggered changes in the international environment, leading to a sharp decline of foreign direct investment (FDI) compared to pre-pandemic level. To evaluate the investment risk of FDI and make optimal investment decision becomes the most important issue for investors. This paper focuses on the evaluation of investment risk for FDI. First, an index system for risk evaluation of FDI is constructed. Then, we introduce the probabilistic linguistic entropy and cross entropy measures, based on which, a programming model is developed to identify the objective attribute weights. A composite weight derivation method, which takes both the objective attribute weights and the subjective attribute weights into account, is further introduced. In view of attributes' uncertainty and fuzziness and the conflicting characteristics of some attributes, the VIKOR (the Serbian name: VlseKriterijumska Optimizacija I Kompromisno Resenje, means multi-criteria optimization and compromise solution) method is used to evaluate the risk of FDI under the probabilistic linguistic environment. Furthermore, a case study is presented to illustrate the proposed method. The comparative analysis and some further discussions verify the validity of the proposed method for the FDI risk evaluation.

Geographic information system-based multi-criteria decision-making analysis for investment assessment of wind-photovoltaic-shared energy storage power stations: a case study of Shanxi Province.

As the center of the development of power industry, wind-photovoltaic (PV)-shared energy storage project is the key tool for achieving energy transformation. This research seeks to construct a feasible model for investment appraisal of wind-PV-shared energy storage power stations by combining geographic information system (GIS) and multi-criteria decision-making (MCDM) method. Firstly, a comprehensive criteria system is established from the perspectives of orography, economy, resources, climate, and society, and the evaluation data is described using probabilistic linguistic term sets (PLTSs). Then, to avoid the weight deviation produced by the single weighting approach, a comprehensive weighting model including the best-worst method (BWM) and entropy weight method is provided to calculate the weights of criteria. Next, expert weights are calculated based on trust analysis. Finally, alternatives are ranked by the improved gained and lost dominance score (GLDS) method. To verify the validity of the model, an empirical investigation is carried out in Shanxi Province. The results show that the economy is the primary factor influencing the investment decision. Among all the projects approved by the government, alternative F4 located in Yanzhuang Town, Yuanping City is the best investment object. Furthermore, to illustrate the stability of the result, triple sensitivity analysis and comparative analysis are conducted in Shanxi Province. This study expands the application scope of GIS and MCDM method by first providing support for government and investors to identify optimal investment targets.

Research on social ecological evaluation of the spatial form of old urban blocks based on dual probabilistic linguistic term sets

Under the rapid process of urbanization, many early renovated urban villages have also encountered many problems. Due to the rapid development of urban construction and the continuous changes in spatial functions, early renovated urban villages have already encountered problems such as unreasonable commercial distribution, lack of parking spaces, reduced commercial vitality, and commercial activities crowding out affecting the normal lives of villagers. There is a serious contradiction between the need for development and the quality of life of villagers. Due to the fixed nature of architectural space, only by fully understanding the essential morphological characteristics of the space can we find the optimal solutions for different space usage functions, and obtain the matching of the optimal solutions in the existing space requirements. The social ecological evaluation of the spatial form of old urban blocks is a multi-attribute group decision making (MAGDM). Recently, the grey relational analysis (GRA) and CRITIC method has been used to cope with MAGDM issues. The dual probabilistic linguistic term sets (DPLTSs) are used as a tool for characterizing uncertain information during the social ecological evaluation of the spatial form of old urban blocks. In this manuscript, the dual probabilistic linguistic GRA (DPL-GRA) method is built to solve the MAGDM under DPLTSs. The CRITIC method is used to obtain the attributes weights. In the end, a numerical case study for social ecological evaluation of the spatial form of old urban blocks is given to validate the proposed method.

Projection-based TOPSIS method to MAGDM in dual probabilistic linguistic information environment

The dual probabilistic linguistic term sets (DPLTSs) are more effective than PLTSs in solving the problem of multi-attribute group decision-making (MAGDM). In this paper, an improved TOPSIS method is developed combining the TOPSIS method and projection measure of DPLTS to supplement the existing research. Firstly, considering the mathematical characteristics of DPLTS, this paper defines the concepts of the module, cosine function, and projection of DPLTS, and then proves the mathematical properties of the cosine function. Secondly, considering the uncertainty of decision-making problems, the weight-solving models are established respectively under the condition that the weight information is completely unknown and partially known. Furthermore, a novel DPLPrj-TOPSIS approach is established based on the projection measure proposed. It involves integrating experts’ DPLTS evaluations, normalizing different DPLTSs, calculating alternatives’ relative closeness and score, etc. Secondly, the proposed method’s feasibility is demonstrated through a case study that entails selecting network promotion plans for food manufacturers. Finally, the proposed method’s effectiveness and validity are verified by comparing and analyzing it with the traditional TOPSIS method based on a distance measure and other existing decision methods.

A novel Multi-Criteria Decision Making framework based on Evidential Reasoning dealing with missing information from online reviews

Online reviews are a valuable tool for Multi-Criteria Decision Making (MCDM) because they provide insightful information on several aspects. However, not all reviews yield complete information on all the necessary criteria for the MCDM problem. In practice, users might not effectively analyze all of them due to a lack of knowledge or time constraints. Despite this shortcoming, these online reviews still offer useful information that would be lost if neglected. Therefore, this paper proposes a framework that offers a new approach to using online reviews in MCDM and effectively addresses missing information on a given criterion or criteria. This new approach first establishes an information processing mechanism to transform online reviews into Probabilistic Linguistic Term Sets (PLTSs) with interval uncertainty. Afterward, a weight determination model is defined to calculate the criteria weights, which are given as interval values to reflect the uncertainty of the criteria and consider information from online reviews to better capture the opinions of reviewers. Next, the Evidential Reasoning (ER) algorithm is extended to the PLTSs with interval uncertainty environment to fuse the evaluation information and generate the interval-valued expected utilities of the alternatives by considering the uncertainty related to the missing information. Finally, a case study is conducted to illustrate the implementation process of the proposed framework, and a comparative analysis is carried out to evaluate its performance.

Application Of Probabilistic Linguistic Term Sets and Prospect Theory in Multi-Attribute Decision Making: Aviation Industry Evaluation

With the increasing complexity and diversification of current decision objectives, partial data absence in evaluating certain decision criteria is common. Therefore, this paper introduces a fuzzy evaluation method using probabilistic linguistic term sets and integrates it with prospect theory. This integration allows reflecting decision-makers' preferences while addressing the issue of data absence for evaluation. Additionally, the paper employs the entropy-weighted Analytic Hierarchy Process (AHP) to evaluate other criteria, and all criteria are evaluated using the TOPSIS method, forming a comprehensive evaluation methodology. Finally, the proposed methodology is applied to assess the aviation industry level in eastern coastal provinces represented by Zhejiang Province. Finally, the proposed methodology is applied to assess the aviation industry level in eastern coastal provinces represented by Zhejiang.

Large-scale consensus with dynamic trust and optimal reference in social network under incomplete probabilistic linguistic circumstance

Consensus plays a pivotal role in large-scale group decision-making, and the social network relationship significantly impacts the consensus reaching process (CRP). Consequently, there is considerable focus on achieving large-scale consensus within social network (LSC-SN). Typically, experts are used to expressing their evaluations with language that can be effectively characterized by probabilistic linguistic term set (PLTS). However, the existing distance measure of PLTS exhibits drawbacks, and PLTSs provided by experts might be incomplete. To address the two challenges, this research defines an improved distance measure and proposes an estimation method for incomplete PLTS from the perspectives of trust relationships, collaborative filtering, and confidence level. Subsequently, in the CRP, a hierarchical clustering algorithm based on the trust-similarity measure is developed to cluster experts who share mutual trust and similar evaluations. Then, a consensus model employing dynamic trust and optimal reference is introduced to achieve both intra-cluster and inter-cluster consensus simultaneously. Finally, to illustrate the feasibility and advantage of the proposed model, a numerical experiment and the comparative analyses are conducted.

A linguistically asymmetric similarity decision model integrating item tendency for rating predictions

Neighbourhood-based collaborative filtering (CF) methods typically rely only on user rating information for similarity calculation, without considering linguistic concepts (terms) that reflect user fuzzy preferences. However, in real-world decision-making processes, users often prefer to express their preferences for items linguistically rather than numerically. Inspired by this, we propose a probabilistic linguistic term set–based item similarity method that transforms absolute ratings into linguistic terms to capture the degree of importance users place on explicit aspects and opinions. Furthermore, we take into account the positive impact of users’ preferred consistency towards items on similarity results and introduce a Bhattacharyya coefficient–based item tendency to adjust semantic similarities, enhancing the reliability of predictions. In addition, we account for the asymmetric relation between items when selecting appropriate neighbours to optimise rating predictions. The experiments on two benchmark data sets indicate that our method outperforms existing similarity methods across various evaluation metrics. Specifically, compared with the state-of-the-art method, intuitionistic fuzzy set–based hybrid similarity model (IFS-HSM), the proposed model improves the performance by at least 2.1% and 1.9%, respectively, within the metrics mean absolute error ( MAE) and F1. Moreover, our approach provides a new insight for measuring similarity between items from both qualitative and quantitative perspectives.

A 2-additive Choquet integral-based multi-criterion decision-making method with complex linguistic information in drug value assessment

With the escalating incidence and mortality rates of lung cancer, the targeted drugs assessment has emerged a key problem, serving as the foundation for incorporating targeted drugs into the national basic medical insurance. This paper executes drug value assessment within a multi-criterion decision-making framework. Recognizing that experts naturally provide assessments in linguistic representations during drug evaluations, we employ the generalised probabilistic linguistic term set to uniformly model diverse types of linguistic information. Considering the bounded rationality of experts, we propose a method to obtain expert weights through minimizing regret degree of experts. Based on the determined weights of experts, a method to simplify the generalised probabilistic linguistic term set is developed. Afterwards, this study establishes a 2-additional Choquet integral-based aggregation method to fuse the assessments of drugs considering interactive criteria. To examine the effectiveness of the proposed method, we apply the proposed method in drug value assessment for lung cancer. The proposed method provides a feasible attempt to address decision-making problems involving complex linguistic information.

Exploration of Smart Elderly Service Supply and Demand Matching for Multi-source Data

Abstract Under the background of population aging, the rational use of resources for senior care services has more difficulty, leading to increasingly prominent conflicts between supply and demand. This paper uses the Gini coefficient, cohort effect, and other methods to build a matching supply and demand model for innovative senior care services based on the multi-source data of senior care services. The probabilistic linguistic term set is used for evaluation and a calculation method is proposed to match satisfaction. The model’s feasibility is demonstrated by analyzing arithmetic examples. Five types of senior care demand groups can be obtained through clustering analysis, with three kinds of intelligent senior care, namely, competent institutions, smart communities, and smart homes, in which the Gini coefficient value of community senior care facilities in X city is 0.4203, and there is an imbalance between supply and demand. The method proposed in this paper identifies five types of elderly groups, which can be matched with different innovative senior care services for elderly groups with distinct characteristics.

A two-stage decision framework for GIS-based site selection of wind-photovoltaic-hybrid energy storage project using LSGDM method

To alleviate the instability of renewable energy generation and reduce the cost of energy storage, a wind-photovoltaic-hybrid energy storage project that combines hydrogen storage and electric thermal storage has been developed. Selecting the appropriate location is essential. Therefore, a two-stage decision framework is proposed to select the optimal site. In the first stage, geographic information system is used to assess the suitability of the study area and identify potential locations. In the second stage, the large-scale group decision-making method is employed for further evaluation. Considering the uncertainty of information, the probabilistic linguistic term sets are used to describe evaluation information. Then, experts are clustered via transitive closure algorithm, the weights of the experts and the subgroups are calculated according to the similarity and the importance of experts, and the size of subgroups, respectively. Furthermore, the weight of the criteria is calculated by maximum deviation method. Finally, the improved tomada de decisaointerativa e multicritévio method is used to rank the feasible sites. To verify the practicability of the method, an empirical study is conducted in Inner Mongolia Autonomous Region. Through sensitivity and comparative analyses, site A3 is identified as the optimal location, which facilitates the layout of wind-photovoltaic-hybrid energy storage projects.