The proportional hesitant fuzzy linguistic term set (PHFLTS) has been effectively employed in analyzing the group’s hesitancy in linguistic group decision making (LGDM). The application of PHFLTS assists in capturing the individual’s hesitancy across diverse time periods. It is acknowledged that a single word could potentially convey various meanings to different decision makers, such differences can be proficiently managed by utilizing personalized individual semantic (PIS) models. Previous approaches for calculating PIS failed to incorporate the individual’s updating preference information over time, which increases the risk that the computation of PIS is affected by random factors in a specific moment. In our current research, individual linguistic preference gathered over a time period are leveraged to form the PHFLTS. Additionally, a consistency driven optimization model based on PHFLTS is formulated to obtain PIS of linguistic terms. Subsequently, a fuzzy representation model termed as the fuzzy envelope of PHFLTS is introduced to facilitate the computation with words processes, integrating PHFLTS in LGDM. The practicality and legitimacy of these proposed models are evaluated through a comparative analysis. Lastly, these proposed models are tested and applied in a dedicated case study to further prove their usefulness and efficacy.

In group decision-making, a consensus-reaching process (CRP) is critical to minimize conflicts among decision-makers. Non-cooperative behaviors during the CRP may slow the consensus achievement or even lead to consensus failure. Previous research has not thoroughly identified various non-cooperative behaviors nor has it developed distinct management strategies for different CRP stages. This study aims to provide a systematic approach for identifying and addressing non-cooperative behaviors at different CRP stages, employing tailored management for each behavior type. We introduce and apply a concept named ‘comprehensive score’ to facilitate varied responses to non-cooperative behaviors throughout the CRP. A null-norm operator-based self-management weight generation mechanism is proposed to monitor experts’ historical performance, while a systematic analysis of experts’ characteristics enables detailed classification of non-cooperative behaviors. Through the research, we find that there are seven types of non-cooperative researches which needs to be respectively addressed according to its effects. The proposed management scheme improves the efficiency of CRP. Besides, the current research enriches the mechanisms for identifying and handling non-cooperative behaviors. It offers methodological references for non-cooperative behaviors management in more complex decision-making scenarios.

In most real-life decision-making situations, experts tend to utilize linguistic information rather than numerical values to express their preferences or evaluations on alternatives. Considering the complexity of the decision-making problems, it is usually difficult to use single linguistic terms to elicit experts' preferences. Linguistic expressions that are close to cognition of human-being, such as comparative linguistic expression (CLE), are suggested to be applied in such cases. Three-way decision (3WD) has been proved an effective manner to handle multiattribute decision-making (MADM) problems, however there is a lack of 3WD methods dealing with linguistic expressions. By combining CLE and 3WD, a new multiattribute three-way group decision-making (3WGDM) method incorporating CLE (called CLE-3WGDM method) is proposed. A novel personalized numerical scale computation method, based on predecision in 3WGDM, is introduced to manage diverse interpretations of CLE for different individuals. Afterward, the attribute weights are calculated through a novel optimization model, which applies the principle of deviation maximization and minimum entropy of CLE. A novel 3WD-social network method is presented to compute the weights of experts. Comparative analysis with other existing methods have been carried out to verify the feasibility of the proposed one. Finally, the CLE-3WGDM method is applied to a traditional chinese medicine (TCM) decision problem.

Generally, the similarity between objects is often measured by symmetric operators, such as Cosine, Dice, and Jaccard similarity. However, the ratio model originally proposed by Tversky pointed out that the similarity using the feature matching method tends to be asymmetric. Furthermore, in many practical situations, the existing similarity measures using the feature matching method have some limitations: the calculation formulas are symmetrical, it is not intuitive based on binary features, and it is not easy to calculate based on fuzzy sets. To overcome such limitations, some other asymmetries have proposed to directly combine Tversky's ratio model with the classical symmetric similarity metric, which in turn leads to the inability to identify different features between the compared objects and affects their similarity accuracy. Therefore, aiming to avoid these, this paper will focus on extending Tversky's ratio model to a series of 3-parameter asymmetric similarity metrics (3p-ASM), using three conditional parameters to describe both common and different features. First, the set-based 3p-ASM is achieved due to the general and fuzzy set-theoretic operations, when estimating features in {0, 1} and [0, 1], respectively. Then, considering that the estimated values of features can also be expressed as vectors, it will be extended to the vector based 3p-ASM. Finally, a vector form of 3p-ASM is compared with existing classical methods and a comparative analysis is performed to demonstrate its effectiveness and validity. It is then applied to the KNN model in order to select the most similar items.

Group decision making (GDM) problems widely exist in various scenarios of daily life. In most GDM scenarios, decision makers are not able to express their opinions on a certain solution/alternative with precise numerical values, but express preferences in the form of linguistic variables. So how to efficiently compile linguistic information more completely is an important issue that scholars have to overcome. This paper proposes a new GDM method based on extended hesitant fuzzy linguistic term set (EHFLTS). A fuzzy semantic representation model named type-1 fuzzy envelope of EHFLTS is presented to assist the computing with words processes, and to reduce the possible information loss. A concept of extended context-free grammar related to rough comparison linguistic expression (RCLE) is proposed to facilitate the extraction of decision maker preferences in the decision-making process. Finally, the GDM method on the basis of EHFLTS fuzzy envelope is applied to a scenario where a vehicle company chooses a tire supplier.

In order to incorporate linguistic information into decision making, it is necessary to apply computing with words (CW) techniques. Traditional CW models use only single and simple linguistic terms to represent both input and output, which limits the flexibility in information processing. Recent researches on computing with comparative linguistic expression, including extension models, has partially overcome this limitation. Nonetheless, the flexibility of linguistic information expression remains limited due to the discrete distributions of primary terms. A complete CW framework should include both encoding and decoding technologies for linguistic information, but previous researches have primarily focused on fuzzy encoding approaches, while ignoring fuzzy decoding techniques for linguistic expressions. To improve the accuracy and interpretability of CW in dealing with linguistic expressions, this research proposes a novel model called 2-tuple comparative linguistic expression (2-TCLE). To establish a framework for studying fuzzy representations of linguistic expressions, both fuzzy encoding and decoding approaches for 2-TCLE will be presented in a systematic manner that are performed to match each other. A novel linguistic computational model for dealing with 2-TCLE is presented and then applied to solve a multi-criteria group decision making case study.

Large-scale group decision-making (LS-GDM) problems are common in the daily life of human beings. Both information fusion and computing with words (CWW) technologies in LS-GDM suffer from challenges. In the current research, a proportional hesitant fuzzy linguistic term set (PHFLTS) will be applied to capture the preferences of sub-groups in LS-GDM, which decreases the information lost in information fusion processes. Novel fuzzy semantic representation models of PHFLTS, such as type-1 fuzzy envelope and interval type-2 fuzzy envelope, are respectively studied. The application of the proposed fuzzy entropies facilitates the CWW process with the PHFLTS under the framework of a fuzzy linguistic approach. In particular, linguistic uncertainties contained in the PHFLTS can be reflected in a comprehensive way when the type-2 fuzzy envelope is applied, which contributes to the decrease in the information lost during the CWW process. A novel LS-GDM method cooperating with the fuzzy semantic models of PHFLTS is proposed, in which weights for the sub-groups are determined by size, cohesion, and degree of reliability among the sub-groups. Finally, the proposed decision method as well as CWW tools are applied to the process of urban renewal plan selection.

Multi-criteria group decision making (MCGDM) is a common activity in human-beings' daily life. In real-world problems is common that decision makers prefer to use linguistic values instead of numerical values to express their opinions/preferences on the alternatives. Solving MCGDM problems under linguistic environment suffers difficulties such as loss of information during the computing with words (CWW) processes. Existing fuzzy encoding technology is still limited to single word, thus it is difficult to apply previous fuzzy encoding methodologies to carry out CWW processes when more complex linguistic information appears in MCGDM. To overcome these limitations, a novel MCGDM method has been proposed, in which extended hesitant fuzzy linguistic term sets (EHFLTS) is applied to decrease information loss in preference aggregation process. Novel type 1 and type-2 fuzzy envelopes of EHFLTS are proposed to decrease information loss in CWW processes. A new context-free grammar and the notion of rough comparative linguistic expression (RCLE) are introduced to supplement the computation with fuzzy envelopes of EHFLTS, and to increase the flexibility of preference elicitation. The proposed fuzzy encoding models and syntax extend the fuzzy perceptual computing technology from single words to EHFLTS and RCLE. Finally, the proposed MCGDM method which adopts fuzzy envelopes of EHFLTS is applied in a cross-border e-commerce selection situation.

Through the application of various time series methods, the paper considers the ruling factor of the subject and predicts the GDP, unemployment rate from 2021 to 2024 based on its historical data from 2009 to 2016. The three exponential smoothing method is adopted to predict the GDP from 2021 to 2024, lower limit of the GDP is calculated by using the emergency impact factor optimization, then the optimal scheme is selected through comparative analysis. Afterwards, based on the data from 2009 to 2016, the autoregressive model is applied to predict the upper limit of unemployment rate from 2021 to 2024, the average model is used to get the Treasury bonds and GINI index from 2021 to 2024. Combining above economic data, the analytic hierarchy process(AHP) was used to calculate the weight values, and to predict the overall economic situation of the research object in the following four years. The ruling person factors and emergency factors are also considered to optimize the predicted economic data to realize technological innovation. The current research provides a reference for relevant governments in policy setting to promote economic development worldwide.

A novel hybrid soft set model called intertemporal hesitant fuzzy soft set is proposed, and then, it is showed how it can deal with group decision making problems. This model can be used to incorporate hesitant information that varies across time, when the alternatives are described by their degree of agreement with various characteristics. According to the period of time (whether it is indefinitely long or with a known termination date), the proposed model is, respectively, called long-term and short-term intertemporal hesitant fuzzy soft set. Corresponding group decision making approaches are provided, where the application of Quasi-Hyperbolic discounting permits to deal with the time-inconsistent experts’ preferences. Both the effect of scores of hesitant fuzzy elements and the effect of uncertainty contained in hesitant information are considered in the proposed decision approaches.

The use of hesitant fuzzy linguistic term sets (HFLTS) contributes to the elicitation of comparative linguistic expressions (CLEs) in decision contexts when experts hesitate among different linguistic terms to provide their assessments. Since the existing representation models for linguistic expressions based on HFLTS do not properly consider the uncertainty caused by the inherent vagueness of such linguistic expressions, it is necessary to improve their modeling to cope with such vagueness. In this paper, we propose a new fuzzy envelope for the HFLTS in form of type-2 fuzzy sets for representing CLEs. Such an envelope overcomes the limitation of existing representations in coping with inherent uncertainties and facilitates the processes of computing with words for linguistic decision making problems dealing with CLEs.

In real-life linguistic decision making, participates may hesitate when they are requested to provide evaluations on alternatives due to the uncertainty and vagueness of the information. Single terms are usually not flexible enough for experts to express their opinion, thus more elaborated linguistic expressions, such as comparative linguistic expressions (CLEs), are needed. However, because of the lack of researches on fuzzy representation models of CLEs, when CLEs are adopted in decision making, it is difficult to carry out computing with words (CWW). To fill this gap, we come up with a new T2F-representation model for CLEs in this research by introducing a new T2FE of hesitant fuzzy linguistic term sets (HFLTSs). The proposed model decreases the information losing during the CWW processes when CLEs are used in decision making, by applying T2FSs to represent linguistic information. Therefore, it contributes to increase the flexibility for experts to extract and express linguistic information.

The notion of linguistic value soft set was proposed to handle linguistic decision making problems under uncertainty. It is based on soft set theory and the fuzzy linguistic approach. However, in real-world situations the decision makers may not only need single linguistic terms to elicit their knowledge about alternatives but also more elaborate linguistic expressions such as, comparative linguistic expressions. Linguistic value soft sets cannot deal with these situations in a satisfactory manner. Hence, we propose one step further towards a complete combination of soft set theory and hesitant fuzzy linguistic term sets to put forward a new model called hesitant linguistic expression soft set that facilitates the elicitation of linguistic information with soft sets. Afterwards, a novel multi-criteria group decision making approach with a consensus reaching process, by using hesitant linguistic expression soft sets, is presented. Some illustrative examples show the feasibility and implementation of our novel proposals.

Popular decision making methods by using fuzzy soft sets belong to two main categories, namely, score-based methods and fuzzy choice values based methods. It is necessary an application background to choose which one is better, since each of them makes sense in specific decision making situations and both of them could be improved. Therefore, in this contribution we focus on improving the former one. To improve the score based method, it is provided a novel adjustable algorithm by using fuzzy soft set that introduces thresholds when comparing two membership function values and afterwards coming up with new concepts of scores.

Hybrid soft sets, such as fuzzy soft sets and rough soft sets, have been extensively applied to decision making. However in both cases, there is still a necessity of providing improvements on approaches to obtain better decision results in different situations. In this paper several proposals for decision making are provided based on both hybrid soft sets. For fuzzy soft sets, a computational tool called D-score table is introduced to improve the decision process of a classical approach and its convenience has been proved when attributes change across the decision process. In addition, a novel adjustable approach based on decision rules is introduced. Regarding rough soft sets, several new decision algorithms to meet different decision makers' requirements are introduced together a multi-criteria group decision making approach. Several practical examples are developed to show the validity of such proposals. (c) 2018 Elsevier B.V. All rights reserved.

Consensus reaching processes (CRPs) in group decision making (GDM) attempt to reach a mutual agreement among a group of decision makers before making a common decision. Different consensus models have been proposed by different authors in the literature to facilitate CRPs. Classical CRP models focus on achieving an agreement on GDM problems in which few decision makers participate. However, nowadays, societal and technological trends that demand the management of larger scale of decision makers add new requirements to the solution of consensus-based GDM problems. This paper presents a comparative study of different classical CRPs applied to large-scale GDM in order to analyze their performance and find out which are the main challenges that these processes face in large-scale GDM. Such analyses will be developed in a java-based framework (AFRYCA 2.0) simulating different scenarios in large scale GDM. (C) 2017 Elsevier B.V. All rights reserved.

In this work, the axiomatical definition of similarity measure, distance measure and inclusion measure for interval-valued intuitionistic fuzzy soft set (IV IFSSs) are given.An axiomatical definition of entropy measure for IV IFSSs based on distance is firstly proposed, which is consistent with the axiomatical definition of fuzzy entropy of fuzzy sets introduced by De Luca and Termini.By different compositions of aggregation operators and a fuzzy negation operator, we obtain eight general formulae to calculate the distance measures of IV IFSSs based on fuzzy equivalences.Then we discuss the relationships among entropy measures, distance measures, similarity measures and inclusion measures of IV IFSSs.We prove that the presented entropy measures can be transformed into the similarity measures and the inclusion measures of IV IFSSs based on fuzzy equivalences.

Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some existing hybrid models has been carried out. Some foundational properties of modified soft rough sets (MSR sets) are analyzed. It is pointed out that MSR approximation operators are some kinds of Pawlak approximation operators, whereas approximation operators of Z-soft rough fuzzy sets are equivalent to approximation operators of rough fuzzy sets. The relationships among F-soft rough fuzzy sets, M-soft rough fuzzy sets and Z-soft rough fuzzy sets are surveyed. A new model called soft rough soft sets has been provided as the generalization of F-soft rough sets, and its application in group decision-making has been studied. Various soft rough sets models show great potential as a tool to solve decision-making problems, and a depth study of the connections among these models contributes to the flexible application of soft rough sets based decision-making approaches.

The incremental updating of lower and upper approximations under the variation of information systems is an important issue in rough set theory. Many incremental updating approaches with respect to different kinds of indiscernibility relations have been proposed. The grade indiscernibility relation is a fuzzification of classical Pawlak's indiscernibility relation which can characterize the similarity between objects more precisely. Based on fuzzy rough set model, this paper discusses the approaches for dynamically acquiring of the upper and lower approximations with respect to the grade indiscernibility relation when adding and removing an attribute or an object, and changing the attribute value of the object, respectively. Since the approaches are used in succession, they make the approximations can be updated correctly and effectively when any kind of possible change in the information system. Finally, extensive experiments on data sets from University of California, Irvine (UCI) show that the incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method.