Interval-valued Hesitant Fuzzy Sets Research Articles

Interval-Valued Hesitant Fuzzy Linguistic Multiattribute Decision-Making Method Based on Three-Parameter Heronian Mean Operators

Numerous variants have been proposed for sets of linguistic terms and the interval-valued hesitant fuzzy set (IVHFS). In particular, the interval-valued hesitant fuzzy linguistic set (IVHFLS) is more suitable for defining the hesitancy and inconsistency inherent in the human cognitive processes of decision making. A key aggregation operator is Heronian mean (HM), based on which the correlation among aggregated arguments can be captured. However, the existing HM operators partially overlook the correlation among more than two arguments and lack the properties of idempotency and reducibility. In this work, the limitations of HM operators are first analyzed. Then, two new HM variants are introduced: three-parameter weighted Heronian mean (TPWHM) and three-parameter weighted geometric Heronian mean (TPWGHM). Thus, the reducibility, idempotency, monotonicity, and boundedness properties are proven for the two computational procedures, and unique situations are mentioned. Furthermore, two more elaborate operators are also introduced which are called the interval-valued hesitant fuzzy linguistic TPWHM (IVHFLTPWHM) and the interval-valued hesitant fuzzy linguistic TPWGHM (IVHFLTPWGHM). The main properties, as well as unique situations of these two computational procedures, are discussed. Finally, the introduced methods are clarified by illustrative examples. In addition, the parameter effects on the decision-making outcomes are discussed and comparisons with other reference methods are made.

A Two-Sided Stable Matching Model of Cloud Manufacturing Tasks and Services considering the Nonlinear Relationship between Satisfaction and Expectations

To improve the satisfaction of both service demanders (SDs) and service providers (SPs) in the matching of cloud manufacturing (CMfg) tasks and services, a two-sided stable matching model of CMfg tasks and service considering the nonlinear relationship between satisfaction and expectations is proposed. As the expectations of SDs and SPs are difficult to be quantified directly, an evaluation method based on interval-valued hesitant fuzzy linguistic sets (IVHFLSs) is first presented. Next, a nonlinear model of satisfaction and expectations is built to quantify the satisfaction, which achieves accurate quantification of satisfaction. Then, a two-sided stable matching model of CMfg tasks and service is built, which takes the satisfaction of SDs and SPs as the optimization goals and considers the individual rationalities and blocking pairs. Finally, an adaptive genetic algorithm (AGA) is designed to solve the proposed two-sided matching model. A practical application and comparison analysis is used to verify the effectiveness and superiority of the research.

A New Interval-Valued Hesitant Fuzzy-Based Optimization Method

An interval-valued hesitant fuzzy set (IVHFS) is a best tool to address uncertainty and hesitation of a production planning problem (PPP) which appears in engineering, agriculture, and industrial sectors. Often, a PPP is formulated as a multiobjective linear programming problem (MOLPP) and therefore, it is very necessary to develop a suitable and realistic method to deal MOLPP with uncertainty and hesitation. In this paper, we define a set of possible interval-valued hesitant fuzzy degrees for all objectives, and using this, a MOLPP is converted into a interval-valued hesitant fuzzy linear programming (IVHFLPP). Further, we introduce a new optimization technique based on a new operation of IVHFS, and later it is implemented in a computational method to search a Pareto optimal solution of the considered problem. Further, a PPP is solved by using the proposed method and the result shows the superiority of the proposed computational method over the existing methods.

Establishment of social stability risks evaluation model based on GAHP and IVHFSs

The construction of hydraulic projects inevitably involves land requisition and resettlement, with considerable impact on the society, the environment, and the economy of the project site, and leading to social stability risk events. Therefore, it is necessary to systematically assess social stability risk to put forward corresponding countermeasures. By applying WSR theory (Wuli-Shili-Renli Theory) to the investigation of the case-study of the Jiangxiang Reservoir Project, this paper constructs an evaluation index system for the risk to social stability from land requisition and resettlement, from the three dimensions of “physics”, “matter”, and “human principle”. The GAHP (Group-decision Analytic Hierarchy Process) method is used to determine the index weights, while the index values of each risk factor are determined by using the interval valued hesitant fuzzy sets (IVHFSs) method. A comprehensive assessment of risks to social stability from land requisition and resettlement in the Jiangxiang Reservoir Project is performed, and coping strategies for major social stability risk factors are proposed. This paper effectively supports the development of assessments of risks to social stability from land requisition and resettlement in other hydraulic projects.

A probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory

With the increasing complexity of the decision environment, the fuzzy theory has attracted the extensive attention of scholars. Probabilistic interval-valued hesitant fuzzy set, as a complex ambiguous information representation tool, dedicates to depict uncertain information as complete as possible. Thus, this paper proposes a probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory and interval evidential reasoning approach. In view of the uncertainties in evaluations, the interval evidential reasoning approach is an effective tool to deal with the fuzziness and ignorance, which is first applied in probabilistic interval-valued hesitant fuzzy information in this paper. Besides, an interval projection measure is proposed to consider both distance and direction simultaneously, so as to avoid the problem of information losses in the decision process. On this basis, a novel regret-rejoice function is developed. Then, an extended gained and lost dominance score method based on regret theory and interval evidential reasoning approach is developed, which considers the regret avoidance behavior of experts. Finally, a case study on supplier selection of epidemic prevention products is applied to elucidate and illustrate the application of the proposed method in this paper.

An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection.

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E4 when the distributors focus on the criteria against 10% certainty degree and E1 is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E4 and the worst is E2 against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.

On distance measure and TOPSIS model for probabilistic interval-valued hesitant fuzzy sets: application to healthcare facilities in public hospitals

PurposeThe purpose of the development of the paper is to construct probabilistic interval-valued hesitant fuzzy Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) model and to improve some preliminary aggregation operators such as probabilistic interval-valued hesitant fuzzy averaging (PIVHFA) operator, probabilistic interval-valued hesitant fuzzy geometric (PIVHFG) operator, probabilistic interval-valued hesitant fuzzy weighted averaging (PIVHFWA) operator, probabilistic interval-valued hesitant fuzzy ordered weighted averaging (PIVHFOWA) operator, probabilistic interval-valued hesitant fuzzy weighted geometric (PIVHFWG) operator and probabilistic interval-valued hesitant fuzzy ordered weighted geometric (PIVHFOWG) operator to cope with multicriteria group decision-making (MCGDM) problems in an efficient manner.Design/methodology/approach(1) To design probabilistic interval-valued hesitant fuzzy TOPSIS model. (2) To improve some of the existing aggregation operators. (3) To propose the Hamming distance, Euclidean distance, Hausdorff distance and generalized distance between probabilistic interval-valued hesitant fuzzy sets (PIVHFSs).FindingsThe results of the proposed model are discussed in comparison with the aggregation-based method from the related literature and found the effectiveness of the proposed model and improved aggregation operators.Practical implicationsA case study concerning the healthcare facilities in public hospital is addressed.Originality/valueThe notion of the proposed distance measure is used as rational tool to extend TOPSIS model for probabilistic interval-valued hesitant fuzzy setting.

A new risk evaluation methodology based on FMEA, MULTIMOORA, TPOP, and interval-valued hesitant fuzzy linguistic sets with an application to healthcare industry

Purpose The healthcare system is regarded as one of the most critical service industries. The surgical unit is the heart of hospitals in that any failures directly affect the safety of patients, so they should be managed thoroughly. It is an intricate multi-attributes decision-making problem with uncertainty. Uncertain information in the form of fuzzy sets theory has been applied widely to describe the different aspects of system uncertainty. This study aims to present a new methodology to manage the healthcare system failures due to the multi-attributes decision-making process. Design/methodology/approach This study introduces a new risk evaluation methodology by failure mode and effect analysis (FMEA) and MULTIMOORA method. Group decision-making process in this methodology is presented under uncertain information in the form of interval-valued hesitant fuzzy linguistic sets (IVHFLSs). IVHFLSs encompass both qualitative and quantitative interpretation of experts to reflect their preferences, as well the ability and flexibility of derivation of linguistic information by several linguistic terms increase. To avoid the different ranking order of MULTIMOORA approaches, a new interval multi-approaches multi-attribute methodology, namely, technique of precise order preference (TPOP), is extended to provide precise ranking order. Findings The application and precision of proposed integrated IVHFL-MULTIMOORA methodology with TPOP is examined in a case study of healthcare systems. The results indicate the superiority of proposed methodology to prioritize and assess the failures as well as handling system uncertainty. Originality/value This study addresses the challenges of an organization to prioritize potential failures by implementing FMEA method. Moreover, this paper contributes to making the manager's ability in decision-making. The value of this study can be discussed in two aspects. First and foremost, this study provides a new FMEA-based methodology to rank failures precisely. The results prove that the proposed methodology is more robust to changes of different ranking order methods, applied by FMEA. On the other hand, using the capability of IVHFLSs allows collecting accurate information in an ambiguous and uncertain environment.

A modified class of correlation coefficients of hesitant fuzzy information

Due to the importance of correlation coefficient in data analysis, researchers have shown interest in the concept of correlation coefficient for the extensions of fuzzy sets, in particular, for a recent established extension known as hesitant fuzzy set (HFS). Most of the existing correlation coefficients for fuzzy sets return the value one to reflect a perfect linear relationship between objects, but they do not give us sufficient information about the scale with that the objects are correlated. This can be regarded as a disadvantage from the decision-making viewpoint. Moreover, some of the existing correlation coefficients were undefined in the case that the two objects are the same. To overcome such drawbacks, we propose an approach for deriving the modified correlation coefficients of HFSs based on hesitancy degree and then extend the approach to that of interval-valued hesitant fuzzy sets. Furthermore, we put forward a number of new correlation coefficients for HFSs based on Jaccard’s and Dice’s similarity criteria. Then, we give a practical example to illustrate the application of the improved correlation coefficients for HFSs in medical diagnosis. However, comparing the results of the proposed correlation coefficients with those of the other existing definitions shows that the diagnosis results may be quite different, and this is due to their orientation.

An effective similarity measurement under epistemic uncertainty

The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such interpretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets.

Analysis of acceptable additive consistency and consensus of group decision making with interval-valued hesitant fuzzy preference relations

Interval-valued hesitant fuzzy sets are efficient to denote the hesitant and uncertain judgments of decision makers. To further research the utilization of this type of fuzzy sets, this paper limits to study group decision making (GDM) with interval-valued hesitant fuzzy preference relations (IVHFPRs). First, an additive consistency index is defined for interval fuzzy preference relations, by which we derive a new acceptable additive consistency concept for IVHFPRs. Then, new models based on acceptable additive consistency are built for ascertaining unknown values, and new models for judging the acceptable additive consistency of IVHFPRs are constructed. When the consistency of IVHFPRs is unacceptable, new models based on consistency and uncertain degree are constructed for obtaining acceptable additive consistency IVHFPRs that can ensure the smallest total adjustment and the minimum number of adjusted intervals. For GDM case, a new consensus index is defined to measure the agreement degree of individual judgments. When the consensus level does not satisfy requirement, new models for reaching the additive consistency and consensus requirements are built. Furthermore, a new acceptable additive consistency- and consensus-based algorithm for GDM with incomplete and unacceptable additive consistency IVHFPRs is provided. Finally, an example is given to indicate the utilization of the new algorithm and comparison analysis is made.

A developed multi-criteria group decision-making method based on interval valued hesitant fuzzy linguistic term sets and mentality parameter

Hesitant fuzzy linguistic term set (HFLTS) can be considered as a very practical tool in addressing decision problems where people are hesitant to provide their linguistic assessments while avoiding the possible loss of information. Therefore, HFLTS enhances the flexibility to get and represent linguistic information. This paper deals with this kind of decision making problems by proposing the concept of interval valued hesitant fuzzy linguistic term sets (IVHFLTS) since it can be considered as an extension of both a linguistic term set and an interval-valued hesitant fuzzy set. This new combination deals with both quantitative and qualitative evaluations. By introducing the mentality parameter for IVHFLTS, we develop a multi-criteria group decision-making model to deal with hesitant fuzzy linguistic information which avoids the possible loss of information. In order to show the applicability and the efficiency of the proposed method, an example for the selection of the best alternative is given as well as the ranking of the alternatives from the best to worst. The promising numerical results prove that this model is available.

Empirical analysis of organizational quality defect management enabling factors identification based on SMT, interval-valued hesitant fuzzy set ELECTRE and QRA methods

Quality is of great significance in enterprises, strengthening and identifying enabling factors of quality defect management are one of core goals of organizational operation management. In this study, sense-making theory is adopted to identify organ

A method to multi-attribute decision-making based on interval-valued q-rung dual hesitant linguistic Maclaurin symmetric mean operators

The aim of this paper is to propose a new multi-attribute decision-making (MADM) method to rank all feasible alternatives in complex decision-making scenarios and determine the optimal one. To this end, we first propose the notion of interval-valued q-rung dual hesitant linguistic sets (IVq-RDHLSs) by combining interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) sets with linguistic terms set. The proposed IVq-RDHLSs utilize IVq-RDHF membership and non-membership degrees to assess linguistic terms, so that they can fully express decision-makers’ evaluation information. Additionally, some related concepts such as the operational rules, score and accuracy functions, and ranking method of IVq-RDHLSs are presented. Considering the good performance of the classical Maclaurin symmetric mean (MSM) in integrating fuzzy information, we further generalize MSM into IVq-RDHLSs to propose the interval-valued q-rung dual hesitant linguistic MSM operator, the interval-valued q-rung dual hesitant linguistic dual MSM operator, as well as their weighted forms. Afterwards, we study the applications of IVq-RDHLSs and their aggregation operators in decision-making and propose a new MADM method. Some real decision-making problems in daily life are employed to prove the rightness of the proposed method. We also attempt to demonstrate the advantages and superiorities of our proposed method through comparing with some other methods in this paper.

Multiple criteria decision making with hesitant interval-valued fuzzy sets based on hesitance degree and least common multiple principle

Multiple criteria decision making with hesitant interval-valued fuzzy sets based on hesitance degree and least common multiple principle

Interval-Valued Hesitant Fuzzy Stochastic Decision-Making Method Based on Regret Theory

Different studies show that human beings are usually limited rational, their regret aversion behavior is playing an important role in the process of stochastic decision-making. However, such psychological behavior is neglected in current studies. The interval-valued hesitant fuzzy sets can more effectively depict the uncertain information than hesitant fuzzy sets. Therefore, we propose an interval-valued hesitant fuzzy stochastic decision-making approach based on group satisfaction degree and regret theory. Firstly, based on the score and variance function, a novel group satisfaction degree is defined, which can fully reflect the overall level and group divergence. Secondly, the attribute weights optimization model based on the group satisfaction degree and the deviation of attribute values is constructed to obtain the weight vector of attributes. Then, the regret value and the rejoice value are obtained by the novel regret-rejoice function, and the alternatives are ranked according to the total psychological perception values of the decision maker. Finally, we illustrated the application of the developed method with an emergency decision-making problem. Sensitivity and comparative analyses are implemented to demonstrate the superiority, stability, and validity of the proposed method based on regret theory.

Ancient Chinese Character Image Segmentation Based on Interval-Valued Hesitant Fuzzy Set

To address the low segmentation accuracy caused by the rich glyph styles of ancient Chinese characters and the complex layout of ancient Chinese books, which affects the retrieval and recognition results, an algorithm for the layout image analysis of ancient Chinese books and Chinese character image segmentation is proposed. The initial segmentation results were obtained through the projection method of the layout of ancient Chinese books, and the connected component analysis of the above results was carried out to determine the rough divided blocks of under-segmentation and over-segmentation. Considering under-segmentation of adhesive Chinese characters, the improved K-means clustering method was used to segment adhesive blocks to obtain single-character images. To address the over-segmentation of character components separation, a method based on interval-valued hesitant fuzzy set is proposed. This method analyzed the features of the connected component in the block, characterized the over-segmentation connected component. The hesitant fuzzy distances between other connected components and the standard merge evaluation interval number were calculated in sequence. The connected component with the smallest distance was preferentially merged with the over-segmentation connected component until no over-segmentation connected component remained in the block. The experimental segmentation accuracy was 89.94%.

Generalized Shapley Choquet Integral Operator Based Method for Interactive Interval-Valued Hesitant Fuzzy Uncertain Linguistic Multi-Criteria Group Decision Making

This paper develops a new method based on generalized hybrid Shapley Choquet integral for interval-valued hesitant fuzzy uncertain linguistic multi-criteria group decision making (MCGDM), where interactive characteristics of criteria is taken into account. First, a score function and a new accuracy function are defined to rank the interval-valued hesitant fuzzy uncertain linguistic elements (IVHFULEs). Based on the Shapley Choquet integral, some generalized Shapley Choquet operator for IVHFULEs are proposed including an interval-valued hesitant fuzzy uncertain linguistic generalized Shapley Choquet (IVHFULGSC) operator and an interval-valued hesitant fuzzy uncertain linguistic generalized hybrid Shapley Choquet (IVHFULGHSC) operator and some attractive properties for these two operators are investigated in detail. Then a Shapley Choquet integral-based Minkowski distance between interval-valued hesitant fuzzy uncertain linguistic sets (IVHFULSs) is defined. Subsequently, based on the maximization deviation method, a linear programming model is built to determine the individual fuzzy measure on criteria set for each decision maker (DM). By utilizing the individual closeness coefficients matrices, a new multi-objective fractional programming model which maximizes the collective relative closeness degrees of all alternatives is constructed to obtain the fuzzy measure on DMs set. The individual decision matrices are aggregated into the collective one by using the IVHFULGHSC operator. To obtain the collective Shapely fuzzy measure on criteria set, a linear programming model is established by maximizing the deviation of the evaluations of different alternatives on each criterion. Then, the collective closeness coefficients of alternatives are calculated to rank the alternatives. Thus, a new method based on generalized hybrid Shapley Choquet integral operator is brought forward for MCGDM with IVHFULEs. Finally, an example of investment on shared bikes is provided to illustrate the applicability of the proposed method and a validity test is conducted to demonstrate the effectiveness of the proposed method.

A Prospect Theory Based Probabilistic Interval-Valued Hesitant Fuzzy Sets with Interval Reference Point and Incomplete Weight Information for Multi-Criteria Decision Making

In this paper, we introduce probabilistic interval-valued hesitant fuzzy sets (PIVHFS) and probabilistic interval-valued hesitant fuzzy elements (PIVHFE), then define correlation operations. At the same time, the hybrid distance measures of PIVHFE and interval fuzzy number are defined, and the hybrid distance measures of two PIVHFEs are also defined. Considering the psychological behavior of decision makers, we use interval fuzzy number decision makers' psychological interval reference points to calculate the gains and losses of evaluation value. Furthermore, based on incomplete weight information, the grey relational analysis (GRA) method is extended to calculate the optimal weight. Then, based on the traditional TOPSIS method, the decision-making method is proposed. Finally, the proposed method is applied to an example, and the sensitivity analysis and stability analysis of the proposed method are also discussed.

A distance measure, similarity measure and possibility degree for hesitant interval-valued fuzzy sets

A hesitant fuzzy set allows the membership degree to take a set of possible values. When experts cannot easily express their membership judgments with exact values, a hesitant fuzzy set can be extended to a hesitant interval-valued fuzzy set (HIVFS). This set bases the membership degree on a set of possible intervals. To improve the existing distance models that ignore the triangle inequality property and extend the possibility degree for interval numbers, axiom definitions of the distance measure and possibility degree of HIVFSs are proposed. Additionally, a series of distance measure models, similarity models and possibility degree models is generated. A comparative analysis shows that the new distance models satisfy the triangle inequality property but that the existing models cannot and that the possibility degree model can generate the priority degree for each pair of HIVFSs but the distance model cannot.