Bidirectional Projection Method for Probabilistic Linguistic Multi-criteria Group Decision-Making Based on Power Average Operator

Data modeling/aggregating, in many uncertain real-world' problems such as decision-making processes, has gotten more attention in recent years. Due to a variety of uncertainty sources, various types of fuzzy sets, and various types of averaging-based aggregation functions have been proposed. The power average operator (PAO), as a nonlinear operator, is more appropriate than other averaging-based functions for situations where different values are given on a single subject. In this paper, PAO will be extended to be used in the aggregation process of given pseudo-hesitant fuzzy elements (pseudo-HFEs), and some needed properties have been discussed, too. Then, four kinds of PAO with pseudo-HFEs, i.e., power average operator of pseudo-HFEs, power weighted average operator of pseudo-HFEs, power ordered weighted average operator of pseudo-HFEs and power hybrid average operator of pseudo-HFEs, will be defined. To solve a multi-attribute group decision-making (MAGDM) problem, the evaluation step done by both decision-makers and self-assessment will be quantified by pseudo-HFEs. Then the PAO will be applied to aggregate the row elements of the resulting decision matrix. The ranking orders of obtained pseudo-HFEs, show the options' orders. Finally, the proposed method will be used to solve a multi-attribute group decision-making problem, illustrated numerically, analyzed, and validated.

To address the grey target group decision-making method (GDMM) concerning the aggregation of decision-maker information and the approach to ranking alternatives via bidirectional projection (BP), this paper develops a novel methodological framework that optimizes both information integration and alternative evaluation, where a new transformation mechanism between the three-parameter interval grey number (TPIGN) and dual connection number (CN) is established by integrating an induced TPIGN weighted average (ITPIGN-WA) operator with an improved bidirectional projection method (IBPM). The results confirm that the new framework leads to more reliable and effective group decision making (GDM). The new TPIGN conversion mechanism and the set pair potential (SPP)-based ITPIGN-WA better captures decision-maker preferences than previous operators, and the introduction of the IBPM further refines alternative ranking. This dual innovation enriches the theoretical system of grey target decision making and provides significant applied value for enhancing the quality and effectiveness of GDM processes in uncertain environments.

Fault diagnosis is an extensively applied issue for checking and identifying the faults of objects, which comes from the combination of various theories and technologies. The contributing factors of a fault are complex owing to the uncertainty of the actual environment and the relative importance of fault criteria. Consequently, these causes fails to be considered felicitously in many conventional methods. In this paper, a neutrosophic set based fault diagnosis method based on power average operator is proposed to resolve this matter. The neutrosophic set generated from multi-stage fault sample data would be aggregated via the power average operator, then by using the defuzzification of neutrosophic set, the fault diagnosis results could be obtained. The combination of power average operator and neutrosophic set can be used for handling the relative importance of criteria, and the uncertainty of fault data. Finally, an illustrative example was provided to demonstrate the reasonableness and effectiveness of the proposed method by comparing with the existing methods.

Hesitant interval neutrosophic linguistic sets (HINLSs) are one of the core generalization of various sets, such as neutrosophic set (NS), interval neutrosophic set (INS), and interval neutrosophic linguistic set (INLS). HINLS can represent the uncertainty, inconsistency, and reluctance of assessment specialists by expressing qualitative and quantitative information. The goal of this article is to introduce a novel MADM technique that can account for changes in the semantic environment as well as negative consequences of experts’ excessive evaluation values. First, several innovative operational rules based on Schweizer-Sklar (SS) t -norm and t -conorm and a novel comparison procedure for HINLS are established by integrating different linguistic scale functions. This allows for varied semantic settings to be handled. Then, various innovative HINL Schweizer-Sklar power aggregation operators (AOs) are suggested, containing hesitant interval neutrosophic SS power average (HINLSSPA) operator, weighted hesitant interval neutrosophic SS power average (WHINLSSPA) operator, hesitant interval neutrosophic SS power geometric average (HINLSSPGA) operator, weighted hesitant interval neutrosophic SS power geometric average (WHINLSSPGA) operator, some core properties, and various special cases of these AOs are examined. Additionally, based on the initiated AOs, a multiple attribute decision making (MADM) technique with HINL information is anticipated. Finally, a numerical example is illustrated to show the effectiveness and practicality of the anticipated MADM method. A comparison with existing approaches are also discussed.

The technology of wind power is being widely developed worldwide. Ensuring the reliable operation of wind turbine systems is of significance. A popular tool to identify the potential risk of an engineering system is the failure mode and effect analysis (FMEA) method. However, when conducting a FMEA in a complex and uncertain environment, experts may find it challenging to select an appropriate linguistic term for the evaluation. The probabilistic linguistic term sets (PLTSs) are a useful fuzzy set to help experts in describing their assessment. However, different experts may assign different semantic values to the same linguistic terms, and this aspect has not been extensively examined in the existing studies. Therefore, considering the psychological behaviour of experts and the semantics of linguistic terms in the risk ranking process, an improved FMEA based on the probabilistic linguistic information and TODIM (an acronym in Portuguese of interactive and multicriteria decision making) method was developed to identify the risks in wind turbine systems. Furthermore, to demonstrate the utility of the proposed model, it was applied in a floating offshore wind turbine system. The effectiveness and the validity of the model were verified by comparing with some other methods.

The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.

The cubic q -rung orthopair fuzzy set (Cq-ROFS) is a basic simplification of several fuzzy notions, including fuzzy set (FS), interval valued FS (INVFS), intuitionistic FS (INTFS), q -rung orthopair FS (q-ROFS), and INV q -rung orthopair FS (INVq-ROFS). By the degrees of INVq-ROFS and q-ROFS, Cq-ROFS exposes fuzzy judgement, and this is one of the advanced mathematical tools to handle more complicated assessment information in multiple attribute group decision-making (MAGDM) problems. In this article, firstly, encouraged from power average (PA) operator, generalized MSM operator, and generalized dual MSM operator, two novel aggregation operators (AOs) such as cubic q -rung orthopair fuzzy power generalized Maclaurin symmetric mean (Cq-ROFPWGMSM) operator and cubic q -rung orthopair fuzzy power generalized dual Maclaurin symmetric mean (Cq-ROFPWGDMSM) operator are initiated by merging PA operator with GMSM and GDMSM operators and some core characteristics of these AOs are investigated. Furthermore, some core cases with respect to different general parameters values are also investigated and found that some aggregation operators are special cases of the initiated AOs. Secondly, the weighted form of these newly initiated aggregation operators is also offered. Thirdly, two MAGDM models are offered based on Cq-OFPGWMSM and Cq-ROFPGWDMSM operators. Lastly, a numerical example about the selection of the best assistant professor of the year is taken as an application to show the effectiveness and capability of the initiated approaches. There is also a comparison with existing decision-making models.

The power average (PA) operator can reduce the influence of unreasonable information given by biased decision makers effectively, while Heronian mean (HM) operator can take into account the correlation information between attribute variables in multiple attribute decision making (MADM). Pythagorean fuzzy set (PFS) is a useful tool to handle uncertain information, which has been widely applied in kinds of areas. In order to better infuse the Pythagorean fuzzy evaluation, in this paper we unify the advantages of the PA operator and HM operator, and present the Pythagorean fuzzy power Heronian mean (PFPHM) operator and the Pythagorean fuzzy weighted power Heronian mean (PFWPHM) operator. Some merits of the developed operators are further explored. Furthermore, on the basis of the PFWPHM operator, an approach for MADM under PFS situation is presented. Finally, a numerical case concerning investment company selection is illustrated to demonstrate the availability and feasibility of the developed approach.

As a generalization of intuitionistic fuzzy sets, neutrosophic sets (NSs) can be better handle the incomplete, indeterminate and inconsistent information, which have attracted the widespread concerns for researchers. In this paper, some new aggregation operators are proposed under single-valued neutrosophic environment. Firstly, the definition and operational laws of single-valued neutrosophic numbers (SVNNs) are introduced. Then, the single-valued neutrosophic power average (SVNPA) operator and the single- valued neutrosophic power weighted average (SVNPWA) operator are developed, and some properties of SVNPWA operator are also analyzed. Furthermore, a method for solving multi-criteria decision-making (MCDM) problems is explored based on the power aggregation operators and cosine similarity measures. Finally, an illustrative example is shown to verify the effectiveness and practicality of the proposed method.

To solve the multi-attribute decision making (MADM) problems with Pythagorean uncertain linguistic variable, an extended bi-directional projection method is proposed. First, we utilize the linguistic scale function to convert uncertain linguistic variable and provide a new projection model, subsequently. Then, to depict the bi-directional projection method, the formative vectors of alternatives and ideal alternatives are defined. Furthermore, a comparative analysis with projection model is conducted to show the superiority of bi-directional projection method. Finally, an example of graduate’s job option is given to demonstrate the effectiveness and feasibility of the proposed method.

As a critical activity in occupational risk management, the occupational health and safety risk assessment (OHSRA) aims at assessing occupational hazards in the workplace and prioritizing them to ensure employees’ safety and reduce occupational risk to an acceptable level. In this paper, we develop a new integrated OHSRA model for the risk evaluation and prioritization of occupational hazards based on probabilistic linguistic information and social network consensus analysis. The probabilistic linguistic term sets are applied to handle the hesitant risk evaluations of occupational hazards provided by experts. A combinative distance-based assessment technique is introduced for determining the risk priority of the identified occupational hazards. Additionally, the social network consensus analysis with minimum adjustment distance is used to help individual experts reach consensus. Finally, a healthcare case study is implemented for illustrating the developed OHSRA model and its effectiveness is validated with a sensitivity analysis and a comparative analysis.

In general, the information associated with real-life problems is ambiguous and imprecise, interval-valued intuitionistic hesitant fuzzy sets are an excellent medium to represent the ambiguity of information. The assessment obtained by the Bonferroni mean (BM) can manifest the correlation among the arguments. In this study, the power average operator is fused with the Bonferroni mean under the interval-valued intuitionistic hesitant fuzzy environment to develop some novel power Bonferroni mean operators such as the generalized interval-valued intuitionistic hesitant fuzzy power Bonferroni mean (GIVIHFPBM) and the generalized interval-valued intuitionistic hesitant fuzzy power geometric Bonferroni mean (GIVIHFPGBM). The most prominent characteristic of these proposed operators is that they can not only reflect the correlation among the attributes but also have the unique ability to permit the aggregated values to assist and strengthen each other. Due to this exceptional feature, the GIVIHFPBM and the GIVIHFPGBM operators can reduce the abnormality that may occur in the preference order of the overall aggregated arguments. Further, we investigate some of the special cases and discussed some of the desired properties of the proposed operators. Moreover, an MCDM method is developed based on the proposed operators. Finally, the proposed MCDM method is demonstrated with a numerical example.

Multi-criteria outranking method based on probability distribution with probabilistic linguistic information

QUALIFLEX is a flexible method to solve the multi-criteria decision-making problem with a few alternatives. Moreover, the linguistic term is a very general way used by decision makers (DMs) to express their real perceptions. In particular, the probabilistic linguistic information, including the probability of each linguistic term, can simulate the vague perceptions of the DMs well. Therefore, the main contributions of this paper are constructing two novel QUALIFLEX with probabilistic linguistic information. First, based on the classical QUALIFLEX, it has been extended under probabilistic linguistic circumstance. Secondly, it is common for the DMs to have different risk attitudes for gains and losses when making their decisions under uncertainty, which is well explained by prospect theory (PT). Hence, PT has been integrated into the extended QUALIFLEX. Then, in this paper, a prospect QUALIFLEX is proposed as well. The feasibility and validity of the proposed methods have been verified by a numerical example in venture capital. The comparative and simulated analysis shows that the latter method with prospect framework is more appropriate than the former one because of the inherent psychological behaviors of the DMs and its excellent ability in identifying the similar alternatives. Furthermore, the ranking results derived from the prospect QUALIFLEX do not change with the different values of parameters. It reveals that the prospect QUALIFLEX is stable and reliable.

Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment