The multi-attribute group decision-making method based on the interval grey uncertain linguistic generalized hybrid averaging operator

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome.

Novel approach to multi-attribute group decision-making based on interval-valued Pythagorean fuzzy power Maclaurin symmetric mean operator

Plant location selection (PLS) is a typical and complex multi-attribute group decision-making (MAGDM) problem, which requires consideration of several alternatives and multiple attributes. However, existing research results on PLS lack sufficient consideration of complex relationship patterns between attributes, which often leads to inaccurate decision results. Thus, in this paper, a new MAGDM technique is proposed to solve the problem of PLS, in which complex interrelationship structures exist between multi-inputs and attribute values are represented as interval-valued intuitionistic uncertain linguistic variables (IVIULVs). First, to solve the shortcomings of the existing operations, some new operational rules are redefined for IVIULVs based on linguistic scale functions and Archimedean T-conorms and T-norms. These new rules of operation hold the closedness, and are flexible for semantic transformation processing. Then, to more accurately reflect the partition structure and the complex interrelationship pattern among multi-input arguments, we extend the traditional Hamy mean and propose the partitioned Hamy mean (PHAM), which can eliminate the impact of unrelated attributes on the results and meet the semantic conversion needs of different decision makers. Furthermore, we develop two new fuzzy linguistic aggregation operators: interval-valued intuitionistic uncertain linguistic PHAM (IVIULPHAM) and its weighted version (IVIULWPHAM). Finally, a novel MAGDM technique (IVIUL-MAGDM) based on the IVIULWPHAM operator is proposed to solve the problem of PLS. Several examples of PLS are also illustrated to show the validity and advantages of the IVIUL-MAGDM method by comparing with the other existing MAGDM methods.

Selecting an optimum technique for disposing of biomedical waste is a frequently observed obstacle in multi-attribute group decision-making (MAGDM) problems. The MAGDM is commonly applied to tackle decision-making states originated by obscurity and vagueness. The interval-valued q-rung orthopair fuzzy soft set is a novel variant of fuzzy sets. The main objective of this study is to introduce the interval-valued q-rung orthopair fuzzy soft Einstein-ordered weighted and Einstein hybrid weighted aggregation operators. Based on developed aggregation operators, a novel decision-making approach, the Evaluation based on the Distance from the Average Solution introduced to solve the MAGDM problem. The execution of the proposed approach demonstrates the significant impact of determining the most effective strategy to handle biomedical waste. Our proposed approach's practicality is confirmed by a case study focusing on selecting the most effective technique for Biomedical Waste (BMW) treatment. This study shows that autoclaving is the most effective method for the disposal of BMW. Comparative and sensitivity analysis confirms the consistency and effectiveness of our methodology. The comparative study indicates the effects of the proposed strategy are more feasible and realistic than the prevailing techniques.

A sequential multiple attribute three-way group decision-making method to heterogeneous MAGDM problems with unknown weight information

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.

The recruitment of university researchers can be considered a multi-attribute group decision-making (MAGDM) problem. MAGDM is a familiar issue with uncertainty and fuzziness in the decision-making field. Generalized hesitation fuzzy numbers (GHFNs) as a new expanded form of hesitation fuzzy numbers (HFNs) can better express the uncertain information in MAGDM. The TODIM is a very classical and widely used method to deal with the MAGDM issue. In this paper, we integrate cumulative prospect theory (CPT) into TODIM to consider not only decision makers’ subjective risk preferences but also their confidence level to obtain more reasonable choices under risk conditions. Therefore, we propose the GHF CPT-TODIM approach to tackle the MAGDM issue. Meanwhile, in the GHF environment, it is proposed to use the volatility of attribute information (entropy weighting method) to obtain the importance of attributes, obtain the unknown attribute weight, and enhance the rationality of weight information. Finally, the validity and usefulness of the technique are verified by applying the GHF CPT-TODIM technique to the recruitment of university researchers and comparing it with the existing GHF MAGDM method, which offers a new way to solve the MAGDM problem with GHFNs.

This paper proposes a new method to deal with the multi-attribute group decision making (MAGDM) problem. Firstly, a new distance measure between two linguistic terms is defined, then a new linguistic information aggregation operator based on the distance measure is proposed and their properties are studied. Secondly, in order to deal with multi-attribute group decision making problem under linguistic environment, a similarity measure between two linguistic preference matrices is proposed. The aggregation operator and the similarity measure are applied to a MAGDM problem. Finally, a numerical example is proposed to prove that the new operator is effective in the MAGDM problems. This method avoid the case that a numerical value times a linguistic information and the results of evaluation are still belongs to the original linguistic term set no matter how to calculate. By using the supporting of the order, the linguistic information can not be lose in the aggregation process. Keywords-Distance measure; linguistic information; aggregation operator; similarity measure; MAGDM

The aim of this paper is to define some new operation laws for trapezoidal cubic hesitant fuzzy (TrCHF) numbers and define some new aggregation operators. In order to extend these operational laws of the trapezoidal cubic hesitant fuzzy numbers (TrCHFNs), we constructed a series of aggregation operator so called trapezoidal cubic hesitant fuzzy averaging and geometric aggregation operators. Furthermore, these aggregation operators applied to group decision making. Finally, a numerical example is used to illustrate the validity of the proposed approach in group decision-making problems.

An intuitionistic fuzzy set (IFS) is a valuable tool to execute uncertain and indeterminate information. IFSs are more suitable to identify decision-maker’s evaluation data in decision-making problems. Intuitionistic fuzzy aggregation operators (AOs) are of enormous consequences in multiple attribute group decision-making (MAGDM) problems with an intuitionistic fuzzy environment. Consequently, the main impacts of this article are: firstly, to instigate various new novel generalized power AOs based on Schweizer-Sklar operational rules for IFS. Secondly, the study aims to discuss characteristics and particular cases of AOs. The core edge of proposed AOs is that they can eradicate the influence of uncomfortable data which could be too high or too low, making them more admirable for efficiently solving more and more complex MAGDM problems. Thirdly, we instigate two new algorithms to deal with MAGDM established on the generalized Schweizer-Sklar power AOs. Lastly, we appertain the anticipated method and algorithms to health care waste treatment technology selection (HCW-TT) to show the competence of the anticipated method and algorithms. The prevailing novelties of these items are duplex. Firstly, new generalized AOs established on Schweizer-Sklar operational rules are initiated for IFNs. Secondly, two new approaches for IF MAGDM are initiated, one for known decision-makers (DMs) and attributes weights, while the other for unknown DMs and attributes weights.

Multi-attribute group decision-making based on q-rung orthopair fuzzy Aczel–Alsina power aggregation operators

Neutrosophic theories and methods are suitable for handling a variety of uncertain information, especially in complex decision-making situations. Nowadays, how to study multi-attribute group decision-making (MAGDM) problems in neutrosophic environments is a vital task for scholars and practitioners. Granular computing is a popular mathematical framework for uncertain problems, and it has been proved as a useful tool for solving MAGDM problems. In this chapter, a new neutrosophic multigranulation model for MAGDM is proposed, and some theoretical models and decision-making algorithms are presented. Finally, some case studies and comparative analysis are performed to show the merit of the presented models and algorithms. In general, this chapter is conducive to neutrosophic decision-making communities and intelligent decision-making methods.

Because of the complexity of decision-making environment, the uncertainty of fuzziness and the uncertainty of grey maybe coexist in the problems of multi-attribute group decision making. In this paper, we study the problems of multi-attribute group decision making with hybrid grey attribute data (the precise values, interval numbers and linguistic fuzzy variables coexist, and each attribute value has a certain grey degree), and present a new grey hybrid multi-attribute group decision making method based on grey linguistic 2-tuple. Concretely, the concept of grey linguistic 2-tuple is defined based on the traditional linguistic 2-tuple, and the transformation methods of transforming the precise values, interval numbers and linguistic fuzzy variables into the grey linguistic 2-tuples are presented respectively. Further, a new grey linguistic 2-tuple weighted averaging (emph{GLTWA}) operator is presented to aggregate multiple decision makers' individual decision information into comprehensive decision information, and then a ranking method based on grey 2-tuple correlation degree is presented to rank all alternatives and to select the winners. An application decision making example of supplier selection is also given to validate the method developed and to highlight the implementation, practicality and effectiveness of the presented method.

To quantify the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. RUs include S-shaped RU and non-S-shaped RU. Each RU affords a framework where the psychological factors explicitly enter the decision problem via the basic utility function, reference point and loss aversion coefficient. Under the general framework, we derive a generalized ordered weighted S-shaped RU proportional averaging (GOSP) operator and a generalized ordered weighted non-S-shaped RU proportional averaging (GONSP) operator, respectively. The GOSP operator implies the risk attitude of the DM for relative losses is risk-seeking, while GONSP operator indicates the risk attitude in this case is risk-averse. As a special case, GONSP operator can degenerate into GOWPA operator which means that the attitude of the DM is risk-neutral. Each operator satisfies the desirable properties of general operator, i.e., monotonicity, commutativity, idempotency and boundedness. Furthermore, we consider hyperbolic absolute risk aversion (HARA) function as the basic utility function, and define an S-shaped HARA and a non-S-shaped HARA utility functions. Based on the two new RUs, we propose GOSP–HARA operator and GONSP–HARA operator. Every operator covers many existing aggregation operators. To ascertain weights of such operators, the paper builds an attribute-deviation weight model and a DMs-deviation weight model. Based on these RU operators and weight models, an approach is addressed for solving multiple attribute group decision-making problem. At last, an example is provided to show the feasible of our approach.

Applications of T-spherical fuzzy aczel-alsina power muirhead mean operators in identifying the most effective water purification process for commercial purpose