MAGDM based on triangular Atanassov’s intuitionistic fuzzy information aggregation

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.

Intuitionistic fuzzy information aggregation under confidence levels

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

Shakeel et al. (Soft Comput 24: 1585–1597, 2020) proposed the concept of a Pythagorean uncertain linguistic hesitant fuzzy set (PULHFS), some arithmetic operations of Pythagorean uncertain linguistic hesitant fuzzy sets (PULHFSs), an approach for comparing PULHFSs and a Pythagorean uncertain linguistic hesitant fuzzy weighted averaging (PULHFWA) operator as well as it extensions. Also, using the proposed comparing approach and the proposed aggregation operators, Shakeel et al. proposed a method for solving multi-attribute group decision making (MAGDM) problems. In future other researchers may use Shakeel et al.’s work in their research work. However, it is observed that the approach for comparing PULHFSs and aggregation operators, proposed by Shakeel et al. (Soft Comput 24: 1585–1597, 2020), are not appropriate. Hence, the method for solving MAGDM problems, proposed by Shakeel et al., is also not appropriate. The aim of this note is to make the researchers aware of the inappropriateness of Shakeel et al. work. Furthermore, point out that to resolve the inappropriateness of Shakeel et al. work (Soft Comput 24: 1585–1597, 2020) is a challenging open research problem.

A new fuzzy multi-attribute group decision-making method with generalized maximal consistent block and its application in emergency management

This paper aims to put forward a hesitant fuzzy multi-attribute group decision making (MAGDM) method based on the weighted power aggregation operators in social network. From the point of view of social network analysis, decision makers (DMs) are interconnected in the process of MAGDM. Furthermore, the dimension of the obtained hesitant fuzzy element (HFE) by original power operators will be greater with the increasing number of attributes and alternatives and DMs, which will lead to the problem of “intermediate expression swell". This paper combines the order operation laws with the power operators to redefine two novel hesitant fuzzy power aggregation operators to simplify the involved calculation and explore new operators’ properties. Meanwhile, when two given elements have different number of values, we use the strength of social ties and social influence to develop an algorithm for extending the HFEs objectively. On the other hand, the PageRank algorithm and the deviation method are used to determine DMs’ combined weights. The feasibility of the proposed hesitant fuzzy MAGDM method based on social network is illustrated by the application to the actual issue of decision making and the comparative analysis with the existing method.

With respect to the multi-attribute group decision-making (MAGDM) problems with the interval grey uncertain linguistic variables (IGULVs), the MAGDM method based on the interval grey uncertain linguistic generalized hybrid averaging (IGULGHA) operator is proposed. Firstly, the operation rules, the properties and the comparing method of the IGUVs are introduced. Then, some aggregation operators such as interval grey uncertain linguistic generalized ordered weighted aggregation (IGULGOWA) operator and interval grey uncertain linguistic generalized hybrid aggregation (IGULGHA) operator are defined, and some properties such as idempotency, commutativity, monotonicity and boundedness are proved, and then, the decision-making methods based on these operators are presented to solve the group decision-making problems. Finally, a numerical example is used to show the proposed method, and the influence of the different position weight vector w and the different parameter � on decision-making is analysed. The result shows that the method is simple and effective.

This paper proposes a compromise model, based on the technique for order preference through similarity ideal solution (TOPSIS) methodology, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. This compromise programming method is based on the assumption that the optimal alternative is closer to fuzzy positive ideal solution (FPIS) and at the same time, farther from fuzzy negative ideal solution (FNIS).An aggregating function that is developed from LP- metric is based on the particular measure of ‘‘closeness” to the ‘‘ideal” solution.An efficient distance measurement is utilized to calculate positive and negative ideal solutions. The solution process is as follows: first, the decomposition algorithm is used to divide the large-dimensional objective space into a two-dimensional space. A multi-objective identical crisp linear programming is derived from the fuzzy linear model for solving the problem. Then, a single-objective large-scale linear programming problem is solved to find the optimal solution. Finally, to illustrate the proposed method, an illustrative example is provided.

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

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 purpose of this research study is to extend the multi-attribute group decision-making (MAGDM) methods to hesitant fuzzy soft set (HFS-set), hesitant fuzzy soft topology (HFS-topology) and HFS-Hausdorff spaces in group decision-making environment, as HFS-set is more superior tool to capture vagueness, hesitancy and incompleteness in individual evaluations. In order to obtain optimal decisions in MAGDM, we present two algorithms based on hesitant fuzzy soft set and hesitant fuzzy soft topology. Lastly, we present MAGDM method by using HFS-Hausdorff space to deal with hesitancy and uncertainty. The developed methods have the ability to solve MADGM problems in which the assessment information on available alternatives, provided by the experts, is presented by hesitant fuzzy soft sets. Furthermore, the efficiency of proposed algorithms is shown by applying them to the real-world problems. We use reduct, optimum reduct, aggregate HFS-sets and weight vector according of given alternatives, priority of the attributes and customer demand for best MAGDM in the selection of car.

It is proposed to use fuzzy similarity in fuzzy decision-making approach to deal with the supplier selection problem in supply chain system. According to the concept of fuzzy TOPSIS earlier methods use closeness coefficient which is defined to determine the ranking order of all suppliers by calculating the distances to both fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) simultaneously. In this paper we propose a new method by doing the ranking using similarity. New proposed method can do ranking with less computations than original fuzzy TOPSIS. We also propose three different cases for selection of FPIS and FNIS and compare closeness coefficient criteria and fuzzy similarity criteria. Numerical example is used to demonstrate the process. Results show that the proposed model is well suited for multiple criteria decision-making for supplier selection. In this paper we also show that the evaluation of the supplier using traditional fuzzy TOPSIS depends highly on FPIS and FNIS, and one needs to select suitable fuzzy ideal solution to get reasonable evaluation.

An extended multi-expert concept lattice-based heterogeneous multi-attribute group decision-making approach

Multiattribute group decision making based on intuitionistic 2-tuple linguistic information

Faced with the increasing complexity and uncertainty of decision-making information, interval-valued Fermatean hesitant fuzzy sets (IVFHFSs) were presented as a novel mathematical model that handled uncertain data more effectively. However, existing multi-attribute group decision-making (MAGDM) methods based on IVFHFSs do not thoroughly investigate the operational laws. Also, these existing MAGDM methods do not take into account the connections between attributes and are less flexible. To address these issues, this paper proposes a new MAGDM method based on Einstein Bonferroni operators under IVFHFSs. First, we thoroughly examine the operational laws of Einstein t-norms under the IVFHFSs to further extend the study of the operational laws. Then, we introduce the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean operator and the interval-valued Fermatean hesitant fuzzy Einstein weighted Bonferroni mean operator under Einstein t-norms. Our suggested aggregation operators consider the relationship between attributes and are far more flexible in comparison to the current approaches. Later, a novel MAGDM method based on Einstein Bonferroni operators under the IVFHFSs is given. Finally, the practicality and validity of the proposed method are demonstrated by a cardiovascular disease diagnosis application.