MAGDM Problems Research Articles

Fuzzy soft covering-based multi-granulation fuzzy rough sets and their applications

In this paper, with the aid of fuzzy soft $$\beta $$ -neighborhoods, we introduce fuzzy soft covering-based multi-granulation fuzzy rough set models. We examine some of the relevant properties of fuzzy soft covering based on optimistic, pessimistic, and variable precision multi-granulation fuzzy rough set models. Then, we give fuzzy soft coverings based on $$\psi $$ -optimistic and $${\mathscr {D}}$$ -optimistic ( $$\psi $$ -pessimistic and $${\mathscr {D}}$$ -pessimistic) multi-granulation fuzzy rough sets from fuzzy soft measures. It also discusses the interactions between these forms of fuzzy soft coverings based on multi-granulation fuzzy rough sets. Eventually, we apply the proposed models for solving MAGDM problems. The effectiveness and feasibility of our approach are noted from the introduced comparisons between our method and some methods given in the previous studies.

VIKOR Method for MAGDM Based on Q-Rung Interval-Valued Orthopair Fuzzy Information and Its Application to Supplier Selection of Medical Consumption Products.

The VIKOR model has been considered a viable tool for many decision-making applications in the past few years, given the advantages of considering the compromise between maximizing the utility of group and minimizing personal regrets. The q-rung interval-valued orthopair fuzzy set (q-RIVOFS) is a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and has emerged to solve more complex and uncertain decision making problems which IFS and PFS cannot handle. In this manuscript, the key innovation is to combine the traditional VIKOR model with q-RIVOFS to develop the q-rung interval-valued orthopair fuzzy VIKOR model. In the new developed model, to express more information, the attribute’s values in MAGDM problems are depicted by q-RIVOFNs. First of all, some basic theories and aggregation operators of q-RIVOFNs are simply introduced. Then we develop the origin VIKOR model to q-RIVOFS environment and briefly express the computing steps of this new established model. Thereafter, the effectiveness of the model is verified by an example of supplier selection of medical consumer products and through comparative analysis, the superiority of the new method is further illustrated.

Attributes Weight Determination in Magdm Problems using Some Numerical Method Techniques

Here MAGDM problems are explored. Attribute weight data given are in the form of problems involving numerical method solutions. The decision information during this study is in the shape of Intuitionistic Fuzzy Numbers (IFNs) derived from Intuitionistic Fuzzy Sets (IFSs). The IFOWA operator and IFHA operator are used for collecting the combined matrix. The modified Euler-Cauchy method and Heun method are used to calculate the unidentified weights. Effectiveness of the projected method is established using Numerical Illustrations.

Cubic Fuzzy multi-attribute group decision-making with an application to plant location selected based on a new extended Vikor method

This paper presents a new concept of trapezoidal cubic fuzzy numbers and solves the plant location selection (PLS) problem based on a new decision method with cubic fuzzy information captured through trapezoidal cubic fuzzy numbers. In the decision process, the unknown weights of the criteria are unearthed by using the Shannon entropy theory and the weights of the decision makers by integrating the Evidence theory with Bayes approximation. Based on trapezoidal cubic fuzzy numbers, we extend the classical VIKOR method to solve the MAGDM problems under cubic fuzzy environment based on the TrCFNs on proposed method.

A Novel SIR·Choquet Method for Multiple Attributes Group Decision-Making with Interval Grey Linguistic

Considering both the fuzziness caused by uncertainties and the greyness caused by inadequate information, the interval grey linguistic (i.e. IGL) variables were proposed and various multiple attributes group decision-making (i.e. MAGDM) methods have been developed. However, few approaches take the decision-maker’s (i.e. DM’s) preference structure and risk attitude into account. In this paper, the classical method named superiority and inferiority ranking (i.e. SIR) method is extended to solve the MAGDM problems in an IGL environment. First, the level of the DM’s risk attitude is taken into account when dealing with the IGL variables, and a novel G-Hamming distance is developed. Then, the Gaussian criterion, which has been mostly selected by users, is employed to describe the DM’s preference structure. Moreover, the Choquet integral is introduced as an appropriate aggregation procedure for the classical SIR method to cope with the interdependent or interactive characteristics among attributes. Finally, the SIR·Choquet method is presented in detail and two numerical examples are given to show the validity and practicality of the proposed method.

Some Single-Valued Neutrosophic Power Heronian Aggregation Operators and Their Application to Multiple-Attribute Group Decision-Making

The power Heronian aggregation (PHA) operator can use the advantages of power average and the Heronian mean operator, which together could take into account the interrelationship of the aggregated arguments, and therefore alleviate the effects caused by unreasonable data through considering the support degree between input arguments. However, PHA operators cannot be used to process single-valued neutrosophic numbers (SVNNs), which is significant for extending it to SVNNs. We propose some new PHA operators for SVNNs and introduce a novel MAGDM method on the basis of the proposed operators. Firstly, the definition, properties, comparison method, and operational rules of SVNNs are introduced briefly. Then, some PHA operators are proposed, such as the single-valued neutrosophic power Heronian aggregation (SVNPHA) operator, the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) operator, single-valued neutrosophic geometric power Heronian aggregation (SVNGPHA) operator, single-valued neutrosophic weighted geometric power Heronian aggregation (SVNWGPHA) operator. Furthermore, we discuss some properties of these new aggregation operators and several special cases. Moreover, the method to solve the MAGDM problems with SVNNs is proposed, based on the SVNWPHA and SVNWGPHA operators. Lastly, we verified the application and effectiveness of the proposed method by using an example for the MAGDM problem.

Induced Choquet Integral Aggregation Operators with Single-Valued Neutrosophic Uncertain Linguistic Numbers and Their Application in Multiple Attribute Group Decision-Making

For real decision-making problems, aggregating the attributes which have interactive or correlated characteristics by traditional aggregation operators is unsuitable. Thus, applying Choquet integral operator to approximate and simulate human subjective decision-making process, in which independence among the input arguments is not necessarily assumed, would be suitable. Moreover, using single-valued neutrosophic uncertain linguistic sets (SVNULSs) can express the indeterminate, inconsistent, and incomplete information better than FSs and IFSs. In this paper, we studied the MAGDM problems with SVNULSs and proposed two single-valued neutrosophic uncertain linguistic Choquet integrate aggregation operators where the interactions phenomena among the attributes or the experts are considered. First, the definition, operational rules, and comparison method of single-valued neutrosophic uncertain linguistic numbers (SVNULNs) are introduced briefly. Second, induced single-valued neutrosophic uncertain linguistic Choquet ordered averaging (I-SVNULCA) operator and induced single-valued neutrosophic uncertain linguistic Choquet geometric (I-SVNULCG) operator are presented. Moreover, a few of its properties are discussed. Further, the procedure and algorithm of MAGDM based on the above single-valued neutrosophic uncertain linguistic Choquet integral operator are proposed. Finally, in the illustrative example, the practicality and effectiveness of the proposed method would be demonstrated.

A decision variable-based combinatorial optimization approach for interval-valued intuitionistic fuzzy MAGDM

Some interval-valued intuitionistic fuzzy information MAGDM problems with combinatorial optimization characteristics have so many feasible alternatives that they can hardly be enumerated and evaluated. Moreover, due to the lack of quantitative functions, they are difficult to be solved with traditional combinatorial optimization methods. Therefore, by combining the MAGDM with combinatorial optimization, we propose a decision variable-based combinatorial optimization approach for the purpose of solving the interval-valued intuitionistic fuzzy MAGDM problems in this paper. Firstly, the utility evaluation matrix of decision maker is defined and the interval-valued intuitionistic fuzzy weighted average operator is used to aggregate utility evaluation matrices with decision makers’ preference information. Then, the 0–1 integer decision variable is introduced and a combinatorial optimization model is established for the interval-valued intuitionistic fuzzy MAGDM problem. For the purpose of comparison, a multi-attribute decision-making method based on the weighted relative distance is adopted to rank different alternatives. Besides, an artificial bee colony algorithm improved by integer encoding, ranking selection and elite guidance is used to solve the combinatorial optimization model. Finally, two applications of the approach are proposed: research group dispatch and group weapon-group target assignment. Through the comparison of the algorithms, the feasibility of the proposed approach was verified.

A Heterogeneous Multiattribute Group Decision‐Making Method Based on Intuitionistic Triangular Fuzzy Information

How to aggregate decision information in heterogeneous multiattribute group decision making (HMAGDM) is vital. The aim of this paper is to develop an approach to aggregating decision data into intuitionistic triangular fuzzy numbers (ITFNs) for heterogeneous MAGDM problems with real numbers (RNs), interval numbers (INs), triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), and triangular intuitionistic fuzzy number (TIFNs). Using the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) and geometry entropy method, we first present a general approach to aggregating heterogeneous information into ITFNs, which takes the group consistency of experts into account. Based on the collective intuitionistic triangular fuzzy decision matrix and extended TOPSIS, a multiple objective mathematical program is constructed to determine the optimal attribute weights. Subsequently, a new method to solve HMAGDM problems is presented based on the aforementioned discussion. A trustworthy service selection example is provided to verify the practicality and effectiveness of the proposed method.

Hybrid Binary Logarithm Similarity Measure for MAGDM Problems under SVNS Assessments

Single valued neutrosophic set is an important mathematical tool for tackling uncertainty in scientific and engineering problems because it can handle situation involving indeterminacy. In this research, we introduce new similarity measures for single valued neutrosophic sets based on binary logarithm function. We define two type of binary logarithm similarity measures and weighted binary logarithm similarity measures for single valued neutrosophic sets. Then we define hybrid binary logarithm similarity measure and weighted hybrid binary logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures.Then, we define a new entropy function for determining unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid binary logarithm similarity measure. We present an illustrative example to demonstrate the effectiveness of the proposed strategy. We conduct a sensitivity analysis of the developed strategy. We also present a comparison analysis between the obtained results from proposed strategy and different existing strategies in the literature.

An extended LINMAP method for MAGDM under linguistic hesitant fuzzy environment

The linear programming technique for multidimensional analysis of preference (LINMAP) is a representative decision making method with respect to preference information for given alternatives. In the classical LINMAP method, all of the decision data is known precisely or is given as crisp values. It cannot be used to solve the MAGDM problems under the linguistic hesitant fuzzy environment. In this paper, an extended LINMAP method is proposed to solve the MAGDM problems in which all the attribute values of alternatives and the truth degrees of all pair-wise alternatives' comparisons are in the form of linguistic hesitant fuzzy sets (LHFSs). In this method, a formula is first presented to calculate the similarity coefficient for the LHFS. On the basis of this, the weight of each expert with respect to each attribute is determined using the support function of the power average (PA) operator. Meanwhile, the collective consistency and inconsistency measurements are introduced to depict the incomplete pair-wise comparison preference relations on alternatives provided by the experts. Then, a linear programming model is constructed to determine the optimal weights of attributes. Furthermore, by calculating the comprehensive ranking values, the ranking of alternatives can be determined. Finally, a numerical example is used to illustrate the use of the proposed method.

TOPSIS and Choquet integral hybrid technique for solving MAGDM problems with interval type-2 fuzzy numbers

There are two very usful methods for solving MAGDM problems, called TOPSIS method and Choquet integral method. Because of the ability of Choquet integral method in managing of interaction criteria, we combined it with TOPSIS method to use from their benefits. First, we will introduce a new method for computing the distance between IT2FNs. Then, we proposed a hybrid method based on TOPSIS and Choquet integral in fuzzy type-2 environment. Numerical examples are considered to illustrate the proposed methods.

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.

Evolving a linear programming technique for MAGDM problems with interval valued intuitionistic fuzzy information

It is believed that multi attribute decision making problem is an ill-defined and unstructured problem. This difficulty intensifies while considering the uncertainty of decision makers’ information about the problem. In recent years, interval valued intuitionistic fuzzy sets (hereafter IVIFs) as a generalization of ordinal fuzzy sets, became a well-known and widely applied framework for dealing with uncertainty of decision making problems. However, the mathematical programming aspects of interval valued intuitionistic fuzzy sets besides their applications in decision making problems are neglected. To reinforce the mathematical programming approach in IVIF environment, an IVIF multi attribute group decision making problem is formulated as a linear programming model. Using a variable transformation and the notion of aggregation operators, the proposed model is transformed into an equivalent linear programming model solvable by common approaches. Application of the proposed method is represented in a group decision making problem and the results are compared with similar methods, proving the compatibility of the proposed method with previous ones. The solid and understandable logic with computational easiness are the main advantages of the proposed method. Solving interval valued intuitionistic fuzzy linear programming problems can be applied lucratively in other problems being formulated in this context.

A GRA method for investment alternative selection under dual hesitant fuzzy environment with incomplete weight information

Dual hesitant fuzzy set DHFS, which permits the possible membership degrees and non-membership degrees of an element having sets of values in [0,1], is considered as a powerful tool to express uncertain information in the process of multiple attribute group decision making MAGDM. In this paper, we study the MAGDM problems in which the attribute values take the form of dual hesitant fuzzy elements and the weights of attributes and decision makers take the form of real numbers. Firstly, the normalized Hamming distance of the dual hesitant fuzzy elements is defined. Then, a new method for dealing MAGDM problems under dual hesitant fuzzy environment is proposed on the basis of grey relational analysis GRA theory. For the incompletely known and completely unknown information of attribute weight, some optimization models are established to determine the weights of attributes. Finally, a numerical example of investment alternative selection is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

Extension of VIKOR Method for Multi-Attribute Group Decision Making with Incomplete Weights

In this paper, we First utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

A novel SIR method for multiple attributes group decision making problem under hesitant fuzzy environment

In this paper, an extension of SIR method, a multiple attributes hesitant fuzzy group decision making technique, to a group decision environment is investigated, where the individual decision value and the weights of attributes and experts are provided as hesitant fuzzy information. We first introduce some concepts of hesitant fuzzy set and interval-valued hesitant fuzzy set. Then, the hesitant fuzzy superiority and inferiority ranking HF-SIR method and the interval-valued hesitant fuzzy superiority and inferiority ranking IVHF-SIR method are proposed in detail. Furthermore, the approach to MAGDM problem based on the HF-SIR and IVHF-SIR method is given under hesitant fuzzy environment. Finally, a comparative analysis is illustrated with a numerical example.

Some prioritized aggregating operators with linguistic information and their application to multiple attribute group decision making

In this paper, we investigate the linguistic multiple attribute group decision making MADM problems in which the attributes and experts are in different priority level. Motivated by the ideal of prioritized aggregation operators R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 482008 263-274., we develop some prioritized aggregation operators for aggregating linguistic information, and then apply them to develop some models for linguistic multiple attribute group decision making MAGDM problems in which the attributes and experts are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some linguistic power aggregating operators and their application to multiple attribute group decision making

We investigate the multiple attribute group decision making MAGDM problems in which the attribute values take the form of linguistic variables. Motivated by the ideal of power aggregation R.R. Yager, The power average operator, IEEE Transactions on Systems, Man, and Cybernetics Part A 31 2001 724--731, in this paper, we develop some power aggregation operators for aggregating 2-tuple linguistic information, and then apply them to develop some models for multiple attribute group decision making with linguistic information. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness.