Uncertain Linguistic Aggregation Operators Research Articles

Decision-Making Approach Based on Bipolar Complex Fuzzy Uncertain Linguistic Aggregation Operators

Decision-Making Approach Based on Bipolar Complex Fuzzy Uncertain Linguistic Aggregation Operators

Some interactive uncertain linguistic aggregation operators based on Shapley function and their application

In this paper, two uncertain linguistic aggregation operators named the induced uncertain linguistic hybrid Shapley arithmetical averaging (IULHSAA) operator and the induced uncertain linguistic hybrid Shapley geometric mean (IULHSGM) operator are defined. These operators do not only globally consider the importance of the elements and their ordered positions but overall reflect the correlations between them, respectively. Furthermore, to reduce the complexity of solving a fuzzy measure, the induced uncertain linguistic hybrid 2-additive Shapley arithmetical averaging (IULHASAA) operator and the induced uncertain linguistic hybrid 2-additive Shapley geometric mean (IULHASGM) operator are defined. Moreover, if the weight information of experts and attributes is incompletely known, models for the optimal fuzzy measures are established. Meanwhile, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, which considers the correlative characteristics between experts as well as between attributes. Finally, a numerical example is provided to illustrate the developed procedure.

An Approach of Interval-Valued Picture Fuzzy Uncertain Linguistic Aggregation Operator and Their Application on Supplier Selection Decision-Making in Logistics Service Value Concretion

With respect to multiple criteria group decision-making (MCGDM) problems in which both the criteria weights and the expert weights take the form of crisp numbers and attribute values take the form of interval-valued picture fuzzy uncertain linguistic numbers, some new group decision-making analysis methods are developed. Firstly, some operational laws, expected value, and accuracy function of interval-valued picture fuzzy uncertain linguistic numbers are introduced. Then, an interval-valued picture fuzzy uncertain linguistic averaging and geometric aggregation operators are developed. Furthermore, some desirable properties of the developed operators, such as commutativity, idempotency, and monotonicity, have been studied. Based on these operators, an approach to multiple criteria group decision-making with interval-valued picture fuzzy uncertain linguistic information has been proposed. Finally, a practical example of 3PL supplier selection in logistics service value concretion is taken to test the defined method and to expose the effectiveness of the defined model.

The q-Rung Orthopair Hesitant Fuzzy Uncertain Linguistic Aggregation Operators and Their Application in Multi-Attribute Decision Making

This paper combines the q-rung orthopair hesitant fuzzy sets (q-ROHFSs) with the uncertain linguistic variables, and proposes the q-rung orthopair hesitant fuzzy uncertain linguistic sets (q-ROHFULSs). In addition, the Schweizer-Sklar T-norm is introduced, and a multi-attribute decision-making method based on the q-rung orthopair hesitant fuzzy uncertain linguistic Schweizer-Sklar aggregation operators is established. Firstly, based on the Schweizer-Sklar T-norm, the operational properties of q-rung orthopair hesitant fuzzy uncertain linguistic elements are defined, and the score function, accuracy function and ranking method of the q-rung orthopair hesitant fuzzy uncertain linguistic elements are proposed. Secondly, the q-rung orthopair hesitant fuzzy uncertain linguistic Schweizer-Sklar Bonferroni mean (BM) operator and geometric Bonferroni mean (GBM) operator, Maclaurin symmetric mean (MSM) operator and dual Maclaurin symmetric mean (DMSM) operator, Maclaurin mean (MM) operator and dual Maclaurin mean (DMM) operator are defined. The calculation formulas of the operators are given, the related properties are studied, and the special forms of the operators are discussed. Finally, a multi-attribute decision-making model based on the q-rung orthopair hesitant fuzzy uncertain linguistic aggregation operators is established, and the feasibility and effectiveness of the decision-making method are demonstrated through calculation examples and comparative analyses.

Some q ‐rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making

Some <i>q</i> ‐rung orthopair uncertain linguistic aggregation operators and their application to multiple attribute group decision making

Multiple attribute decision making based on interval-valued Pythagorean uncertain linguistic aggregation operators

Multiple attribute decision making based on interval-valued Pythagorean uncertain linguistic aggregation operators

Picture uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making

PurposeThe purpose of this paper is to develop some picture uncertain linguistic aggregation operators based on Bonferroni mean operators, which is combined with multiple attribute decision-making (MADM) and has applied the proposed MADM model for selecting the service outsourcing provider of communications industry under picture uncertain linguistic environment.Design/methodology/approachThe service outsourcing provider selection problem of communications industry can be regarded as a typical MADM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MADM problems with picture uncertain linguistic information based on traditional Bonferroni mean operator.FindingsThe results show that the proposed model can solve the MADM problems within the context of picture uncertain linguistic information, in which the attributes are existing interaction phenomenon. Some picture uncertain aggregation operators based on Bonferroni mean have been developed. A case study of service outsourcing provider selection problem of communications industry is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the picture uncertain linguistic decision information in which the attributes are not independent so as to select the most suitable supplier.Research limitations/implicationsThe proposed methods can solve the picture uncertain linguistic MADM problem, in which the interactions exist among the attributes. Therefore, it can be used to solve service outsourcing provider selection problems and other similar management decision problems.Practical implicationsThis paper develops some picture uncertain aggregation operators based on Bonferroni mean and further presents two methods based on the proposed operators for solving MADM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.Social implicationsIt is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.Originality/valueThe paper investigates the MADM problems with picture uncertain linguistic information based on traditional Bonferroni mean operator and develops the picture uncertain linguistic Bonferroni mean operator and picture uncertain linguistic geometric Bonferroni mean operator, picture uncertain linguistic weighted Bonferroni mean operator and picture uncertain linguistic weighted geometric Bonferroni mean operator for aggregating the picture uncertain linguistic information, respectively. Finally, a numerical example concerning the service outsourcing provider selection problem of communications industry is provided to illustrate the effectiveness and feasibility of the proposed methods.

Picture uncertain linguistic aggregation operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problems with picture uncertain linguistic information. Then, we utilize arithmetic and geometric operations to develop some picture uncertain linguistic aggregation operators: picture uncertain linguistic weighted average (PULWA) operator, picture uncertain linguistic weighted geometric (PULWG) operator, picture uncertain linguistic ordered weighted average (PULOWA) operator, picture uncertain linguistic ordered weighted geometric (PULOWG) operator, picture uncertain linguistic hybrid average (PULHA) operator and picture uncertain linguistic hybrid geometric (PULHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the picture uncertain linguistic multiple attribute decision making problems. Finally, a practical example for micro-credit risk evaluation of micro-credit companies is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Interval-valued dual hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problem based on the arithmetic and geometric aggregation operators with interval valued hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we shall develop some aggregation operators for aggregating interval valued hesitant fuzzy uncertain linguistic information: interval valued hesitant fuzzy uncertain linguistic arithmetic aggregation operators, interval valued hesitant fuzzy uncertain linguistic geometric aggregation operators, interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, interval valued hesitant fuzzy uncertain linguistic prioritized aggregation operators, interval valued hesitant fuzzy uncertain linguistic power aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we shall utilize these operators to develop some approaches to solve the interval valued hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Pythagorean uncertain linguistic aggregation operators for multiple attribute decision making

Pythagorean uncertain linguistic aggregation operators for multiple attribute decision making

An Approach to Multicriteria Group Decision-Making with Unknown Weight Information Based on Pythagorean Fuzzy Uncertain Linguistic Aggregation Operators

With respect to multicriteria group decision-making (MCGDM) problems in which the experts have different priority levels, the criteria values are in the form of Pythagorean fuzzy uncertain linguistic variables (PFULVs), and the information about weights of experts and criteria is completely unknown, a novel decision-making method is developed. Firstly, the concept of PFULV is defined, and some operational laws, score function, accuracy function, and normalized Hamming distance of PFULVs are presented. Then, to aggregate information given by all experts, the Pythagorean fuzzy uncertain linguistic prioritized weighted averaging aggregation (PFULPWAA) operator and the Pythagorean fuzzy uncertain linguistic prioritized weighted geometric aggregation (PFULPWGA) operator are proposed. Furthermore, in order to get a comprehensive evaluation value for each alternative, the Pythagorean fuzzy uncertain linguistic Maclaurin symmetric mean aggregation (PFULMSMA) operator and the weighted PFULMSMA (WPFULMSMA) operator are proposed. Moreover, to obtain the information about the weights of criteria, the model based on grey relational analysis (GRA) method is established. Finally, a method of MCGDM with PFULVs is developed, and an application example is given to illustrate the validity and feasibility of the provided procedure.

Multiple attribute decision-making method based on 2-dimension uncertain linguistic density generalized hybrid weighted averaging operator

Two-dimension uncertain linguistic variables (2DULVs) are very effective tools in describing the uncertain and fuzzy information, which are composed of I class linguistic information and II class linguistic information. Density aggregation operators not only consider the importance of all attributes but also take the importance of the density and the order positions of attributes into account, so they can more accurately deal with the fuzzy decision-making problems. In this paper, firstly, some basic theories, such as the definition, the expectation value and the operational laws of the 2DULVs, are briefly introduced. Then, some density aggregation operators based on 2DULVs are proposed, such as 2-dimension uncertain linguistic density arithmetic aggregation operators, 2-dimension uncertain linguistic density geometric aggregation operators and 2-dimension uncertain linguistic density generalized aggregation operators. Furthermore, we propose a multiple attribute decision-making method based on the 2-dimension uncertain linguistic density generalized hybrid weighted averaging operators. Finally, we use an illustrative example to demonstrate the practicality and effectiveness of the proposed method.

Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision making problem based on the arithmetic and geometric aggregation operators with interval valued hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we shall develop some aggregation operators for aggregating interval valued hesitant fuzzy uncertain linguistic information: interval valued hesitant fuzzy uncertain linguistic arithmetic aggregation operators, interval valued hesitant fuzzy uncertain linguistic geometric aggregation operators, interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic aggregation operators, induced interval valued hesitant fuzzy uncertain linguistic correlated aggregation operators, interval valued hesitant fuzzy uncertain linguistic prioritized aggregation operators, interval valued hesitant fuzzy uncertain linguistic power aggregation operators. The prominent characteristic of these proposed operators are studied. Then, we shall utilize these operators to develop some approaches to solve the interval valued hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

An Approach to Uncertain Linguistic Multi-Attribute Group Decision Making Based on Interactive Index

In this paper, two uncertain linguistic Choquet aggregation operators called the induced uncertain linguistic hybrid generalized Shapley Choquet weighted averaging (IULHGSCWA) operator and the induced uncertain linguistic hybrid generalized Shapley Choquet geometric mean (IULHGSCGM) operator are defined. To reduce the complexity of solving a fuzzy measure, the induced uncertain linguistic hybrid 2-additive generalized Shapley Choquet weighted averaging (IULHAGSCWA) operator and the induced uncertain linguistic hybrid 2-additive generalized Shapley Choquet geometric mean (IULHAGSCGM) operator are presented. When the weight information is incompletely known, models for the optimal fuzzy measures on an expert set, on an attribute set and on their ordered sets are built, respectively. Furthermore, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, which can cope with the interdependent or correlative characteristics between elements. Finally, a practical application is selected to illustrate the validity and practicability of the developed procedure.

Uncertain Linguistic Power Geometric Operators and Their Use in Multiattribute Group Decision Making

Based on the extended triangular norm, several new operational laws for linguistic variables and uncertain linguistic variables (ULVs) are defined. To avoid the limitations of existing linguistic aggregation operators, a series of extended uncertain linguistic (UL) geometric aggregation operators are proposed on the basis of the extended triangular norm. In addition, a multiattribute group decision making (MAGDM) method dealing with UL information is developed based on the extended UL geometric aggregation operators. Finally, an example is presented to show the efficiency of the developed approach in solving MAGDM problems.

A Group Decision Making Approach Based on Interval-Valued Intuitionistic Uncertain Linguistic Aggregation Operators

This paper investigates group decision making problems in which the criterion values take the form of interval-valued intuitionistic uncertain linguistic numbers (IIULNs). First, some additive operational laws of IIULNs are defined. Subsequently, some new arithmetic aggregation operators, such as the interval-valued intuitionistic uncertain linguistic weighted averaging (IIULWA) operator, interval-valued intuitionistic uncertain linguistic ordered weighted averaging (IIULOWA) operator and interval-valued intuitionistic uncertain linguistic hybrid aggregation (IIULHA) operator, are proposed which are based on the operational laws. Furthermore, an approach to group decision making with interval-valued intuitionistic uncertain linguistic information is developed, which is based on the IIULWA and IIULHA operators. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.

Some generalized interval-valued hesitant uncertain linguistic aggregation operators and their applications to multiple attribute group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the assessment values of attributes take the form of interval-valued hesitant uncertain linguistic elements, a novel MAGDM method is proposed in this paper. Firstly, the concept, operational laws and score function of interval-valued hesitant uncertain linguistic elements (IVHULEs) are introduced. Then, based on the operational laws of IVHULEs, some generalized aggregation operators are proposed for aggregating the interval-valued hesitant uncertain linguistic information, including the generalized interval-valued hesitant uncertain linguistic weighted aggregation operators, the generalized interval-valued hesitant uncertain linguistic ordered weighted aggregation operators and the generalized interval-valued hesitant uncertain linguistic hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed. Based on the proposed operators, an approach to multiple attribute group decision making with unknown weight information is developed under interval-valued hesitant uncertain linguistic environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

Group Decision Making Based on Induced Generalized Uncertain Linguistic Aggregation Operators

Aims: The aim of this paper is to investigate group decision making based on induced generalized uncertain linguistic aggregation operators Study Design: In this paper, we propose some new operational laws of linguistic variables and uncertain linguistic variables on the basis of the extended triangular conorm and triangular norm, study their properties and relationships. Place and Duration of Study: The existing operational laws of linguistic variables and uncertain linguistic variables may have some drawbacks. Methodology: Based on new operational laws of linguistic variables and uncertain linguistic variables, we develop two new uncertain linguistic aggregation operators including the induced generalized uncertain linguistic ordered weighted averaging (IGULOWA) operator and induced generalized uncertain linguistic ordered weighted geometric (IGULOWG) operator. Results: Some desirable properties and special cases of the IGULOWA and IGULOWG operators are studied, and then, the IGULOWA and IGULOWG operators are utilized to develop an approach for multiple attribute group decision making with uncertain linguistic information. Conclusion: A practical application of the developed approach to an investment problem is given. Original Research Article British Journal of Applied Science & Technology, 4(19): 2699-2751, 2014 2700

Model for multiple attribute group decision making with uncertain linguistic information

We investigate the multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of uncertain linguistic variables. Motivated by the idea of power geometric aggregation, in this paper, we develop some uncertain linguistic power geometric aggregation operators: the uncertain linguistic power weighted geometric (ULPWG) operator and the uncertain linguistic power ordered weighted geometric (ULPOWG) operator, and then apply them to multiple attribute group decision making problems with uncertain linguistic information. Finally, an illustrative example for evaluating the urban land intensive use in the Three Gorges reservoir area is given to verify the developed approaches and to demonstrate its practicality and effectiveness.

Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making

Hesitant fuzzy sets, originally proposed by Torra, can be used as an efficient tool for dealing with situations in which experts hesitate between several numerical values to define the membership of an element in a quantitative setting. However, similar situations may occur in qualitative settings where experts hesitate between several possible linguistic terms to assess the membership of an element. To deal with such cases, Rodriguez et al. [21] introduced the concept of a hesitant fuzzy linguistic term set HFLTS. A hesitant fuzzy linguistic term set is an ordered finite subset of consecutive linguistic terms of a linguistic term set. However, it is noted that there are situations where the linguistic terms contained in the hesitant fuzzy linguistic term set are not consecutive. To address this issue, in this paper, we extend the hesitant fuzzy linguistic term set and introduce the concept of a hesitant fuzzy linguistic set HFLS by combining the hesitant fuzzy set and the fuzzy linguistic approach. Then, we develop some hesitant fuzzy linguistic aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy linguistic sets HFLSs. We also investigate the relationships among these operators. Furthermore, we extend the hesitant fuzzy linguistic set to uncertain linguistic environments, i.e., present the concept of a hesitant fuzzy uncertain linguistic set HFULS. We develop some hesitant fuzzy uncertain linguistic aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy uncertain linguistic sets HFULSs. We study the relationships among these operators. Next, we utilize the hesitant fuzzy linguistic aggregation operators to develop an approach to multiple attribute group decision making with hesitant fuzzy linguistic information and utilize the hesitant fuzzy uncertain linguistic aggregation operators to develop an approach to multiple attribute group decision making with hesitant fuzzy uncertain linguistic information. Finally, we apply both the developed approaches to two numerical examples.