Linguistic Aggregation Research Articles

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

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs). Firstly, mo...

A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment

We develop a new multiple attribute decision making approach for dealing with 2-tuple linguistic information, called the 2-tuple linguistic induced generalized ordered weighted averaging distance (2LIGOWAD) operator. This generalization includes a wide range of 2-tuple linguistic aggregation distance operators such as the 2-tuple linguistic induced ordered weighted averaging distance (2LIOWAD) and the 2-tuple linguistic induced Euclidean ordered weighted averaging distance (2LIEOWAD) operators. We study some of its main properties, and we further generalize the 2LIGOWAD operator by using the Quasi-arithmetic means. Finally we present an application of the developed operator to a group decision making problem about selection of strategies.

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.

Some generalized dependent aggregation operators with 2-dimension linguistic information and their application to group decision making

With respect to the multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of the 2-dimension linguistic information, a new decision making method is proposed. Firstly, motivated by the ideals of dependent aggregation operator (Z.S. Xu, Dependent uncertain ordered weighted aggregation operators, Information Fusion 9 (2008), 310–316), some 2-dimension linguistic dependent aggregation operators are developed, including a 2-dimension linguistic generalized dependent ordered weighted averaging (2DLGDOWA) operator and a 2-dimension linguistic generalized dependent hybrid weighted averaging (2DLGDHWA) operator which can relieve the influence of unfair 2-dimension linguistic arguments on the aggregated results by assigning low weights to those “false” and “biased” ones. Furthermore, some desirable properties of these operators are studied, such as commutativity, idempotency, monotonicity and boundedness, and some special case are analyzed. Then based on these operators, an approach to multiple attribute group decision making with 2-dimension linguistic information is proposed. Finally, an illustrate example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Hesitant fuzzy linguistic information aggregation in decision making

As a generalisation of fuzzy linguistic set (FLS), a hesitant fuzzy linguistic term set (HFLTS) is introduced to provide a linguistic and computational basis to increase the richness of linguistic elicitation based on the fuzzy linguistic approach and the use of context-free grammars by using comparative terms. And the HFLTS is a very useful tool to deal with fuzzy linguistic uncertainty, which can be accurately and perfectly described in terms of the opinions of experts. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy linguistic information. We first discuss the relationship between FLS and HFLTS, based on which we develop some operations for hesitant fuzzy linguistic elements. The correlations among the aggregation operators are further discussed. Based on the developed operators, we introduce a method for decision making with hesitant fuzzy linguistic information. Finally, we give their application in decision making problems.

Trapezoid fuzzy 2-tuple linguistic aggregation operators and their applications to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of trapezoid fuzzy 2-tuples. Firstly, we develop some trapezoid fuzzy 2-tuple linguistic aggregation operators based on the operational laws of trapezoid fuzzy 2-tuples, such as the trapezoid fuzzy 2-tuple weighted geometric (TFTWG) operator, the trapezoid fuzzy 2-tuple ordered weighted geometric (TFTOWG) operator, the generalized trapezoid fuzzy 2-tuple weighted average (GTFTWA) operator and the generalized trapezoid fuzzy 2-tuple ordered weighted average (GTFTOWA) operator. Then, we study some desirable properties of the developed operators, such as idempotency, monotonicity, commutativity and boundedness, and analyze some special cases of these operators. Furthermore, we propose an approach to multiple attribute decision making under trapezoid fuzzy linguistic environment based on the GTFTWA and TFTWG operators. Finally, an illustrative example is given to verify the proposed approach 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.

Multi-attribute group decision making methods with proportional 2-tuple linguistic assessments and weights

AbstractThe proportional 2-tuple linguistic model provides a tool to deal with linguistic term sets that are not uniformly and symmetrically distributed. This study further develops multi-attribute group decision making methods with linguistic assessments and linguistic weights, based on the proportional 2-tuple linguistic model. Firstly, this study defines some new operations in proportional 2-tuple linguistic model, including weighted average aggregation operator with linguistic weights, ordered weighted average operator with linguistic weights and the distance between proportional linguistic 2-tuples. Then, four multi-attribute group decision making methods are presented. They are the method based on the proportional 2-tuple linguistic aggregation operator, technique for order preference by similarity to ideal solution (TOPSIS) with proportional 2-tuple linguistic information, elimination et choice translating reality (ELECTRE) with proportional 2-tuple linguistic information, preference ranking organi...

Evaluation on Functions of Urban Waterfront Redevelopment Based on Proportional 2-Tuple Linguistic

AbstractAs a planning strategy, “connectivity” has been used to promote the functions of Urban Waterfront space to revitalize the city. By analyzing the hierarchy of functions of Urban Waterfront, namely ecological function, social function and context function, an index system of assessing its functions is proposed. In order to overcome the drawbacks which are only used numerical scales or simple linguistic values in the traditional expert evaluation for the functions of Urban Waterfront, a proportional 2-tuple linguistic representation model is introduced. Some proportional 2-tuple linguistic aggregation operators are proposed, such as PTWA, PTOWA, PTHA operators. A group decision making procedure to evaluate the functions of urban waterfront by the proposed proportional 2-tuple linguistic operators is developed. A case study of two typical redevelopment projects in West Lake Waterfront of Hangzhou of China is also provided.

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

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic and geometric operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic arithmetic aggregation operators, hesitant fuzzy linguistic geometric aggregation operators, hesitant fuzzy linguistic correlated aggregation operators, induced hesitant fuzzy linguistic aggregation operators, induced hesitant fuzzy linguistic correlated aggregation operators, hesitant fuzzy linguistic prioritized aggregation operators, hesitant fuzzy linguistic power aggregation operators. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach.

Single valued neutrosophic trapezoid linguistic aggregation operators based multi-attribute decision making

Multi-attribute decision making (MADM). Play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, single valued neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation SVNTrLWAA operator and neutrosophic trapezoid linguistic weighted geometric aggregation SVNTrLWGA operator is presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

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

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs). Firstly, motivated by the idea of hesitant fuzzy linguistic elements and intuitionistic fuzzy numbers, the concept, operational laws and comparison laws of HIFLEs are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic fuzzy linguistic information, such as hesitant intuitionistic fuzzy linguistic weighted aggregation operators, hesitant intuitionistic fuzzy linguistic ordered weighted aggregation operators and hesitant intuitionistic fuzzy linguistic hybrid aggregation operators. Some desirable properties of these operators and the relationships between them are discussed. Furthermore, the hesitant intuitionistic fuzzy linguistic set is extended to hesitant intuitionistic fuzzy uncertain linguistic set, and some hesitant intuitionistic fuzzy uncertain linguistic aggregation operators are developed. Based on the hesitant intuitionistic fuzzy linguistic weighted average (HIFLWA) operator, an approach to MADM is proposed under hesitant intuitionistic fuzzy linguistic environment. Finally, a practical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness.

Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators

For multi-criteria group decision making problems with intuitionistic linguistic information, we define a new score function and a new accuracy function of intuitionistic linguistic numbers, and propose a simple approach for the comparison between two intuitionistic linguistic numbers. Based on the intuitionistic linguistic weighted arithmetic averaging ILWAA operator, we define two new intuitionistic linguistic aggregation operators, such as the intuitionistic linguistic ordered weighted averaging ILOWA operator and the intuitionistic linguistic hybrid aggregation ILHA operator, and establish various properties of these operators. The ILOWA operator weights the ordered positions of the intuitionistic linguistic numbers instead of weighting the arguments themselves. The ILHA operator generalizes both the ILWAA operator and the ILOWA operator at the same time, and reflects the importance degrees of both the given intuitionistic linguistic numbers and the ordered positions of these arguments. Furthermore, based on the ILHA operator and the ILWAA operator, we develop a multi-criteria group decision making approach, in which the criteria values are intuitionistic linguistic numbers and the criteria weight information is known completely. Finally, an example is given to illustrate the feasibility and effectiveness of the developed method.

Dual hesitant fuzzy linguistic aggregation operators and their applications to multi-attribute decision making

This paper studies the multi-attribute decision making (MADM) problems under two situations that the attributes are independent and correlative, respectively, in which the attribute values take the form of dual hesitant fuzzy linguistic elements and the weights of attributes take the form of real numbers. Firstly, the concept, operational laws, score function and accuracy function of dual hesitant fuzzy linguistic element (DHFLE) are defined. For the situation that the attributes are independent, some dual hesitant fuzzy linguistic geometric aggregation operators are proposed. Considering that there exists prioritization among the attributes, we propose several dual hesitant fuzzy linguistic prioritized aggregation operators based on the prioritized average (PA) operator. Moreover, some desirable properties and special cases of these operators are investigated in detail. Based on the proposed operators, two novel approaches to MADM with dual hesitant fuzzy linguistic information are proposed. Finally, a numerical example for investment alternative selection is given to illustrate the application of the proposed methods.

A LINGUISTIC AGGREGATION OPERATOR INCLUDING WEIGHTS FOR LINGUISTIC VALUES AND EXPERTS IN GROUP DECISION MAKING

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice.

Linguistic Multi-Attribute Decision Making with a Prioritization Relationship

In this paper we consider linguistic information aggregation problems where a prioritization relationship exists over attributes. The authors define a prioritized 2-tuple ordered weighted averaging (PTOWA) operator to aggregate satisfactions of alternatives under attributes with a linear prioritized ordering. The authors then use the PTOWA and a TOWA operator to aggregate linguistic information where attributes are partitioned into some categories of which prioritization between categories exists. Finally, two illustrative examples are employed to show the feasibility of the proposed method.

A new linguistic computational model based on discrete fuzzy numbers for computing with words

In recent years, several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed. However, until now all of them rely on the special semantics of the linguistic terms, usually fuzzy numbers in the unit interval, and the linguistic aggregation operators are based on aggregation operators in [0,1]. In this paper, a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model. In this framework, no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented. These aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set. Finally, an example of a multi-expert decision-making problem in a hierarchical multi-granular linguistic context is given to illustrate the applicability of the proposed method and its advantages.

Some hybrid aggregating operators in linguistic decision making with Dempster–Shafer belief structure

In this paper, we have studied the Dempster–Shafer theory of evidence in situations of decision making with linguistic information and we develop a new aggregation operator: belief structure generalized linguistic hybrid averaging (BS-GLHA) operator and a wide range of particular cases. we have developed the new decision making model with Dempster–Shafer belief structure that uses linguistic information in order to manage uncertain situations that cannot be managed in a probabilistic way. We have seen that all these approaches are very useful for representing the new approaches in a more complete way selecting for each situation the particular case that it is closest to our interests in the specific problem analyzed. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method. We have pointed out that the results and decisions are dependent on the linguistic aggregation operator used in the decision making process.

Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making

The induced 2-tuple linguistic generalized ordered weighted averaging (2-TILGOWA) operator is presented. This new aggregation operator extends previous approaches by using generalized means, order-inducing variables in the reordering of the arguments and linguistic information represented with the 2-tuple linguistic approach. Its main advantage is that it includes a wide range of linguistic aggregation operators. Thus, its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with our interests or beliefs. We further generalize the 2-TILGOWA by using quasi-arithmetic means and Choquet integrals. The result is the Quasi-2-TILOWA operator and the 2-tuple linguistic induced quasi-arithmetic Choquet integral aggregation. We conclude this paper by analysing the applicability of this new approach in a multi-person linguistic decision-making problem concerning product management.