2-tuple Linguistic Aggregation Operators Research Articles

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

A novel linguistic decision-making method based on the voting model for large-scale linguistic decision making

The notable characteristic of large-scale linguistic decision-making problems is that there are so many decision makers who provide linguistic assessments by using fuzzy linguistic representation models. In real-world applications, fuzzy linguistic terms mean different things for different people, and linguistic assessments based on different linguistic representation models may be simultaneous in the same large-scale linguistic decision-making problems. To this end, a novel linguistic decision-making method based on the voting model is proposed in the paper to deal with multi-linguistic assessments provided by decision makers. In large-scale linguistic decision process, evaluation-based voting is defined and multi-linguistic decision matrix is designed to represent multi-linguistic assessments provided by decision makers by using different linguistic representation models, and properties of the decision matrix are analyzed to show that linguistic assessments based on different linguistic representation models can be simultaneously represented. Based on multi-linguistic decision matrix, a new linguistic decision-making framework is developed to deal with large-scale linguistic decision-making problems with multi-linguistic assessments, in which normalization of multi-linguistic decision matrix and trust degrees of linguistic terms are contained, and more important, based on trust degrees of linguistic terms and 2-tuple fuzzy linguistic aggregation operators, an uniform fusion method of multi-linguistic assessments is proposed to aggregate multi-linguistic assessments of large-scale linguistic decision-making problems. Finally, user experiences of shared bikes, which are a large-scale linguistic decision-making problem in real-world applications, are employed to show the new decision-making framework and the uniform fusion method of multi-linguistic assessments, and furthermore, compared with existing linguistic decision-making methods analyzed in the example, it seems that multi-linguistic decision matrix and the uniform fusion method are useful and effective tools to deal with large-scale linguistic decision-making problems with multi-linguistic assessments.

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems.

Analysis of Robot Selection Based on 2-Tuple Picture Fuzzy Linguistic Aggregation Operators

The aim of this article is to propose the 2-tuple picture fuzzy linguistic aggregation operators and a decision-making model to deal with uncertainties in the form of 2-tuple picture fuzzy linguistic sets; 2-tuple picture fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a number of aggregation operators, namely, 2-TPFLWA, 2-TPFLOWA, 2-TPFLHA, 2-TPFLWG, 2-TPFLOWG, and 2-TPFLHG operators. The distinguished feature of the developed operators are studied. At that point, we used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple picture fuzzy linguistic information. Then, a practical application of robot selection by manufacturing unit is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent approaches is conducted to reveal the advantage of our developed method. Results indicate that the proposed method is suitable and effective for decision-making problems.

2-tuple intuitionistic fuzzy linguistic aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decisionmaking (MADM) problems with 2-tuple intuitionistic fuzzylinguistic information. Then, we utilize arithmetic and geometricoperations to develop some 2-tuple intuitionistic fuzzy linguisticaggregation operators. The prominent characteristic of theseproposed operators are studied. Then, we have utilized theseoperators to develop some approaches to solve the 2-tupleintuitionistic fuzzy linguistic MADM problems. Finally, apractical example for enterprise resource planning (ERP) systemselection is given to verify the developed approach and todemonstrate its practicality and effectiveness.

A note on “Picture 2-tuple linguistic aggregation operators in multiple attribute decision making”

By combining picture fuzzy set and 2-tuple linguistic representation model, Wei et al. (Soft Comput 22(3):989–1002, 2018) proposed the concept of picture 2-tuple linguistic set and presented some operational laws of picture 2-tuple linguistic numbers (P2TLNs). On the basis of operational laws of P2TLNs, some picture 2-tuple linguistic aggregation operators have been further developed. However, some operational laws and results derived by aggregation operators proposed by Wei et al. (Soft Comput 22(3):989–1002, 2018) are conflict with definition of picture 2-tuple linguistic number (P2TLN). In this short note, we propose some novel operational laws of P2TLNs and develop one adjusted picture 2-tuple linguistic aggregation operator, i.e., the adjusted picture 2-tuple linguistic weighted averaging operator.

Model for Multiple Attribute Decision Making Based on Picture 2-Tuple Linguistic Power Aggregation Operators

In this article, the authors investigate the multiple attribute decision making problems with picture 2-tuple linguistic information. The utilized power average and power geometric operations used to develop some picture 2-tuple linguistic power aggregation operators: picture 2-tuple linguistic power weighted average (P2TLPWA) operator, picture 2-tuple linguistic power weighted geometric (P2TLPWG) operator, picture 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, picture 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, picture 2-tuple linguistic power hybrid average (P2TLPHA) operator and picture 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators is studied. This article has utilized these operators to develop some approaches to solve the picture 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Optimized interval 2-tuple linguistic aggregation operator based on PGSA and its application in MAGDM

Optimized interval 2-tuple linguistic aggregation operator based on PGSA and its application in MAGDM

Interval-valued 2-tuple hesitant fuzzy linguistic term set and its application in multiple attribute decision making

The hesitant fuzzy linguistic term sets can retain the completeness of linguistic information elicitation by assigning a set of possible linguistic terms to a qualitative variable. However, sometimes experts cannot make sure that the objects attain these possible linguistic terms but only provide t he degrees of confidence to express their hesitant cognition. Given that the interval numbers can denote the possible membership degrees that an object belongs to a set, it is suitable and convenient to provide an interval-valued index to measure the degree of a linguistic variable to a given hesitant fuzzy linguistic term set. Inspired by this idea, we introduce the concept of interval-valued 2-tuple hesitant fuzzy linguistic term set (IV2THFLTS) based on the interval number and the hesitant fuzzy linguistic term set. Then, we define some interval-valued 2-tuple hesitant fuzzy linguistic aggregation operators. Afterwards, to overcome the instability of subjective weights, we propose a method to compute the weights of attributes. For the convenience of application, a method is given to solve the multiple attribute decision making problems with IV2THFLTSs. Finally, a case study is carried out to validate the proposed method, and some comparisons with other methods are given to show the advantages of the proposed method.

Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making

Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making

Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making

Bipolar 2-tuple linguistic aggregation operators in multiple attribute decision making

Picture 2-Tuple Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Decision Making

In this paper, we investigate the multiple attribute decision-making problems with picture 2-tuple linguistic information. Then, we utilize Bonferroni mean and geometric Bonferroni mean operations to develop some picture 2-tuple linguistic aggregation operators: picture 2-tuple linguistic Bonferroni mean operator and picture 2-tuple linguistic geometric Bonferroni mean operator. Some desired properties and special cases of the developed operators are discussed in detail. Furthermore, considering the importance of the input arguments, we propose the picture 2-tuple linguistic weighted Bonferroni mean operator and picture 2-tuple linguistic weighted geometric Bonferroni mean operator. Finally, a practical example for selecting the service outsourcing provider of communications industry is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Picture 2-tuple linguistic aggregation operators in multiple attribute decision making

In this paper, we investigate the multiple attribute decision-making problems with picture 2-tuple linguistic information. Then, we utilize arithmetic and geometric operations to develop several picture 2-tuple linguistic aggregation operators. The prominent characteristic of these proposed operators is studied. Then, we have utilized these operators to develop some approaches to solving the picture 2-tuple linguistic multiple attribute decision-making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

2-tuple linguistic aggregation operators based on subjective sensation and objective numerical scales for multi-criteria group decision-making problems

Many 2-tuple linguistic aggregation operators and linguistic multi-criteria group decision-making (MCGDM) approaches have been successfully applied to numerous problems, they are difficult to reflect the different semantics of linguistic terms, distances between adjacent linguistic terms, and the subjective sensations of decision-makers in diverse decision-making problems. In this paper, some 2-tuple linguistic aggregation operators are proposed, which are based on the subjective sensation scale and objective numerical scale, and a method is developed, which is based on the proposed operators, to overcome the aforementioned limitations. Firstly, the subjective sensation scale based on linguistic term sets, the subjective sensation scale and objective numerical scale based on 2-tuples are presented. Then some 2-tuple linguistic operators based on the two scales are developed; namely the generated extended 2-tuple weighted averaging (GE2T-WA) operator, generated extended 2-tuple ordered weighted averaging (GE2T-OWA) operator, generated extended 2-tuple weighted geometric (GE2T-WG) operator and generated extended 2-tuple ordered weighted geometric (GE2T-OWG) operator. Subsequently, based on the GE2T-WA and GE2T-OWA operators, or on the GE2T-WG and GE2T-OWA operators, a MCGDM method is developed. Finally, an example is provided and the proposed method is compared with some existing approaches, using the same illustrative example, for confirming its feasibility and rationality.

2-tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection

Purpose– The purpose of this paper is to develop some 2-tuple linguistic aggregation operators based on Muirhead mean (MM), which is combined with multiple attribute group decision making (MAGDM) and applied the proposed MAGDM model for supplier selection under 2-tuple linguistic environment.Design/methodology/approach– The supplier selection problem can be regarded as a typical MAGDM problem, in which the decision information should be aggregated. In this paper, the authors investigate the MAGDM problems with 2-tuple linguistic information based on traditional MM operator. The MM operator is a well-known mean type aggregation operator, which has some particular advantages for aggregating multi-dimension arguments. The prominent characteristic of the MM operator is that it can capture the whole interrelationship among the multi-input arguments. Motivated by this idea, in this paper, the authors develop the 2-tuple linguistic Muirhead mean (2TLMM) operator and the 2-tuple linguistic dual Muirhead mean (2TLDMM) operator for aggregating the 2-tuple linguistic information, respectively. Some desirable properties and special cases are discussed in detail. Based on which, two approaches to deal with MAGDM problems under 2-tuple linguistic information environment are developed. Finally, a numerical example concerns the supplier selection problem is provided to illustrate the effectiveness and feasibility of the proposed methods.Findings– The results show that the proposed can solve the MAGDM problems within the context of 2-tuple linguistic information, in which the attributes are existing interaction phenomenon. Some 2-tuple aggregation operators based on MM have been developed. A case study of supplier selection is provided to illustrate the effectiveness and feasibility of the proposed methods. The results show that the proposed methods are useful to aggregate the linguistic decision information in which the attributes are not independent so as to select the most suitable supplier.Practical implications– The proposed methods can solve the 2-tuple linguistic MAGDM problem, in which the interactions exist among the attributes. Therefore, it can be used to supplier selection problems and other similar management decision problems.Originality/value– The paper develop some 2-tuple aggregation operators based on MM, and further present two methods based on the proposed operators for solving MAGDM problems. It is useful to deal with multiple attribute interaction decision-making problems and suitable to solve a variety of management decision-making applications.

An Approach to Hesitant Fuzzy Group Decision Making with Multi-Granularity Linguistic Information

The 2-tuple linguistic computational model is an important tool to deal with linguistic information. To extend the application of hesitant fuzzy linguistic term sets and avoid information loss, this paper introduces hesitant fuzzy 2-tuple linguistic term sets that are expressed by using several symbolic numbers in [0,1]. Considering the order relationship between hesitant fuzzy 2-tuple linguistic term sets, measures of expected value and variance are defined. Meanwhile, several induced generalized hesitant fuzzy 2-tuple linguistic aggregation operators are defined, by which the comprehensive attribute values of alternatives can be obtained. Then, models for the optimal weight vector on a decision maker set, on an attribute set and on their ordered sets are constructed, respectively. Furthermore, an approach to multi-granularity group decision making with hesitant fuzzy linguistic information is developed. Finally, an example is selected to illustrate the feasibility and practicality of the proposed procedure.

Some Interval 2-Tuple Linguistic Harmonic Mean Operators and Their Application in Material Selection

We investigate the multiple attribute group material selection problems in which the attribute values take the form of interval 2-tuple linguistic information. Firstly, some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop some interval 2-tuple linguistic aggregation operators called interval 2-tuple hybrid harmonic mean (ITHHM) operator, induced interval 2-tuple ordered weighted harmonic mean (I-ITOWHM) operator, and induced interval 2-tuple hybrid harmonic mean (I-ITHHM) operator and study some desirable properties of the I-ITOWHM operator. In particular, all these operators can be reduced to aggregate 2-tuple linguistic variables. Based on the I-ITHHM and the ITWHM (interval 2-tuple weighted harmonic mean) operators, an approach to multiple attribute group decision-making with interval 2-tuple linguistic information is proposed. Finally, a practical application to material selection problem is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some new Shapley 2-tuple linguistic Choquet aggregation operators and their applications to multiple attribute group decision making

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems with 2-tuple linguistic information. Firstly, motivated by the ideas of Choquet integral and Shapley index, we propose three 2-tuple linguistic aggregation operators called Shapley 2-tuple linguistic Choquet averaging operator, Shapley 2-tuple linguistic Choquet geometric operator and generalized Shapley 2-tuple linguistic Choquet averaging operator. Then we discuss some properties of these operators, such as idempotency, monotonicity, boundary and commutativity. Secondly, if the information about the weights of decision makers (DMs) and attributes is incompletely known, we build two models to determine the optimal fuzzy measures on DM set and attribute set, respectively. Furthermore, we develop a new method for multiple attribute group decision making under 2-tuple linguistic environment based on the proposed operators. Finally, we apply the developed MAGDM method to select the most desirable emergency alternative and the validity of the developed method is verified by comparing the evaluation results with those obtained from the existing 2-tuple correlated aggregation operators.

Multi-criteria Group Decision-Making Approach Based on 2-Tuple Linguistic Aggregation Operators with Multi-hesitant Fuzzy Linguistic Information

In practice, when the frequency of a linguistic term in evaluation information is greater than one, a consensus has been reached and this frequency is regarded to be one by default. However, in case that the frequencies of several elements in a dataset are not identical, their respective importance that was initially distinguishable will become indifferent in a routine processing, which may distort the original intention of decision-makers. As an extension of hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic sets (HFLSs), multi-hesitant fuzzy linguistic term sets (MHFLTSs) are thus proposed on the basis of multi-hesitant fuzzy sets (MHFSs) in this paper, and each multi-hesitant fuzzy linguistic term element (MHFLTE) can contain inconsecutive and repeatable linguistic terms. Besides, inspired by the 2-tuple linguistic model and linguistic scale functions, the transformation functions among linguistic terms, 2-tuples, and numerical data are constructed in a generalized form to cope with different semantics. According to practical conditions, decision-makers’ preferences, or experts’ suggestions, various functions can be chosen after some necessary adjustments. In this way, the original essence of vague evaluations can be retained properly and the accuracy and reliability of final results could be further improved. Furthermore, the basic operations and comparison method of MHFLTEs are given on the basis of the transformation functions, and some 2-tuple linguistic aggregation operators of MHFLTEs are also provided to deal with problems where the criteria weights are known or unknown. Based on these prerequisites, a multi-criteria group decision-making approach is established to process multi-hesitant fuzzy linguistic information. The validity and effectiveness of the proposed approach are finally demonstrated through illustration and comparison analysis.

Dependent Interval 2-Tuple Linguistic Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches.