Intuitionistic Linguistic Numbers Research Articles

Algorithms for multiple attribute group decision making with intuitionistic 2-tuple linguistic information and its application

Recently, the TODIM has been used to deal with multiple attribute decision making (MADM) problems. The intuitionistic 2-tuple linguistic sets (I2TLSs) are useful tools to depict uncertainty in MADM. This paper use TODIM method to solve MADM with the intuitionistic 2-tuple linguistic numbers (I2TLNs). Firstly, the concepts of I2TLNs are briefly presented, and classical TODIM for MADM are introduced. Then, the classical TODIM method is used to solve MADM with I2TLNs, and its important characteristic is to fully consider the decision makers’ bounded rationality which is a real action in MADM. And a comparative analysis is also given. Finally, a numerical example for service outsourcing providers selection is proposed.

A Two-Sided Matching Method for Green Suppliers and Manufacturers with Intuitionistic Linguistic Preference Information

Purpose: Due to the existing methodologies on two-sided matching seldom consider the asymmetry, uncertainty and fuzziness of the preference information, this paper aims to develop a methodology for solving the selection process between green suppliers and manufacturers with intuitionistic linguistic numbers. Methods: This paper first constructs the evaluation indicators for both sides, which are depicted as intuitionistic linguistic numbers. Subsequently, the authors redefine the intuitionistic linguistic numbers’ expected function based on regret theory. By considering the psychological behaviour of the regret aversion of decision makers, the paper constructs the comprehensive perceived values of decision makers. Furthermore, by maximizing the comprehensive perceived values for the two sides, the multi-objectives matching model is established. In addition, this paper adopts a min-max method to transform the multi-objective optimal model into the single-objective model. Conclusions: This paper considers fuzziness and hesitancy of the preference information, and also considering the psychological behaviour of the regret aversion of decision makers, the two-sided matching method proposed by this paper is more validity and effectiveness than existing methods.

A method based on TODIM technique for multi-criteria two-sided matching and its application in person-position matching

It is impossible for agents on both sides to achieve complete rationality in the decision-making process of two-sided matching (TSM). The TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method considering the psychological behavior of decision-makers is well applied in the multiple criteria decision making (MCDM) problems. The TSM is a MCDM problem. Therefore, in this paper, a method based on TODIM technique is introduced to solve the TSM problem, in which the intuitionistic linguistic numbers are utilized to describe the mutual evaluation between candidates and hiring managers. The focus of this paper is to develop a method for the multi-criteria TSM problem under intuitionistic linguistic environment. First, the evaluation matrices of each agent with respect to each criterion are provided by agents on the opposite side, and the weight assigned to each criterion is determined according to the importance of the evaluation criterion to the matching agent. Then, the dominance measurement of each agent over another one can be calculated based on the intuitionistic linguistic TODIM method. Next, a bi-objective optimization model which aims to maximize the overall satisfaction degree of agents on both sides is constructed to attain the optimal matching pair. Furthermore, the feasibility of the solution method is verified by a case study of person-position matching (PPM), and the matching result demonstrates that the proposed method is effective in dealing with multi-criteria PPM problem. Finally, the sensitivity of parameters and some comparative studies are discussed.

Two-additive fuzzy measure-based information integration approach to product design alternative evaluation

Conceptual design is a pivotal stage of new product development in manufacturing industries. Since multiple design alternatives are put forward at this stage, developing advanced evaluation methods is of great importance. Existing methods adopt additive models to integrate evaluation data. They face some inconsistency issues, e.g. inconsistency in the independent assumption and interdependent data, since evaluation criteria are interactional. Fuzzy measure that replaces the additivity with monotonicity has enabled advances in addressing such issues. This work proposes a two-additive fuzzy measure-based information integration approach to product design alternative evaluation for the first time. The evaluation data given by experts are in the form of intuitionistic linguistic numbers. They are more in accordance with the thinking habits of experts because the hesitation degree in linguistic assessment can be revealed. In order to reduce the subjective bias, the decision-making trial and evaluation laboratory method combining with grey relational analysis is applied to adjust evaluation data. Then monotonous two-additive fuzzy measure is identified by nonlinear programming using these data. It makes a good trade-off between computational complexity and presentation capability. Hence, evaluation data can be integrated by non-additive Choquet integral for ranking design alternatives. In comparison to additive model-based methods, the extra effect on the simultaneous satisfaction of criteria can be effectively revealed by the proposed approach. And the robustness of it is demonstrated by the sensitivity analysis. A case study on an elevator's design alternative evaluation is conducted to illustrate the feasibility and practicability of the proposed approach.

The ILHWLAD-MCDM Framework for the Evaluation of Concrete Materials under an Intuitionistic Linguistic Fuzzy Environment

Concrete, one of the sources of energy consumption and carbon emissions, is widely used in the construction industry. The selection of concrete materials raises the question of energy sustainability and turns it into a complex multicriteria decision-making (MCDM) issue. To address this, we present an MCDM framework based on the intuitionistic linguistic hybrid weighted logarithmic averaging distance (ILHWLAD). To begin with, the intuitionistic linguistic numbers are used to deal with the uncertainty and fuzziness of the decision-making process. In addition, in view of the significance and the ordered position of the input arguments, an intuitionistic linguistic hybrid weighted logarithmic averaging distance (ILHWLAD) operator is defined. We, then, initiate the criteria system and present the MCDM framework based on the ILHWLAD to select the finest concrete. A case study involving four alternative materials, namely, autoclaved aerated concrete (AAC), hollow concrete blocks (HCB), expanded polystyrene (EPS), and lime hemp concrete (LHC), is presented to verify the scientificity of the framework.

Multi-criteria group decision-making framework for offshore wind farm site selection based on the intuitionistic linguistic aggregation operators

Offshore wind farms have been rapidly proposed owing to the promotion of sustainable development policies. Site selection contributes to the success of offshore wind farm projects and is a complex multi-criteria group decision-making problem. This paper proposes a multi-criteria group decision-making method based on the intuitionistic linguistic aggregation operators and applies it to the site selection decision-making process of offshore wind farm. To begin with, the intuitionistic linguistic numbers are introduced to deal with the uncertainty and fuzziness in decision-making. An optimization weighting model that comprehensively considers subjective and objective factors is then established, which can effectively reflect the correlations among the criteria. Furthermore, in view of the limited rational behavior of the decision-makers, an extended intuitionistic linguistic aggregation operator is defined, according to which the criteria values can be aggregated into a numerical value for comparison. Finally, a case study in China is conducted to verify the rationality and effectiveness of this method. The research results show that the offshore wind farm located in Laizhou, Dongying is the optimal site, and the ranking results of the alternatives are sensitive to the absolute risk aversion coefficient.

Approach to Multi-Attributes Decision Making With Intuitionistic Linguistic Information Based on Dempster-Shafer Evidence Theory

Considering the limitations of the applications of a Dempster-Shafer evidence theory (DSET) in multiple attributes decision-making (MADM) and the defects of the existing MADM methods with intuitionistic linguistic numbers (ILNs), in this paper, we propose a new MADM approach. First, we provide a method to translate the evaluation values denoted by ILNs into the mass functions (MFs) under the framework of DSET. Second, we calculate the subjective weights of attributes based on the AHP method. Then, we propose a new definition of fuzzy entropy (FE) for ILNs and the objective weights of attributes are calculated by the defined FE. Moreover, we develop a linear objective programming model to obtain the comprehensive weights of attributes based on the obtained subjective and objective weights of attributes. Third, we introduce some procedures to modify the MFs of alternatives on each attribute. On these bases, a new DSET-based MADM approach with ILNs is presented. Furthermore, an application example of hotel selection is used to illustrate the presented approach. At last, some comparative analyses with other MADM methods are conducted to show the feasibility and superiority of the proposed approach.

A Novel Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-making

The intuitionistic fuzzy set (IFS) is an effective tool to express uncertain and incomplete cognitive information with the membership, non-membership, and hesitance degrees. The picture fuzzy set (PFS) is an extension of IFS, and it can contain more information than IFS. Linguistic variables (LVs) can easily describe the complex cognitive information provided by the decision makers. So it is necessary to combine the PFS with the linguistic term and define the picture fuzzy linguistic set (PFLS), then extend Archimedean triangular norms (t-norms) and triangular conorms (s-norms), which are the generalizations of a number of other t-norms and s-norms, such as Einstein, Hamacher, and Frank s-norms and t-norms, to process PFLS. By combining the PFS and the linguistic term, we define the picture fuzzy linguistic set (PFLS) and the operations of the picture fuzzy linguistic numbers (PFLNs). Further, we develop the Archimedean picture fuzzy linguistic weighted arithmetic averaging (A-PFLWAA) operator and discuss a number of properties and special cases of this operator. Besides, we propose an approach to deal with multiple attributes group decision-making (MAGDM) problem on the basis of the developed A-PFLWAA operator. An approach to solve MAGDM problem is proposed on the basis of the A-PFLWAA operator, and the validity and reliability of the proposed method are proven by an illustrative example. The PFLNs are the generalizations of the intuitionistic linguistic numbers (ILNs), and they contain more information than ILNs. In addition, our method cannot only be utilized to solve the problems with ILNs but also be used to deal with the problems with PFLNs, and it is a generalization of a number of the existing methods.

Some new operation rules and a new ranking method for interval-valued intuitionistic linguistic numbers

Some new operation rules and a new ranking method for interval-valued intuitionistic linguistic numbers

Multiattribute Decision Making Method Based on Intuitionistic Linguistic Aggregation Operator

AbstractIn this paper, some new operational laws for intuitionistic linguistic numbers are defined via Archimedean t-norm and s-norm. The prominent feature of these operations is that these operations are closed. Some main properties of these operations, like commutativity, associativity and distribution law, are investigated. Based on these operational laws, intuitionistic linguistic weighted arithmetic averaging operator is given to aggregate intuitionistic linguistic information. Furthermore, in order to reduce uncertain information of intuitionistic linguistic number, hesitancy degree is divided into degrees of membership and non-membership in proportions, and new expected function and score function are built and used to rank intuitionistic linguistic numbers. Finally, an approach is proposed to solve multiattribute decision making problems in which attribute weights are real numbers and attribute values are intuitionistic linguistic numbers, and a real example is provided to show the effectiveness and applicability of the new method.

An extended TODIM approach with intuitionistic linguistic numbers

AbstractIn many practical problems, multiple alternatives are ranked with respect to related criteria, and the criteria's weights are usually unknown. In order to solve this kind of multicriteria decision making (MCDM) problem, this paper proposes an interactive MCDM approach based on an acronym in Portuguese of interactive and multicriteria decision‐making (TODIM) method and nonlinear programming (NLP) with intuitionistic linguistic numbers (ILNs). First, by comparing the existing operations and comparison methods for ILNs, new operations and a new comparison method are defined based on linguistic scale functions to obtain rational results. Second, considering their linguistic terms, membership degrees, and nonmembership degrees as a whole, the generalized distance between ILNs is defined with an adjustable parameter. Third, the total ranking of alternatives is obtained using the proposed NLP‐based TODIM approach based on the generalized ILN distance. Finally, an example of selecting hotels from a tourism website is presented to verify the validity and feasibility of the proposed approach. A comparison with existing methods is also conducted and analyzed.

Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods.

Atanassov's Interval-Valued Intuitionistic Linguistic Multicriteria Group Decision-Making Method Based on the Trapezium Cloud Model

The cloud model, which can implement uncertain transformation between a qualitative concept and its quantitative instantiations, has attracted great attention in multicriteria decision-making problems with linguistic information. This paper proposes some operations and a possibility degree of trapezium clouds, as well as several new aggregation operators: the trapezium cloud weighted arithmetic averaging operator, the trapezium cloud ordered weighted arithmetic averaging operator, and the trapezium cloud hybrid arithmetic operator. Moreover, a method with Atanassov's interval-valued intuitionistic linguistic numbers (AIVILNs) based on trapezium clouds is presented, which can provide solutions to multicriteria group decision-making problems with Atanassov's interval-valued intuitionistic linguistic information. In this method, AIVILNs are first converted into trapezium clouds and aggregated by trapezium cloud aggregation operators. Then, the ranking of alternatives is determined by the possibility degree matrix of trapezium clouds. Finally, an illustrative example confirming the validity and feasibility of the proposed method is given.

Some Geometric Operators for Aggregating Intuitionistic Linguistic Information

With respect to intuitionistic linguistic information aggregation problems, we first define a new score function and a new accuracy function of intuitionistic linguistic number (ILN) and present a simple method for the comparison between two ILNs. Then, based on the intuitionistic linguistic weighted geometric averaging (ILWGA) operator, we propose two new intuitionistic linguistic geometric operators, such as the intuitionistic linguistic ordered weighted geometric (ILOWG) operator and intuitionistic linguistic hybrid geometric (ILHG) operator, and establish various properties of these operators. Furthermore, we apply the ILHG and ILWGA operators to solve multi-criteria group decision making problems, in which the criterion values take the form of ILNs and the criterion weight information is known completely. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed approach.

An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers

The paper proposes the concepts of a single valued neutrosophic linguistic set (SVNLS) and a single valued neutrosophic linguistic number (SVNLN) as a further generalization of the concepts of a linguistic variable, an intuitionistic linguistic set and an intuitionistic linguistic number (ILN). Then, we introduce the basic operational rules of SVNLNs and define a generalized distance measure between SVNLNs. Furthermore, we develop an extended TOPSIS method for a multiple attribute group decision making problem based on the SVNLNs under single valued neutrosophic linguistic environment. Finally, an illustrative example of investment alternatives and the comparative analysis are given to demonstrate the application and effectiveness of the developed approach.

INTUITIONISTIC UNCERTAIN LINGUISTIC WEIGHTED BONFERRONI OWA OPERATOR AND ITS APPLICATION TO MULTIPLE ATTRIBUTE DECISION MAKING

With respect to multiple attribute decision making (MADM) problems, in which attribute values take the form of intuitionistic uncertain linguistic information, a new decision-making method based on the intuitionistic uncertain linguistic weighted Bonferroni OWA operator is developed. First, the score function, accuracy function, and comparative method of the intuitionistic uncertain linguistic numbers are introduced. Then, an intuitionistic uncertain linguistic Bonferroni OWA (IULBOWA) operator and an intuitionistic uncertain linguistic weighted Bonferroni OWA (IULWBOWA) operator are developed. Furthermore, some properties of the IULBOWA and IULWBOWA operators, such as commutativity, idempotency, monotonicity, and boundedness, are discussed. At the same time, some special cases of these operators are analyzed. Based on the IULWBOWA operator, the multiple attribute decision-making method with intuitionistic uncertain linguistic information is proposed. Finally, an illustrative example is given to illustrate the decision-making steps and to demonstrate its practicality and effectiveness.

Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators

With respect to multiple attribute group decision making (MADM) problems in which attribute values take the form of intuitionistic linguistic numbers, some new group decision making methods are developed. Firstly, some operational laws, expected value, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic power generalized weighted average (ILPGWA) operator and an intuitionistic linguistic power generalized ordered weighted average (ILPGOWA) operator are developed. Furthermore, some desirable properties of the ILPGWA and ILPGOWA operators, such as commutativity, idempotency and monotonicity, etc. are studied. At the same time, some special cases of the generalized parameters in these operators are analyzed. Based on the ILPGWA and ILPGOWA operators, two approaches to multiple attribute group decision making with intuitionistic linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their 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.

Atanassov's intuitionistic linguistic ordered weighted averaging distance operator and its application to decision making

In this paper, we introduce the Atanassov's intuitionistic linguistic ordered weighted averaging distance AILOWAD operator. It is a new aggregation operator that unifies distance measures and Atanassov's intuitionistic linguistic variables in the ordered weighted averaging OWA operator. The main advantage of this aggregation operator is that it is able to use the attitudinal character of the decision maker in the aggregation of the distance measures. Moreover, it is able to deal with uncertain situations where the information can assessed with Atanassov's intuitionistic linguistic numbers. We study some of main properties and different particular cases of the AILOWAD operator. We further generalize this approach by using quasi-arithmetic means obtaining the quasi-arithmetic AILOWAD Quasi-AILOWAD operator. We also develop an application of the new approach to a multi-person decision making problem regarding the selection of strategies. Thus, we obtain the multi-person AILOWAD MP-AILOWAD operator. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Intuitionistic linguistic weighted Bonferroni mean operator and its application to multiple attribute decision making.

The intuitionistic linguistic variables are easier to describe the fuzzy information which widely exists in the real world, and Bonferroni mean can capture the interrelationship of the individual arguments. However, the traditional Bonferroni mean can only process the crisp number. In this paper, we will extend Bonferroni mean to the intuitionistic linguistic environment and propose a multiple attribute decision making method with intuitionistic linguistic information based on the extended Bonferroni mean which can consider the interrelationship of the attributes. Firstly, score function and accuracy function of intuitionistic linguistic numbers are introduced. Then, an intuitionistic linguistic Bonferroni mean (ILBM) operator and an intuitionistic linguistic weighted Bonferroni mean (ILWBM) operator are developed, and some desirable characteristics of them are studied. At the same time, some special cases with respect to the parameters p and q in Bonferroni are analyzed. Based on the ILWBM operator, the approach to multiple attribute decision making with intuitionistic linguistic information is proposed. Finally, an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.