Linguistic Intuitionistic Fuzzy Research Articles

A Multiple Attribute Group Decision-making Method Based on the Partitioned Bonferroni Mean of Linguistic Intuitionistic Fuzzy Numbers

As a more effective linguistic information representation model, the linguistic intuitionistic fuzzy number (LIFN), made up of the linguistic membership degree (LMD) and the linguistic non-membership degree (LNMD), plays an important role in describing uncertain-decision information in cognitive activity. The partitioned Bonferroni mean (PBM) operator is constructed based on real conditions, considering that some factors considered by decision-makers are interrelated and some are independent. The PBM operator can aggregate evaluation information under various attributes, which are divided into several independent groups; the factors interact with each other within the same group, but the factors are independent of each other when located in different groups. The classical PBM operators and their extensions can handle many decision-making problems but are unable to handle decision-making problems under a linguistic intuitionistic environment. To take full advantage of the PBM operator and LIFNs, this paper combines the PBM operator with LIFNs to propose several PBM operators for aggregating LIFNs. First, the relative theories about LIFNs are reviewed in brief. Then, linguistic intuitionistic fuzzy partitioned BM aggregation operators and partitioned geometric BM aggregation operators are discussed, including the linguistic intuitionistic fuzzy partitioned Bonferroni mean (LIFPBM) operator, the linguistic intuitionistic fuzzy weighted partitioned Bonferroni mean (LIFWPBM) operator, the linguistic intuitionistic fuzzy partitioned geometric Bonferroni mean (LIFPGBM) operator, and the linguistic intuitionistic fuzzy weighted partitioned geometric Bonferroni mean (LIFWPGBM) operator. Moreover, a novel method constructed on the developed operators is presented to address multiple attribute group decision-making (MAGDM) problems with the LIFNs. The feasibility of the proposed method is given by a numeric example, and the comparative analysis of our proposed method and other methods shows some advantages of these new methods. The developed method is constructed based on LIFNs and the PBM operator, and it is more practical and general than other existing methods and easily describes qualitative information that stems from a decision maker’s cognition. In addition, it can more effectively handle the complex relationship among multiple attributes in MAGDM problems.

Programming model-based group decision making with multiplicative linguistic intuitionistic fuzzy preference relations

A new type of fuzzy sets called multiplicative linguistic intuitionistic fuzzy sets (MLIFSs) is introduced to denote the asymmetric qualitative preferred and non-preferred cognitions of decision makers. Considering the application of MLIFSs, an order relationship is offered and several operational laws are defined. Then, multiplicative linguistic intuitionistic fuzzy preference relations (MLIFPRs) are introduced. A consistency concept is defined and its several properties are researched. A programming model to judge the consistency of MLIFPRs is constructed, and an approach to derive consistent MLIFPRs is provided. Meanwhile, a programming model to ascertain missing values in incomplete MLIFPRs is built. A consensus index is defined to measure consensus and a programming model to improve the consensus level is constructed, which ensures the consistency of individual MLIFPRs. Furthermore, a programing model to determine the weights of the decision makers is established. On the basis of consistency and consensus analysis, an approach to group decision making with MLIFPRs is developed. Finally, an example about evaluating washing machine is selected to show the application of the new method.

Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis

AbstractThe aim of the presented paper is to give a multiattribute decision making (MADM) method under the linguistic intuitionistic fuzzy (LIF) environment using the set pair analysis (SPA) theory. LIF set can express the qualitative information in terms of linguistic variables, whereas the connection number (CN) based on the “identity,” “discrepancy,” and “contrary” degrees of the SPA theory handles the uncertainties and certainties systems. On the basis of these features, we develop some series of linguistic CN (LCN) power weighted and ordered weighted geometric aggregation operator to aggregate the different LCNs. Several properties of the operators are also studied. Afterward, we present a novel MADM method to solve decision‐making problems under LIF set environment and illustrate with several examples to validate it. A comparative analysis is also presented to show the results.

Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties

Linguistic intuitionistic fuzzy set (LIFS) is one of the effective tools to represent the data in form of membership degrees in a qualitative rather than the quantitative aspects. Under this environment, the present paper develops some prioritized aggregation operators which considered the prioritized relationship between the attributes. To achieve it, first, some operational laws on LIF numbers are presented, and hence, based on these, some prioritized aggregation operators, namely, the LIF prioritized weighted, ordered weighted averaging, and geometric aggregation operators, have proposed. The fundamental properties of these operators are also investigated in detail. Furthermore, an approach to solve decision-making problem under LIFS environment has been presented and its efficiency has been verified with an illustrative example.

A Programming-Based Algorithm for Probabilistic Uncertain Linguistic Intuitionistic Fuzzy Group Decision-Making

As an effective tool to express the subjective preferences of decision makers, the linguistic term sets (LTS) have been widely used in group decision-making (GDM) problems, such as hesitant fuzzy LTS, linguistic hesitant fuzzy sets, probabilistic LTS, etc. However, due to the increasing complexity of practical decision-making (DM) problems, LTS still has a lot of room to expand in fuzzy theory. Qualitative uncertainty information in the application of GDM is yet to be improved. Therefore, in order to improve the applicability of linguistic terms in DM problems, a probabilistic uncertain linguistic intuitionistic fuzzy set (PULIFS) that can fully express the decision-maker’s (DM’s) evaluation information is first proposed. To improve the rationality of DM results, we give a method for determining individual weights in the probabilistic uncertain linguistic intuitionistic fuzzy preference relation (PULIFPR) environment. In addition, we present two consistency definitions of PULIFPR to reflect both the assessment information and risk attitudes of decision makers. Subsequently, a series of goal programming models (GPMs) are established, which effectively avoid the consistency check and correction process of existing methods. Finally, the developed method is applied to an empirical example concerning the selection of a virtual reality (VR) project. The advantages of the proposed method are demonstrated by comparative analysis.

Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators

This paper researches decision making with linguistic intuitionistic fuzzy variables. Several linguistic intuitionistic fuzzy operations are first defined. Then, several linguistic intuitionistic fuzzy aggregation operators are provided, including the linguistic intuitionistic fuzzy hybrid weighted arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid weighted geometric mean operator. Considering the interactive characteristics between the weights of elements in a set, several linguistic intuitionistic fuzzy Shapley aggregation operators are presented, including the linguistic intuitionistic fuzzy hybrid Shapley arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid Shapley geometric mean operator. To ensure the application reasonably, several desirable properties are discussed. When the weighting information is incompletely known, models for the optimal fuzzy and additive measures are constructed. After that, an approach to multi-criteria group decision making with linguistic intuitionistic fuzzy information is performed. Finally, a practical example about evaluating different types of engines is provided to illustrate the developed procedure.

Evaluating the Risk of Natural Gas Pipeline Operation Management in Intuitionistic Fuzzy Linguistic Environments

Natural gas pipeline has been regarded as the most cost effective and safest channel of gas transportation and has extraordinary strategic significance for the country. There is a need to control the risks during the operation so as to operate the pipeline safely and smoothly under the complicated business environment. In order to evaluate the risk of natural gas pipeline operation management, this paper proposed an approach to evaluate the risk of natural gas pipeline operation management in intuitionistic fuzzy linguistic environments. Firstly, the evaluation criteria of the risk of natural gas pipeline operation management are established from the strategic risk, market risk, financial risk, operation risk, and legal risk aspects. Then experts are invited to evaluate the risk level and the weight of criteria using the linguistic terms. Rating values with regard to the criteria are in linguistic forms; the linguistic terms are modeled with the intuitionistic fuzzy linguistic model. The linguistic ratings are aggregated as the final results. Finally, the example is given to illustrate the feasibility and practicability of the proposed method.

Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making

Linguistic intuitionistic fuzzy sets can be regarded as a qualitative form of intuitionistic fuzzy sets. This type of fuzzy sets uses a linguistic membership degree and a linguistic non-membership degree to represent the qualitative preferred and non-preferred judgments of decision makers. Preference relation is a useful and efficient tool for decision making that only requires the decision makers to compare two objects at one time. Taking the advantages of linguistic intuitionistic fuzzy sets and preference relations, this paper introduces linguistic intuitionistic fuzzy preference relations (LIFPRs) and studies their application to decision making. To ensure the ranking of objects reasonably, an additive consistency concept is introduced, and several of its desirable properties are discussed. To cope with inconsistent and incomplete LIFPRs, programming model-based methods to derive additively consistent LIFPRs and determine missing values are constructed, respectively. Subsequently, an approach to multi-criteria decision making with LIFPRs is offered, and the application of the new approach is illustrated by using a decision-making problem about evaluating mobile phones.

Correction to: Some Aggregation Operators for Linguistic Intuitionistic Fuzzy Set and its Application to Group Decision-Making Process Using the Set Pair Analysis

Linguistic intuitionistic fuzzy set (LIFS) is the better way to deal with the uncertain and imprecise information in group decision-making problems. On the other hand, the set pair analysis (SPA) theory provides a quantitative analysis to integrate the certainty and uncertainties as a combined system by defining the connection number corresponding to it. In the present paper, we have enhanced the LIFS with the SPA theory and hence defined the linguistic connection number (LCN) and its various operational laws. Based on it, we have developed various aggregation operators, namely LCN weighted geometric, LCN ordered weighted geometric, and LCN hybrid geometric operators with LIFS environment. Also, the shortcoming of the existing operators under LIFS environment has been highlighted and overcomes by the proposed operators. Few properties of these operators have been also investigated. Further, a group decision-making approach has been presented, based on these operators, which has been illustrated by a numerical example to show the effectiveness and validity of the proposed approach.

Scaled Prioritized Operators Based on the Linguistic Intuitionistic Fuzzy Numbers and Their Applications to Multi-Attribute Decision Making

Linguistic intuitionistic fuzzy number (LIFN) is a special intuitionistic fuzzy number which can describe the vagueness existing in the real decision making more easily. The scaled prioritized operator is a special prioritized operator which can express the prioritized relationships for different criteria by prioritized labels in knowable situation and unknowable situation. In this paper, in order to add up the advantages of them together, we propose the scaled prioritized averaging operator for LIFNs (SPLIFA) and the scaled prioritized geometric averaging operator for LIFNs (SPGLIFA) which are suitable for the problems in which the priority relationship between different categories of the attributes are known. Further, we proposed the scaled prioritized weighted averaging operator for LIFNs (SPLIFWA) and the scaled prioritized geometric weighted averaging operator for LIFNs (SPGLIFWA) which are suitable for the problems in which the priority relationship between different categories of the attributes are completely unknown. In the meantime, we discussed some characteristics of them, including idempotency, monotonicity and boundedness. Further we proposed an approach for the multi-attribute decision making on the basis of these operators. In the end, we give an example to illustrate the computing procedure and validity of our proposed method.

The Intuitionistic Fuzzy Linguistic Cosine Similarity Measure and Its Application in Pattern Recognition

We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval-valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. The main advantage of the proposed cosine similarity measures is that the decision-makers can flexibly select the linguistic scale function depending on the actual semantic situation. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval-valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example.

Some Aggregation Operators for Linguistic Intuitionistic Fuzzy Set and its Application to Group Decision-Making Process Using the Set Pair Analysis

Some Aggregation Operators for Linguistic Intuitionistic Fuzzy Set and its Application to Group Decision-Making Process Using the Set Pair Analysis

Multi-Attribute Decision-Making Based on Prioritized Aggregation Operator under Hesitant Intuitionistic Fuzzy Linguistic Environment

A hesitant intuitionistic fuzzy linguistic set (HIFLS) that integrates both qualitative and quantitative evaluations is an extension of the linguistic set, intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS) and hesitant intuitionistic fuzzy set (HIFS). It can describe the qualitative evaluation information given by the decision-makers (DMs) and reflect their uncertainty. In this article, we defined some new operational laws and comparative method for HIFLSs. Then, based on these operations, we propose two prioritized aggregation (PA) operators for HIFLSs: prioritized weighted averaging operator for HIFLSs (HIFLPWA) and prioritized weighted geometric operator for HIFLSs (HIFLPWG). Based on these aggregation operators, an approach for multi-attribute decision-making (MADM) is developed under the environment of HIFLSs. Finally, a practical example is given to show the practicality and effectiveness of the developed approach by comparing with the other representative methods.

A New Intuitionistic Fuzzy Linguistic Hybrid Aggregation Operator and Its Application for Linguistic Group Decision Making

The linguistic aggregation operator is an important decision-making model that is proving effective for dealing with the input data that takes the form of uncertain information. In this paper, considering the principal component of the intuitionistic fuzzy linguistic variables, we develop a new intuitionistic fuzzy linguistic hybrid aggregation (NIFLHA) operator to solve group decision-making problems under the situation with intuitionistic fuzzy linguistic information. Then, we study some of its main properties by utilizing some operational laws of intuitionistic fuzzy linguistic variables and the different families of the NIFLHA operator. Moreover, the multiperson NIFLHA (MP-NIFLHA) operator is introduced to evaluate the opinions of experts. Finally, an illustrative example about a multiperson decision-making problem is developed to reveal the applicability and the availability of the raised operator.

Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making

Linguistic intuitionistic fuzzy numbers (LIFNs) is a new concept in describing the intuitionistic fuzzy information, which membership and non-membership are expressed by linguistic terms, so it can more easily express the fuzzy information, and some research results on LIFNs have been achieved. However, in the existing researches, some linguistic intuitionistic fuzzy aggregation operators are based on the traditional operational rules, and they have some drawbacks for multi-attribute decision making (MADM) in the practical application. In order to overcome these problems, in this paper, we proposed some improved operational rules based on LIFNs and verified their some properties. Then we developed some aggregation operators to fuse the decision information represented by LIFNs, including the improved linguistic intuitionistic fuzzy weighted averaging (ILIFWA) operator and the improved linguistic intuitionistic fuzzy weighted power average (ILIFWPA) operator. Further, we proved their some desirable properties. Based on the ILIFWA operator and the ILIFWPA operator, we presented some new methods to deal with the multi-attribute group decision making (MAGDM) problems under the linguistic intuitionistic fuzzy environment. Finally, we used some practical examples to illustrate the validity and feasibility of the proposed methods by comparing with other methods.

An Extended VIKOR Method for Decision Making Problem with Interval-Valued Linguistic Intuitionistic Fuzzy Numbers Based on Entropy

An Extended VIKOR Method for Decision Making Problem with Interval-Valued Linguistic Intuitionistic Fuzzy Numbers Based on Entropy

Intuitionistic Fuzzy Linguistic Induced Ordered Weighted Averaging Operator for Group Decision Making

With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of intuitionistic fuzzy linguistic variables, a decision analysis approach is proposed. In this paper, we develop an intuitionistic fuzzy linguistic induce OWA (IFLIOWA) operator and analyze the properties of it by utilizing some operational laws of intuitionistic fuzzy linguistic variables. A new method based on the IFLIOWA operator for multiple attribute group decision making (MAGDM) is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM

To better deal with imprecise and uncertain information in decision making, the definition of linguistic intuitionistic fuzzy sets (LIFSs) is introduced, which is characterized by a linguistic membership degree and a linguistic nonmembership degree, respectively. To compare any two linguistic intuitionistic fuzzy values (LIFVs), the score function and accuracy function are defined. Then, based ont-norm andt-conorm, several aggregation operators are proposed to aggregate linguistic intuitionistic fuzzy information, which avoid the limitations in exiting linguistic operation. In addition, the desired properties of these linguistic intuitionistic fuzzy aggregation operators are discussed. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in multiple attribute group decision making (MAGDM).