Linguistic Intuitionistic Fuzzy Set Research Articles

Optimizing bioremediation techniques for soil decontamination in a linguistic intuitionistic fuzzy framework

Bioremediation techniques, which harness the metabolic activities of microorganisms, offer sustainable and environmentally friendly approaches to contaminated soil remediation. These methods involve the introduction of specialized microbial consortiums to facilitate the degradation of pollutants, contribute to soil restoration, and mitigate environmental hazards. When selecting the most effective bioremediation technique for soil decontamination, precise and dependable decision-making methods are critical. This research endeavors to tackle the aforementioned concern by utilizing the tool of aggregation operators in the framework of the Linguistic Intuitionistic Fuzzy (LIF) environment. Linguistic Intuitionistic Fuzzy Sets (LIFSs) provide a robust framework for representing and managing uncertainties associated with linguistic expressions and intuitionistic assessments. Aggregation operators enrich the decision-making process by efficiently handling the intrinsic uncertainties, preferences, and priorities of MADM problems; as a consequence, the decisions produced are more reliable and precise. In this research, we utilize this concept to devise innovative aggregation operators, namely the linguistic intuitionistic fuzzy Dombi weighted averaging operator (LIFDWA) and the linguistic intuitionistic fuzzy Dombi weighted geometric operator (LIFDWG). We also demonstrate the critical structural properties of these operators. Additionally, we formulate novel score and accuracy functions for multiple attribute decision-making (MADM) problems within LIF knowledge. Furthermore, we develop an algorithm to confront the complexities associated with ambiguous data in solving decision-making problems in the LIF Dombi aggregation environment. To underscore the efficacy and superiority of our proposed methodologies, we adeptly apply these techniques to address the MADM problem concerning the optimal selection of a bioremediation technique for soil decontamination. Moreover, we present a comparative evaluation to delineate the authenticity and practical applicability of the recently introduced approaches relative to previously formulated techniques.

Pandemic management by using sentiment analysis and trapezoidal type-2 fuzzy linguistic intuitionistic fuzzy matrix games

In order to explore effective management strategies in the context of epidemics, this study introduces a novel concept: Trapezoidal type-2 fuzzy linguistic intuitionistic fuzzy set (TrT2FLIFS) and proposes a trapezoidal type-2 fuzzy linguistic intuitionistic fuzzy matrix game (TrT2FLIFMG). Subsequently, employing sentiment analysis based on the BosonNLP sentiment lexicon, the study extracts comment data from Weibo related to epidemics made by users and calculates their textual scores. These two methods are integrated and applied to policy selection in epidemic management, along with the introduction of a new ranking function to compare the importance of alternative policies. Finally, a comparative analysis with existing methods is conducted to validate the effectiveness of the proposed approach.

Probabilistic linguistic q-rung orthopair fuzzy Archimedean aggregation operators for group decision-making

To express uncertain and imprecise information systematically, the concept of probabilistic linguistic q-rung ortho-pair fuzzy set (PLqROFS), which is an advanced version of linguistic intuitionistic fuzzy set and linguistic Pythagorean fuzzy set, considering the instantaneous occurrence of stochastic and non-stochastic-uncertainty. There isn't yet any literature on PLqROFSs that addresses the issue of the relative importance of experts and criteria. The evaluation's findings consequently become irrational. Additionally, the aggregation operators that are currently available on PLqROFSs are too rigid. The primary goal is to resolve these problems by creating a new methodology that makes use of a new flexible aggregation operator. In this paper, a novel integrated framework is suggested to address concerns with group decision-making in PLqROFSs settings by combining the strengths of the power average operator (PAO), the Archimedean operator, and the full consistency method (FUCOM). With the extended variance approach on PLqROFSs, the weight of decision experts is methodically determined in this line. Additionally, the FUCOM on PLqROFSs is used to determine the weight of the criterion. Some probabilistic linguistic q-rung ortho-pair fuzzy Archimedean weighted and power weighted aggregation operators are suggested to aggregate decision experts' preferences. To discuss the viability of the suggested technique, the challenge of choosing a CO2 storage location is given. As alternatives, we have taken into account oilfields, gas fields, basalt formations, and coal resources. Basalt is the best choice, according to the outcome. The stability of our method is demonstrated by the sensitivity analysis of the criteria weights. The comparative analysis demonstrates that, in comparison to the ones already in use, our model is more significant and realistic.

A novel linguistic decision making approach based on attribute correlation and EDAS method

One of characteristics of large-scale linguistic decision making problems is that decision information with respect to decision making attributes is derived from multi-sources information. In addition, the number of decision makers, alternatives or criteria of decision making problems in the context of big data are increasingly large. Correlation analysis between decision making attributes has become an important issue of large-scale linguistic decision making problems. In the paper, we concentrate on correlation analysis between decision making attributes to deal with large-scale decision making problems with linguistic intuitionistic fuzzy values. Firstly, we proposed a new similarity measure between two linguistic intuitionistic fuzzy sets to formally define correlation between decision making attributes. Then we propose linguistic intuitionistic fuzzy reducible weighted Maclaurin symmetric mean (LIFRWMSM) operator and linguistic intuitionistic fuzzy reducible weighted dual Maclaurin symmetric mean (LIFRWDMSM) operator to aggregate linguistic intuitionistic fuzzy value decision information of correlational decision making attributes, and analyze several important properties of the two operator. Inspired by evaluation based on distance from average solution (EDAS) method, we design a solution scheme and decision steps to deal with large-scale linguistic intuitionistic fuzzy decision making problems. To show the effectiveness and usefulness of the proposed decision method, we employ the choice of buying a house and the selection of travel destination to demonstrate our method and make comparative analysis with others aggregation operators or methods.

Group decision making based on weighted distance measure of linguistic intuitionistic fuzzy sets and the TOPSIS method

Linguistic intuitionistic fuzzy numbers (LIFNs) are useful to express the uncertainty of qualitative aspects of information, which have received many attentions in recent years. In this paper, we propose the distance measure of linguistic intuitionistic fuzzy sets (LIFSs), where the membership grade and the non-membership grade of each element in the universe of discourse belonging to a LIFS are represented by LIFNs. We also provide the proofs of the validity and some desirable properties of the proposed distance measure of LIFSs. Moreover, we also propose the weighted distance measure of LIFSs. Based on the proposed weighted distance measure of LIFSs and the “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) method, we propose a new group decision making (GDM) approach in the environments of LIFNs. We also use some examples to illustrate the practicability and the feasibility of the proposed GDM approach. The proposed GDM approach can overcome the drawbacks of the existing GDM approaches, where they have the drawbacks that they cannot distinguish the ranking orders of the alternatives in some situations. It provides us a very useful method for dealing with GDM problems in the environments of LIFNs.

2DLIF-PROMETHEE based on the hybrid distance of 2-dimension linguistic intuitionistic fuzzy sets for multiple attribute decision making

2-dimension linguistic intuitionistic fuzzy set (2DLIFS) includes two classes of linguistic intuitionistic fuzzy variables, which has a more powerful and flexible ability in representing and handling uncertainty than 2-dimension linguistic fuzzy set (2DLFS) and intuitionistic fuzzy set (IFS). Distance and similarity are two important tools to quantify the difference and closeness of 2DLIFSs. This paper proposes the Euclidean distance and the cosine similarity measures for 2DLIFSs, respectively. Due to the limitation of the Euclidean distance and the cosine similarity measures for 2DLIFSs, a hybrid distance for 2DLIFSs is introduced by integrating these two measures. Further, based on the hybrid distance for 2DLIFSs, 2DLIF-PROMETHEE methods are introduced to deal with the multiple attribute decision making (MADM) problems under 2DLIF environment. Finally, a numerical example is provided to demonstrate the advantages and practicality of 2DLIF-PROMETHEE methods.

On three perspectives for deriving three-way decision with linguistic intuitionistic fuzzy information

The determination of both thresholds in decision-theoretic rough sets is an important problem of study that has aroused widespread attention in recent years. Although many related methods have been proposed, they may need a substantial amount of computation in model solving even not capture the thresholds in some cases. In this paper, we introduce linguistic intuitionistic fuzzy numbers (LIFNs) into loss functions due to LIFNs integrating the advantages of linguistic terms and intuitionistic fuzzy numbers, and propose a single optimization model-based, threshold-determined method to derive three-way decision. First, we define a novel measure for ranking LIFNs, verify its properties, analyze the relationships between loss functions with LIFNs and establish linguistic intuitionistic fuzzy decision-theoretic rough sets with a novel measure for LIFNs. Second, we investigate linguistic intuitionistic fuzzy, three-way decision methods from three perspectives, especially from the third perspective. We construct a single optimization model for capturing the thresholds that can overcome the shortcomings of the methods from two other perspectives, and the uniqueness of the optimal solution of this model is proven with the aid of the Karush-Kuhn-Tucker (KKT) condition. Third, a single model-based perspective method and its corresponding algorithm are designed to determine the thresholds for linguistic intuitionistic fuzzy information. Last, an illustrative example and simulated experiments are conducted to show the validity of our method.

Probabilistic linguistic q‐ rung orthopair fuzzy Generalized Dombi and Bonferroni mean operators for group decision‐making with unknown weights of experts

In this paper, we develop a multicriteria group decision-making methodology with probabilistic linguistic q-rung orthopair fuzzy sets (PLqROFSs). The benefit of choosing PLqROFSs is that they consider the simultaneous occurrence of stochastic and nonstochastic uncertainty and so are superior to probabilistic hesitant fuzzy sets, linguistic intuitionistic fuzzy sets, and linguistic Pythagorean fuzzy sets. To develop the methodology, we first propose two types of operators, namely, probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi operator which gives the flexibility of choosing the parameter values and probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi Bonferroni mean operator which can consider the interrelationships between criteria. Since both the subjective and objective weights of experts are hardly considered in the current PLqROFSs-based research, so in our proposed methodology, we deploy the thought of consistency and similarity between the experts to calculate the subjective and objective weights, respectively, of the experts and as a result the evaluation results do not get malformed. For measuring the weights of criteria, the gray correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. To exhibit the applicability of the proposed operators, we provide a case study on biomass feedstock selection. Moreover, to make sure that our model is stable, we have investigated a sensitivity analysis of parameters. At the end, we make a comparison of our approach to different existing schemes.

Multi-attribute group decision-making for online education live platform selection based on linguistic intuitionistic cubic fuzzy aggregation operators

The purpose of this study is to propose a multi-attribute group decision-making (MAGDM) method for online education live platform selection based on proposed novel aggregation operators (AOs) under linguistic intuitionistic cubic fuzzy set (LICFS). First, the Archimedean copula and co-copula are extended to handle linguistic intuitionistic cubic fuzzy information (LICFI) and the operational law of linguistic intuitionistic cubic fuzzy variables (LICFVs) based on extended copula (EC) and extended co-copula (ECC) are given. In addition, linguistic intuitionistic cubic fuzzy copula weighted average (LICFCWA) operator and linguistic intuitionistic cubic fuzzy copula weighted geometric (LICFCWG) operator are proposed based on EC and ECC under LICFI; meanwhile, some special forms of LICFCWA and LICFCWG have been obtained by different types generators of ECs and ECCs. Third, a novel MAGDM approach based on proposed LICFCWA (LICFCWG) is constructed to solve the selection problem of the online education live platform in the period of the COVID-19, and a detailed parameter analysis was carried out. Fourthly, LICFS will degenerate into linguistic intuitionistic fuzzy set and intuitionistic cubic fuzzy set, respectively, in different cases. Finally, some comparisons are carried out with other existing proposed MAGDM approaches. By comparing different types of experiments, the effectiveness and flexibility of the proposed approach are also showed.

Novel Transformation Methods Among Intuitionistic Fuzzy Models for Mixed Intuitionistic Fuzzy Decision Making Problems

As an extension of classical fuzzy set, intuitionistic fuzzy set (IFS) has been widely utilized in decision making. Based on IFS, intuitionistic fuzzy value (IFV) and linguistic intuitionistic fuzzy set (LIFS) have also been proposed to represent uncertain assessments of alternatives in different intuitionistic fuzzy decision environment. Theoretically, IFV, IFS or LIFS own themselves processing methods in decision making. However, they may be utilized to represent intuitionistic fuzzy assessments of alternatives in the same decision problem, i.e., multi-decision makers provide IFVs, IFSs or LIFSs to represent uncertain assessments of alternatives in the decision problem. In such case, the significant challenge is to unify IFVs, IFSs and LIFSs in the decision making matrices. In the paper, novel transformation methods are presented to unify IFVs, IFSs and LIFSs. To this end, mixed intuitionistic fuzzy decision matrix is presented to represent IFV, IFS or LIFS assessments of alternatives provided by decision makers, then transformation functions are developed to unify IFVs, IFSs and LIFSs in the decision making matrices, their properties are also analysed. The decision making method is presented to solve the intuitionistic fuzzy decision making problems with IFVs, IFSs or LIFSs, which is consisted of six main phases, accordingly the algorithm is designed to carry out the problems. Illustrative examples show that transformation functions are useful in intuitionistic fuzzy decision environment, the proposed decision making method is an effective and alternative tool for the intuitionistic fuzzy decision making problems with IFVs, IFSs or LIFSs.

Research on decision-making of emergency plan for waterlogging disaster in subway station project based on linguistic intuitionistic fuzzy set and TOPSIS.

Targeted at emergency plans for rainstorm and waterlogging disasters in subway station projects, this work proposes a group decision-making method that uses linguistic intuitionistic fuzzy sets, structural entropy weights, and TOPSIS. An evaluation index system of emergency plans was constructed based on four aspects, namely a scientific basis, completeness, operability, and flexibility. A linguistic interval intuitionistic fuzzy set approach was then used to qualitatively present the decision-makers' understanding of, attitudes about, and preferences for emergency plans. The uncertainty was comprehensively and intuitively represented by the dimensions of the degrees of membership and non-membership. The structural entropy weight method was applied and improved to fully reflect the influences of experts with different characteristics on the index weights. Finally, the TOPSIS method, with a background context of linguistic interval intuitionistic fuzzy sets, was applied. The calculation results of benchmark and verification case highlight the rationality and scientificity of the method proposed in this paper. The emergency decisions regarding waterlogging in 2018 for the Huilong Road West Station Project of Chengdu Metro Line 11 in China were selected as a case study. The case study demonstrates that operability is the most critical of the four primary indicators, and that flexible response to changes in the emergency response level is the most important of the secondary indicators. The uncertainty analysis of data revealed that with the increase of uncertainty, the difference between each scheme and the ideal solution decreased. Compared with the classical TOPSIS method, the new model proposed in this paper is robust and effective, and can be used for similar projects in the future.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Utilizing Linguistic Picture Fuzzy Aggregation Operators for Multiple-Attribute Decision-Making Problems

The linguistic picture fuzzy set (LPFS) is an extension of the linguistic intuitionistic fuzzy set (LIFS), and can contain more information than the LIFS. In this paper, the degrees of positive, neutral and non-membership of PFSs are expressed in linguistic terms, which can more easily describe the uncertain and vague information existing in the real world. By combining the PFS and the linguistic term, we define the LPFS and propose operational rules for linguistic picture fuzzy numbers (LPFNs). We further propose weighted averaging and weighted geometric operators and discuss their properties. Additionally, we propose an approach to deal with a multiple-attribute group decision-making (MAGDM) problem based on the developed aggregation operators. Finally, we present an illustrative example to demonstrate the effectiveness and advantages of the developed method by comparing it with existing methods. In addition, our method can be utilized not only to solve problems with linguistic intuitionistic fuzzy numbers (LIFNs), but also to deal with problems with LPFNs, and is a generalization of a number of existing methods.

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.

A NOVEL HESITANT INTUITIONISTIC FUZZY LINGUISTIC AHP METHOD AND ITS APPLICATION TO PRIORITIZATION OF INVESTMENT ALTERNATIVES

Intuitionistic fuzzy extensions are the most used type of fuzzy extensions in the literature since they better represent decision makers strength of commitment on the considered subject in an effective way including membership and non-membership functions. On the other hand, decision makers may assign more than one intuitionistic fuzzy number in order to capture their hesitancies when they are hesitant in assigning a membership degree and a non-membership degree. Hesitant fuzzy sets, another extension of ordinary fuzzy sets, help decision makers to assign different values on the same element aiming at reflexing decision makers’ hesitation. Utilizing these two types of fuzzy sets capture both uncertainty and ambiguity of the considered problem and helps to eliminate the weaknesses of each fuzzy extension. In this study,hesitant intuitionistic fuzzy linguistic sets (HIFLSs) are used to extend the Analytical Hierarchy Process (AHP). The developed method is applied to investment prioritization problem, based on relevant risk factors. Comparative analyses with intuitionistic fuzzy AHP and hesitant fuzzy AHP methods are realized in order to validate the proposed method. A sensitivity analysis is also conducted for the stability of the results of the hesitant intuitionistic fuzzy linguistic AHP method.

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.

Group decision making approach based on possibility degree measure under linguistic interval-valued intuitionistic fuzzy set environment

<p style='text-indent:20px;'>In the present article, we extended the idea of the linguistic intuitionistic fuzzy set to linguistic interval-valued intuitionistic fuzzy (LIVIF) set to represent the data by the interval-valued linguistic terms of membership and non-membership degrees. Some of the desirable properties of the proposed set are studied. Also, we propose a new ranking method named as possibility degree measures to compare the two or more different LIVIF numbers. During the aggregation process, some LIVIF weighted and ordered weighted aggregation operators are proposed to aggregate the collections of the LIVIF numbers. Finally, based on these proposed operators and possibility degree measure, a new group decision making approach is presented to rank the different alternatives. A real-life case has been studied to manifest the practicability and feasibility of the proposed group decision making method.

An overview of intuitionistic linguistic fuzzy information aggregations and applications

Purpose Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI. Design/methodology/approach First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs. Findings IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs. Originality/value The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.