Linguistic Intuitionistic Fuzzy Numbers Research Articles

Multiple-attribute group decision-making approach using power aggregation operators with CRITIC-WASPAS method under 2-dimensional linguistic intuitionistic fuzzy framework

The 2-dimensional linguistic intuitionistic fuzzy variables (2DLIFVs) provide an efficient tool to model the cognitive information of experts in practical circumstances while considering the reliability of the evaluation results. It is a hybrid model representing qualitative information, which derives from integrating the 2-dimensional linguistic variables (2DLVs) with linguistic intuitionistic fuzzy numbers (LIFNs). In this work, we first define a novel score function to establish a proper ranking order among the 2DLIFVs. Next, we define a new distance measure under a 2-dimensional linguistic intuitionistic fuzzy framework to determine the difference between 2DLIFVs. Some mathematical properties and special cases of the defined distance measure are also discussed. The power average (PA) operators provide aggregation tools, allowing aggregated arguments to support each other in the aggregation process. Motivated by the notion of power average (PA) and power geometric (PG), we define four new aggregation operators (AOs) to aggregate 2DLIFVs by considering information correlation in terms of support degree during the aggregation process. Several mathematical properties of the proposed AOs are also investigated. In addition, a new integrated 2DLIF-CRITIC-WASPAS methodology is developed in the 2-dimensional linguistic intuitionistic fuzzy environment to deal with complex decision issues. In this method, a “Criteria Importance Through Intercriteria Correlation (CRITIC)” approach is used to obtain the associate weights of the attributes, and the “Weighted Aggregated Sum Product Assessment (WASPAS)” method is executed to establish a valid ranking order among the alternatives.Moreover, a real problem of venture capital investment related to renewable energy projects is considered to demonstrate the applicability of the proposed methodology. The evaluation process considers four aspects: the management team, service or product, finance, and the market, which are related to 14 attributes. A sensitivity analysis is carried out to explain the reliability of the obtained results. Comparing the proposed method with some extant methods establishes the strength and robustness of the formulated method in real-world situations.

Group decision making based on linguistic intuitionistic fuzzy Yager weighted arithmetic aggregation operator of linguistic intuitionistic fuzzy numbers

In this paper, we propose two new group decision making (GDM) approaches based on the proposed linguistic intuitionistic fuzzy Yager weighted arithmetic (LIYFWA) aggregation operator (AO) of linguistic intuitionistic fuzzy numbers (LIFNs), where the proposed first GDM considers the situation that experts’ weights and attributes’ weights are completely known; the proposed second GDM approach considers the situation that experts’ weights and attributes’ weights are completely unknown. Firstly, we propose new operational laws for LIFNs based on Yager’s norm, namely, the addition operation operation and the scalar multiplication operation. The proposed addition operation and the proposed scalar multiplication operation of LIFNs can conquer the drawbacks of the existing addition operation and the existing scalar multiplication operation of LIFNs. Then, based on the proposed addition operation and the proposed scalar multiplication operation of LIFNs, we propose the LIYFWA AO of LIFNs. We also prove some properties of the proposed LIFYWA AO. Finally, based on the proposed LIFYWA AO, we propose two new GDM approaches of LIFNs. The proposed GDM approaches can conquer the drawbacks of existing GDM methods, where they cannot distinguish the ranking orders of alternatives in some situations.

Achieving threshold consistency in three-way group decision using optimization methodology and expert-weight-updating-strategy

How to improve and achieve a group consistency under three-way group decision is a key research issue that has recently attracted more and more attention. To deal with this issue, this paper proposes an expert-weight-updating-based approach to achieve a threshold consistency under three-way group decision with various opinions of linguistic intuitionistic fuzzy numbers. First, we use a linguistic intuitionistic fuzzy number (LIFN) to evaluate loss functions among experts due to its advantages in uncertain evaluations, and establish a fundamental model of decision-theoretic rough sets with different opinions of multiple experts. Then, we put forward a single optimization model that is an extension of our previous model, and utilize a mapping technique with such optimization methodology to generate numerical thresholds of individual experts. Second, we employ the normalized Hamming distance to define concepts of similarity measure and group consensus index based on individual thresholds. Then, we design a method to derive initial weights, a strategy to update weights of experts, and an expert-weight-updating-based algorithm to achieve a consensus of group thresholds. Third, via this algorithm, we develop a three-way group decision consensus achieving approach based on linguistic intuitionistic fuzzy opinions with multiple experts. Finally, some experiments and comparative analysis are performed to verify a convergence of our algorithm and the effectiveness of our approach.

Chebyshev Distance Entropy Combined with TODIM Method in Lq-ROFS Multiattribute Group Decision Making

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are composed of a set of q-rung orthopair fuzzy numbers (q-ROFNs) with membership and nonmembership degrees of linguistic variables, which can be regarded as an extension of linguistic intuitionistic fuzzy numbers (LIFNs) and linguistic Pythagorean fuzzy numbers (LPFNs). Compared with LIFNs and LPFNs, Lq-ROFNs have a wider range of applicability because the value of q can have a wider range, thus allowing to handle more multiattribute group decision making (MAGDM) problems. Based on Lq-ROFS, this paper first proposes the Chebyshev distance metric, then develops the Chebyshev distance entropy for deriving objective solution of decision makers’ (DMs’) weight vector and attribute weight vector by combining the metric and entropy measure. The TODIM method has been widely valued by the society and has achieved good results in many MAGDM problems. Subsequently, the TODIM decision method in Lq-ROFS is presented and combined with the Chebyshev distance entropy model as a new decision method (CDE-TODIM) to solve the MAGDM problems. This method process is objective and direct and takes into account the decision maker’s preferences, and the decision results are more persuasive. Finally, the effectiveness and rationality of this MAGDM method are illustrated by a case as well as comparisons.

A personalized individual semantics model for computing with linguistic intuitionistic fuzzy information and application in MCDM

This paper develops a personalized individual semantics (PISs) model for computing with linguistic intuitionistic fuzzy information and applies to evaluate different brands of mobile phones. First, considering that a linguistic term means different things to different decision-makers, a consistency-driven optimization model for checking the additive consistent linguistic intuitionistic fuzzy preference relations (LIFPRs) is constructed by considering the PISs model. Besides, several optimization models are built to determine the PISs of linguistic terms with LIFPRs and obtain the acceptable additive consistent LIFPRs. Second, a new definition of Hamming distance for measuring linguistic intuitionistic fuzzy numbers (LIFNs) is developed by considering the PISs model, and several desirable properties are discussed. Then, the method of deriving the weight vectors of criteria is calculated based on the proposed distance measure. Subsequently, a framework of group decision-making (GDM) process with LIFPRs is offered, and the application of the proposed method is illustrated by using a multi-criteria decision-making (MCDM) problem about evaluating different brands of mobile phones. Finally, the comparative analysis is conducted to show the feasibility of proposed method.

Linguistic q-rung orthopair fuzzy multiple-attribute group decision making based on the grey similarity degree and PROMETHEE II method

Linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs) are an effective tool for representing fuzzy linguistic information, and they can obtain a wider expression scope than linguistic intuitionistic fuzzy numbers and linguistic Pythagorean fuzzy numbers by increasing the value of parameter q. In this paper, we propose a new similarity measure called the grey similarity degree between any two Lq-ROFNs based on the concept of the grey correlation degree. Considering the significance of determining unknown weights, we also propose a grey correlation method to determine each expert’s weight under different alternatives and attributes, and we construct an optimization model to determine incompletely known attribute weights. Furthermore, an approach to linguistic q-rung orthopair fuzzy multiple-attribute group decision making is proposed that combines the grey similarity degree with the PROMETHEE II method. Finally, a numerical example is given to illustrate the effectiveness of the proposed method, and a sensitivity analysis and comparison analysis are also performed.

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.

Comprehensive evaluation of land reclamation schemes in mining areas based on linguistic intuitionistic fuzzy group decision-making.

Schemes to protect the geological environment and reclaim land are core requirements for an application for mining rights and complying with mining regulations. Mining enterprises must be supervised to ensure they fulfill their obligations. To guide oversight of such schemes and to provide references for their compilation and review, this study evaluates land reclamation schemes in mining areas using a multi-attribute group decision-making method. First, linguistic intuitionistic fuzzy numbers are used to describe the evaluation information. Considering the authority and preferences of experts, methods for determining expert weights in four cases are established. Max-min deviation then determines the attribute weights, and a method for linguistic intuitionistic fuzzy group decision-making is proposed. Finally, the practicability of this method is verified through a comparative analysis of land reclamation schemes for four mining areas in Sichuan Province, China. The results show the proposed method to give simple and effective evaluation, making it reasonably applicable to the compilation and review of land reclamation schemes.

Dempster-shafer theory and linguistic intuitionistic fuzzy number-based framework for blending knowledge from knowledge repositories: An approach for knowledge management

Based on Dempster-Shafer Evidence Theory (DSET) and Linguistic Intuitionistic Fuzzy Numbers (LIFN), this study presents a paradigm for Knowledge Blending (KB) that supports the Knowledge Management (KM) process. The KB framework highlights and analyzes knowledge blending, the emergence of new insights, the ordering of knowledge repositories, and selected knowledge entities that are part of such a knowledge combination. The KB method enables the analysis of knowledge repositories using linguistic terms and quantitative variables and the identification of the ordering of knowledge repositories and specific entities. Ordering knowledge repositories and entities during KB is tricky since knowledge providers employ a range of adjectives, rankings, interpretations, and linguistic terms, rendering the KB process ambiguous. To address the issue, we leverage DSET to describe the LIFNs extracted from knowledge sources as Basic Probability Assignments (BPA). Then, we merge subjective and objective weights obtained from knowledge repositories. To amend evidence from knowledge repositories, we apply the combined weight. Finally, the comprehensive evaluation value of each option is quantified using the combination rule of evidence, which aids in the blending of knowledge repositories and entities acquired from the knowledge repositories. We discuss a case study to explain the proposed method and compare it to other approaches in order to demonstrate its viability and usefulness. The case study highlights the value of KM during the knowledge structuring and auditing stages of the KM process.

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.

Multiple attribute group decision making based on advanced linguistic intuitionistic fuzzy weighted averaging aggregation operator of linguistic intuitionistic fuzzy numbers

In this paper, we propose a new multiple attribute group decision making (MAGDM) method based on the proposed advanced linguistic intuitionistic fuzzy weighted averaging (ALIFWA) aggregation operator of linguistic intuitionistic fuzzy numbers (LIFNs). The proposed ALIFWA aggregation operator of LIFNs can overcome the shortcomings of the linguistic intuitionistic fuzzy weighted averaging (LIFWA) aggregation operator, the improved LIFWA (ILIFWA) aggregation operator, and the linguistic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) aggregation operator of LIFNs, which have the shortcomings that the membership degrees and the non-membership degrees of their obtained aggregated LIFNs are indeterminated in some situations. Based on the proposed ALIFWA aggregation operator of LIFNs, we propose a new MAGDM method in linguistic intuitionistic fuzzy environments. The proposed MAGDM method can overcome the drawbacks of the existing MAGDM methods. It offers us a very useful way for handling MAGDM problems in linguistic intuitionistic fuzzy environments.

A MCDM Method with Linguistic Variables and Intuitionistic Fuzzy Numbers to Evaluate Product Development Projects

A MCDM Method with Linguistic Variables and Intuitionistic Fuzzy Numbers to Evaluate Product Development Projects

Linguistic Interval-Valued Intuitionistic Fuzzy Copula Heronian Mean Operators for Multiattribute Group Decision-Making

As a generalization of the intuitionistic fuzzy number (IFN), the linguistic interval-valued intuitionistic fuzzy number (LIVIFN) is a flexible and superior tool to describe complex fuzzy uncertainty information. Heronian mean (HM) operator has the characteristic of considering the relationship between attributes. Extended copulas (ECs) and extended cocopulas (ECCs) are the promotion form of Archimedean t-norm and t-conorm (ATT). ECs and ECCs can generate versatile operational rules and can provide more choice for decision makers (DMs). Therefore, it is very necessary to take advantages of them. In this paper, ECs and ECCs, some specifics of ECs and ECCs, and score and accuracy functions of IVILFNs are gained first. Then, we propose the linguistic interval-valued intuitionistic fuzzy weighted copula Heronian mean (LIVIFWCHM) operator; also, some properties and five specific expressions of the LIVIFWCHM operator are discussed. Moreover, we also propose a new MAGDM approach based on the proposed LIVIFWCHM operator. Finally, a set of examples are used to demonstrate the effectiveness, generality, and flexibility of the proposed method.

Scheme selection of design for disassembly (DFD) based on sustainability: A novel hybrid of interval 2-tuple linguistic intuitionistic fuzzy numbers and regret theory

Design for disassembly (DFD) is an essential design technique to consider the disassembly and recyclability of a product at the initial design stage. An efficient DFD technique provides the disassembling and recycling easily. However, the recent trends of disassembling and recycling are to consider the aspects of environmental and social sustainability. Due to shortage of energy and deterioration of the ecological environment, the sustainable production is an active research topic to use the economic and social benefits as the evaluation standard of a design scheme as well as its environmental characteristics. This paper provides a new approach for DFD based on sustainability. In this regard, a hybrid multi-attribute decision making (MADM) method integrating the regret theory (RT) and the entropy weighting method is firstly developed. To implement the proposed approach, an eight-criterion evaluation system of schemes based on sustainability including the factors of disassembly energy consumption, disassembly accessibility, fastener ratio, toxic material proportion, material recovery rate, disassembly expense, production and use noise, and waste emissions, is established. To better describe the fuzziness of human thinking and to avoid information loss/distortion during information aggregation phases, the evaluation information given by experts is presented by our proposed interval 2-tuple linguistic intuitionistic fuzzy numbers (I2LIFNs). The weight vector of index structure is determined by the entropy weighting method under the fuzzy environment. The RT is employed to get the final order of alternatives by considering and quantitating both the risk attitude and the regret attitude of experts. To show the applicability of this study, a case study including four kinds of refrigerator schemes, is conducted to validate the proposed method. An extensive comparison with other recent and state of the art methods along with a sensitivity analysis of 13 experiments, is executed to verify effectiveness and reliability of the proposed I2LI-RT method. Finally, the experimental results show that: 1) disassembly accessibility (C2), fastener ratio (C3), waste emissions (C8) and disassembly energy consumption (C1) have a large impact on the scheme selection of DFD based on sustainability as those attributes carry relatively the larger weights; 2) our proposed method outperforms other recent and state of the art methods and 3) the chosen scheme A1 is the winner in the majority of the sensitivity analysis cases (10 out of 13). At last but not least, the main finding is to furnish a systematic and efficient decision support tool for sustainable performance evaluation of product schemes of DFD.

Multiple attribute group decision making based on 2-dimension linguistic intuitionistic fuzzy aggregation operators

The 2-dimension linguistic variables (2-DLVs) add a subjective evaluation on the reliability of the evaluation results provided by decision makers, so 2-DLVs are very useful tools for describing uncertain or fuzzy information. This work extends the idea of 2-DLVs by introducing 2-dimension linguistic intuitionistic fuzzy variables (2-DLIFVs) in which 1 class and 2 class information describe in the form of linguistic intuitionistic fuzzy numbers. The paper defines some operational laws, score, and accuracy functions for 2-DLIFVs. Further, we develop some arithmetic and geometric aggregation operators for aggregating 2-DLIF information and prove a number of valuable properties associated with them. Using the proposed aggregation operators, an approach for multiple attribute group decision making with 2-DLIF information is formulated. Finally, an illustrated example is given to verify and prove the validity of the developed method. The computed results are also compared with the existing results.

Novel Multiple Attribute Group Decision-Making Methods Based on Linguistic Intuitionistic Fuzzy Information

As an effective technique to qualitatively depict assessment information, a linguistic intuitionistic fuzzy number (LIFN) is more appropriate to portray vagueness and indeterminacy in actual situations than intuitionistic fuzzy number (IFN). The prominent feature of a Muirhead mean (MM) operator is that it has the powerful ability to capture the correlations between any input-data and MM operator covers other common operators by assigning the different parameter vectors. In the article, we first analyze the limitations of the existing ranking approaches of LIFN and propose a novel ranking approach to surmount these limitations. Secondly, we propound several novel MM operators to fuse linguistic intuitionistic fuzzy (LIF) information, such as the LIF Muirhead mean (LIFMM) operator, the weighted LIF Muirhead mean (WLIFMM) operator and their dual operators, the LIFDMM operator and the WLIFDMM operator. Subsequently, we discuss several desirable properties along with exceptional cases of them. Moreover, two novel multiple attribute group decision-making approaches are developed based upon these operators. Ultimately, the effectuality and practicability of the propounded methods are validated through dealing with a global supplier selection issue, and the comparative analysis and the merits of the presented approaches are demonstrated by comparing them with existing approaches.

A Multi-Attribute Group Decision-Making Method Based on Linguistic Intuitionistic Fuzzy Numbers and Dempster–Shafer Evidence Theory

In this paper, we propose a multi-attribute group decision-making (MAGDM) method based on Dempster–Shafer Evidence Theory (DST) and linguistic intuitionistic fuzzy numbers (LIFNs), in which both the expert weights and attribute weights are unknown. Firstly, we represent LIFNs as basic probability assignments (BPAs) by DST based on linguistic scale function (LSF), and a linear programming model is proposed to combine the objective weights and subjective weights of attributes to obtain the combined weights. At the same time, the experts’ weights are obtained through Jousselme distance. Secondly, we use the weights to correct the evidence, and the comprehensive evaluation value of each alternative is calculated by the combination rule of evidence. Further, a new MAGDM approach with DST and LIFNs is presented. Finally, we give an example to explain the proposed method and compare it with other methods to show the feasibility and superiority.

A multi-attribute decision making method based on the third generation prospect theory and grey correlation degree

Considering the uncertainty of the natural state and the convenience of calculation, based on the third generation prospect theory (3-PT) and grey correlation analysis (GRA), we propose a method to solve the multi-attribute decision-making (MADM) problems where the attributes are described by the linguistic intuitionistic fuzzy numbers (LIFNs). Firstly, we transform the LIFNs into the belief structure that includes identity value and belief degree. Then, the evaluation information represented by belief structure is calculated by using the 3-PT, and the prospect matrix is gotten. The alternatives are ranked by the GRA. Finally, we use the proposed method to calculate an example and compare it with other methods to prove its effectiveness and superiority.

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.

An approach based on linguistic spherical fuzzy sets for public evaluation of shared bicycles in China

In the context of the booming sharing economy, shared bicycles as an important part of the sharing economy have been studied by many scholars, and these researches mainly focus on the socioeconomic characteristics of users and the system design level of shared bicycles, it is very necessary to study the evaluation method of shared bicycles which is a typical multi-attribute decision- making (MADM) problem. Firstly, the linguistic spherical fuzzy numbers (Lt-SFNs) is proposed to express the public’s language evaluation information. Compared with the linguistic intuitionistic fuzzy numbers (LIFNs) and the linguistic q-rung orthopair fuzzy numbers (Lq-ROFNs), Lt-SFNs have a wider information expression range. Then, in order to integrate the language evaluation information, the linguistic spherical fuzzy weighted averaging (Lt-SFSWA) operator is proposed, which can aggregate the group linguistic evaluation information. Further, the MABAC (Multi-Attributive Border Approximation area Comparison) method is extended to the linguistic spherical fuzzy environment and the Lt-SFS-MABAC method is proposed, which can process linguistic evaluation information and select an optimal alternative from a plurality of alternatives. At the same time, the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method is extended to the linguistic spherical fuzzy environment and the Lt-SFS-TODIM method is proposed. Lastly, we conducted sensitivity analysis and comparative analysis of the Lt-SFS-MABAC method, the Lt-SFS-TODIM method and the Lt-SFSWA method. The results show that the Lt-SFS-MABAC method is sensitive to weights, decision makers can use the Lt-SFS-MABAC method to make a realistic evaluation based on the actual environment.