Linguistic Intuitionistic Fuzzy Research Articles

Optimization of autonomous vehicle control system reliability on a commercial scale through LIF dombi methodologies.

The resilient framework of Linguistic Intuitionistic Fuzzy Sets (LIFSs) allows for the representation and management of uncertainties related to intuitionistic judgments and linguistic expressions. Recent advances in passive and active safety systems have reduced highway fatalities. Autonomous vehicles can improve safety, efficiency, and mobility by navigating traffic without a driver. One of the primary benefits associated with this technology is that it reduces the number of traffic collisions that result in millions of fatalities and numerous injuries. In this research work, we devise two novel aggregation operators: the linguistic intuitionistic fuzzy Dombi ordered weighted averaging (LIFDOWA) operator and the linguistic intuitionistic fuzzy Dombi ordered weighted geometric (LIFDOWG) operator, and explore their fundamental structural properties. We provide innovative score and accuracy functions for multiple attribute decision-making (MADM) problems within the framework of LIF knowledge. Moreover, we use these techniques to develop a specialized algorithm for MADM issues that addresses the complexities arising from ambiguous data during the selection process. We also demonstrate the effectiveness of our proposed methods by applying them to solve the MADM scenario of selecting an optimal approach to improve the credibility of autonomous vehicle control systems on a commercial scale. In addition, we also compare and evaluate the authenticity and practicability of the newly designed techniques in comparison to existing methodologies.

Novel Linguistic Intuitionistic Fuzzy Score and Accuracy functions for Linguistic Intuitionistic Fuzzy TOPSIS Method

Abstract: This work proposes various Linguistic Intuitionistic Fuzzy Score and Accuracy functions (LIF-Score and LIFAccuracy), including linguistic degree, membership, non-membership, and hesitancy degree, for Linguistic Intuitionistic Fuzzy Sets (LIFSs) in Multiple Attribute Group Decision Making (MAGDM) problems. The proposed functions are integrated into the Linguistic Intuitionistic Fuzzy-Technique of Order Preference by Similarity to Ideal Solution (LIF-TOPSIS) MAGDM approach to rank the alternatives, and a numerical example demonstrating their use in ranking alternatives is shown in the paper.

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.

Group decision-making method based on advanced aggregation operators with entropy and divergence measures under 2-tuple linguistic Pythagorean fuzzy environment

2-tuple linguistic Pythagorean fuzzy values (2TLPFVs) are flexible and more efficient tools to represent fuzzy linguistic information in complex real-world situations than 2-tuple linguistic values (2TLVs) and 2-tuple linguistic intuitionistic fuzzy values (2TLIFVs). This paper introduces a new score value function for 2TLPFVs and discusses its major properties. Two new aggregation operators (AOs) are presented, namely, the advanced 2-tuple linguistic Pythagorean fuzzy weighted average (Adv-2TLPFWA) operator and the advanced 2-tuple linguistic Pythagorean fuzzy weighted geometric (Adv-2TLPFWG) operator, which aggregate 2-tuple linguistic Pythagorean fuzzy information based on novel operational laws of 2TLPFVs. The work also exhibits several properties of these AOs in detail. Furthermore, the article discusses entropy and divergence measures under the 2-tuple linguistic Pythagorean fuzzy information environment. Finally, a new multiple attribute group decision-making (MAGDM) method is constructed to solve group decision-making problems in the 2-tuple linguistic Pythagorean fuzzy context. A real-life group decision-making problem of selecting the best green supplier for fruits and vegetables is investigated to verify the applicability and validity of the proposed approach. The sensitivity investigation and comparative analysis are conducted to illustrate the advantages of the proposed method.

Improved Hesitant Intuitionistic Fuzzy Linguistic Term Sets and Their Application in Group Decision-Making

Linguistic terms have proven to be more effective for DMs when defining complex and imprecise cognition. Consequently, a variety of novel linguistic models such as fuzzy linguistic approach, hesitant fuzzy linguistic term sets (HFLTSs), and hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs) have been successively proposed. As HIFLTSs provide an effective and symmetrical technique for expressing qualitative decisions by decision-makers, they have attracted substantial scholarly interest. This paper proposes a series of new operational laws to address the current limitations and enhance the applicability and methodology of HIFLTSs. Additionally, we introduce a new score function and an accuracy function that both consider the degree of hesitancy, thus addressing the current shortcomings. Furthermore, the correlation measures and correlation coefficients are established to enrich the framework of the HIFLTSs theory. Finally, a MULTIMOORA approach in the HIFLTS environment is presented, which results in more robustness, simplicity, and effectiveness. A practical example is employed to demonstrate the effectiveness of the proposed approach, and a comparison with related works highlights the advantages and novelty of the proposed model.

Group decision making with incomplete interval-valued linguistic intuitionistic fuzzy preference relations

With the increasing complexity and indeterminacy intensity of the decision making environment, there is a growing lack of widespread utility of traditional preference representations. As a practical yet valid preference expression, interval-valued linguistic intuitionistic fuzzy preference relations (IVLIFPRs) can efficiently represent the pairwise cognitions qualitatively and provide the inclusive support. This study aims at forming a novel group decision making (GDM) method based on the consistency and consensus preference analysis for IVLIFPRs. First, the new concepts of additive consistency and acceptably additive consistency for IVLIFPRs are defined. Based on these definitions, two optimization models are constructed to obtain the incomplete information and acceptably additive consistent IVLIFPRs, respectively. Then, inspired by the Markov model, the derivation approach of DMs' weights is designed. Afterward, the consensus improving process is constructed under the premise of acceptable consistency and smallest information distortion. Accordingly, the normalized priority weights of alternatives are further determined. Thus, a mechanism for the GDM method with incomplete and unacceptably consistent IVLIFPRs is developed. Finally, an application and comparison analysis show that the proposed method comprehensively considers the key steps in the GDM process, so that the logical rationality and technical superiority are well guaranteed.

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.

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.

An Integrated Two-Dimension Linguistic Intuitionistic Fuzzy Decision-Making Approach for Unmanned Aerial Vehicle Supplier Selection

With the rapid development of unmanned aerial vehicles (UAVs) and their applications in problems such as power line inspection, selecting the appropriate UAV supplier according to several sustainable attributes has attracted many interests. In this regard, an integrated multiattribute group decision-making (MAGDM) method based on the best-worst method (BWM) and MULTIMOORA method with two-dimension linguistic intuitionistic fuzzy variables (2DLIFVs) is proposed in this paper for the selection of UAV suppliers. First, the 2DLIFV is utilized to represent the uncertain, fuzzy, and linguistic evaluations of the experts on the evaluation attributes. Second, the two-dimension linguistic intuitionistic fuzzy BWM (2DLIF-BWM) is introduced to compute the weights of the attributes. Then, a novel expert weight calculation method that combines the uncertainty degree and consensus degree of the experts is introduced. Next, the 2DLIF-MULTIMOORA method is proposed, where the aggregation operators and distance measures of the 2DLIFVs are used to determine the ranking results of different alternatives. Finally, a real case of selecting a sustainable UAV supplier for power line inspection is presented to illustrate the process of the proposed method. The experimental results are further analyzed through sensitivity and comparative analyses to show the feasibility and effectiveness of the proposed method. From the results, it can be found that the proposed method can more flexibly represent the uncertain assessments while providing reasonable and reliable results.

A two-stage EDM method based on KU-CBR with the incomplete linguistic intuitionistic fuzzy preference relations

Emergency decision making (EDM) can effectively reduce the loss caused by emergencies. The generation and selection of the alternatives are two key stages of EDM. To improve the efficiency of EDM, we propose a two stage EDM method. In the first stage, a knowledge-unit based case-based reasoning (KU-CBR) method is provided to generate alternatives. In this method, an emergency case representation model based on knowledge-unit is constructed to represent emergency, and a scenario similarity measurement is proposed to retrieve similar historical scenarios, and the alternatives are generated with reference to historical scenarios’ solutions. In the second stage, a decision-making process with linguistic intuitionistic fuzzy preference relations (LIFPRs) is developed to select the optimal alternative. Firstly, to determine missing values in the incomplete LIFPR, a programming model based on additive consistency is constructed. Subsequently, a model is built to obtain the LIFPRs with acceptable additive consistency. Afterward, in order to rank alternatives, a model for deriving the linguistic intuitionistic fuzzy (LIF) priority weights of the alternatives is constructed, and the priority weights can obtained conveniently and quickly. The two-stage EDM method combines the advantages of KU-CBR and LIFPRs, which is demonstrated by a case application of typhoon emergency, and the decision-making process with LIFPRs is compared with an existing method to demonstrate its practicability.

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.

(2012-6338) Design and Analysis of Acceptance Sampling Plans Based on Intuitionistic Fuzzy Linguistic Terms

Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kinds of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.

A Decision-Making Approach Based on New Aggregation Operators under Fermatean Fuzzy Linguistic Information Environment

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.

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.

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

Multi-criteria decision support systems based on linguistic intuitionistic cubic fuzzy aggregation operators

This article is an advanced approach to linguistic intuitionistic fuzzy variable through application of cubic set theory. For instance, we establish the idea of the linguistic intuitionistic cubic fuzzy variable (LICFV) theory and define several operations for LICFV; also establish a series of weighted aggregation operators under linguistic intuitionistic cubic fuzzy information, so called linguistic intuitionistic cubic fuzzy weighted averaging (LICFWA) operator, linguistic intuitionistic cubic fuzzy order weighted averaging (LICFOWA) operator, linguistic intuitionistic cubic fuzzy weighted geometric (LICFWG) operator, linguistic intuitionistic cubic fuzzy order weighted geometric (LICFOWG) operator, linguistic intuitionistic cubic fuzzy hybrid averaging (LICFHA) operator, and linguistic intuitionistic cubic fuzzy hybrid geometric (LICFHG) operator; and further study their fundamental properties and showed the relationship among these aggregation operators. In order to demonstrate the feasibility and practicality of the mentioned new technique, we develop multi-criteria decision-making algorithm under linguistic intuitionistic cubic fuzzy environment. Further, the proposed method applied to mobile phone selection, consider numerical application of mobile phone. Comparing the proposed techniques with other pre-existing aggregation operators, we concluded that the proposed technique is better, reliable, and effective.

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.

Group decision making with heterogeneous intuitionistic fuzzy preference relations

Intuitionistic fuzzy variables are powerful tools to denote positive and negative information simultaneously. Considering the situation where decision makers (DMs) may adopt different types of preference relations to express their judgements, this paper studies group decision making (GDM) with heterogeneous intuitionistic fuzzy preference relations (IFPRs), including intuitionistic fuzzy preference relations (IFPRs), multiplicative intuitionistic fuzzy preference relations (MIFPRs), additive linguistic intuitionistic fuzzy preference relations (ALIFPRs) and multiplicative linguistic intuitionistic fuzzy preference relations (MLIFPRs). We first study their consistency. Then, we discuss the transformation relationships among them. Using consistent MLIFPRs, we further offer a formula for ascertaining DMs’ weights and investigate the consensus. When the individual consensus level is lower than a predefined threshold, a model for increasing the consensus level is built that ensures the smallest total adjustment and allows the adjusted proportions of different judgements to be different. Moreover, we give a new GDM method with heterogeneous IFPRs. Finally, we use an example to illustrate the application of the proposed GDM method and make a comparison of different GDM methods with heterogeneous preference relations.

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.