Intuitionistic Fuzzy Preference Relations Research Articles

A novel intuitionistic fuzzy best-worst method for group decision making with intuitionistic fuzzy preference relations

This paper proposes a new intuitionistic fuzzy best-worst method (IFBWM) for group decision making (GDM) with intuitionistic fuzzy (IF) preference relations (IFPRs). IF values (IFVs) are used to express reference comparisons of criteria. Based on the additive consistency of IFPRs, this paper proposes the definition of additive consistency of IF reference comparisons (IFRCs). Based on the deviation minimization, a linear goal programming model is established to calculate the optimal IF priority weights. By the additive consistency, the consistency index in the closed form is computed by the score function of IFVs. A new approach is devised to enhance the additive consistency of IFRCs. Thus, an IFBWM with the additive consistency of IFRCs is proposed. For GDM with IFPRs, the best criterion and the worst criterion are identified for each decision maker by constructing the score matrix of the IFPR. The individual ranking order of the criteria is obtained by using the proposed IFBWM. Then, the collective ranking order of the criteria is obtained via building a 0–1 integer programming model. Therefore, a GDM method based on the developed IFBWM with IFPRs is proposed. Four examples are analyzed to demonstrate the effectiveness and the advantages of the proposed IFBWM for GDM.

Interaction and risk preference-based group decision-making with intuitionistic fuzzy preference relations

This research proposes a new method to solve group decision-making(GDM) problems with intuitionistic fuzzy preference relations(IFPRs). First, a new definition of multiplicative consistency of IFPR is presented to address the defects of the existing consistency definitions. Then, two programming models are established to obtain the most optimistic and pessimistic consistent IFPRs and corresponding intuitionistic fuzzy priority weights. Also, in order to improve the accuracy of aggregate information, a new method to determine the weights of decision-makers(DMs) is offered by considering the interaction among DMs. Subsequently, by combining the vagueness and non-vagueness of the aggregated information, a multiplicative consistency definition of the collective IFPR is provided. Moreover, to simplify the GDM process, a programming model for solving the priority weight is established, which effectively avoids the consistency test and correction of IFPRs. Finally, the values of the proposed method are illustrated by comparative analysis.

Interactively iterative group decision-making method with interval-valued intuitionistic fuzzy preference relations based on a new additively consistent concept

Interval-valued intuitionistic fuzzy preference relation (IVIFPR) is a powerful instrument for describing uncertain judgement of expert in preference group decision making (PGDM). Nevertheless, the extant additive consistency definitions for IVIFPRs violate the invariance regarding arrangement of objectives. In addition, the modification for comparative judgments in the consensus reaching process (CRP) of existing PGDMs with IVIFPRs do not involve the interaction or communication with experts. Therefore, we propose an PGDM to avoid these situations. First, a new additive consistency definition for IVIFPRs is given satisfying the invariance regarding arrangement of objectives. Then, an interactively iterative algorithm considering minimum information loss is developed to enhance the consistency of IVIFPRs. Next, as to group decision making (GDM) with IVIFPRs, a bi-objective optimization model is constructed to determine the experts’ weights, and an interactively iterative algorithm considering minimum information loss is developed to enhance the consensus level among experts. Furthermore, a fuzzy optimization model is constructed to derive the interval priority weights of objectives from an IVIFPR. Finally, the feasibility and superiority of the proposed GDM method are verified by application examples and analyses. The proposed GDM method has obtained an average of 0.0432 for information deviations and 22/72 for modified judgments on two datasets, respectively, which is one of the best results compared to state-of-art.

Novel evaluation model of teaching quality based on the improved IVIF-BWM and IVIFWMSM

The evaluation of teaching quality plays a crucial role in promoting the improvement of education quality and ensuring the healthy development of education. This study presents a novel teaching quality evaluation model based on improved interval-valued intuitionistic fuzzy Best-Worst method (IVIF-BWM) and interval-valued intuitionistic fuzzy weighted Maclaurin symmetric mean operators (IVIFWMSM). The study is divided into three parts. Firstly, to derive the optimal interval-valued intuitionistic fuzzy weights of criteria, we develop an improved IVIF-BWM by establishing a goal programming model based on the multiplicative consistent interval-valued intuitionistic fuzzy preference relation(IVIFPR), and then we propose the new consistency index (CI) and the consistency ratio (CR) under interval-valued intuitionistic fuzzy environment to verify the reliability of the derived results. Secondly, with regard to the importance and interaction relationships among criteria, IVIFWMSM is used to aggregate evaluation values of alternatives on each evaluation criteria in multi-criteria decision making process. Finally, the proposed teaching quality evaluation model is applied to a case of teaching quality evaluation in higher education and a comparison study with other existing methods are performed. The results demonstrate that the proposed teaching quality evaluation model not only overcomes the shortcomings of previous methods, but also is more accuracy, effective and reasonable for dealing with the teaching quality evaluation under the intuitionistic fuzzy environments.

Interval-valued intuitionistic fuzzy best-worst method with additive consistency

Best-worst method (BWM) has received extensive attention because of its fewer pairwise comparisons and maintenance of consistency. Extending it to various fuzzy environments has become a hot research spot. This paper initiates a new interval-valued intuitionistic fuzzy (IVIF) BWM with additive consistency. Firstly, an IVIF fuzzy preference relation (IVIFPR) is viewed as a directed graph with IVIF weights. An approach is offered to distinguish the best and worst criteria by the defined score out-degree and accuracy out-degree of criteria. The concept of IVIF reference comparisons is introduced. The additive consistency of IVIF reference comparisons is acquired by that of IVIFPR using its left and right intuitionistic fuzzy preference relations. We derive the relationship between the IVIF reference comparisons and the IVIF priority weight vector. Based on this relationship, a linear goal programming model is constructed to generate the IVIF priority weights. Two consistency indexes are analytically obtained and the consistency ratio is then defined to check the consistency of IVIF reference comparisons. For the unacceptably additive consistency, a new approach is put forward to enhance the consistency. Thereby, the proposed IVIF BWM is summarized step by step. Three examples of applications are furnished to demonstrate its effectiveness and validation.

An indirect multicriteria group decision-making method with heterogeneous preference relations and reliabilities of decision-makers

This study proposes a new indirect method to solve multicriteria group decision-making (MCGDM) problems with heterogeneous preference relations and decision-makers’ reliabilities. To unify the heterogeneous preference relations, the transformation of multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), intuitionistic fuzzy preference relations (IFPRs), and linguistic preference relations (LPRs) into distributed preference relations (DPRs) is analyzed. As consistency among DPRs is constructed under the assumption that decision-makers are bounded rationality, the abstract transformation of MPR, FPR, IFPR, and LPR into DPR is defined, and its reality depends on the preferences of decision-makers. Two important properties of abstract transformation, namely, internal consistency and restricted max-max transitivity, were theoretically verified. The reliabilities of decision-makers are involved in MCGDM by estimating the reliability of each criterion to improve solution quality. Based on the four types of abstract transformations, a process for analyzing MCGDM problems with heterogeneous preference relations and decision-makers’ reliabilities is developed. The proposed method is used to analyze a new business selection problem for an enterprise located in Changzhou, Jiangsu, China to demonstrate its applicability and validity.

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 dynamic trust network and influence measure-based consensus model for large-scale group decision-making with incomplete intuitionistic fuzzy preference relations

The proliferation of network technology has led to the focus on large-scale group decision-making (LSGDM).This study establishes a consensus model by constructing dynamic trust networks to address LSGDM problems in an incomplete intuitionistic fuzzy environment. More specifically, an approach to measuring the influence of decision-makers (DMs) is presented by combining opinion similarity and trust relationships among DMs. Subsequently, an estimation method for missing values in incomplete intuitionistic fuzzy preference relations (IFPRs) is given by considering the reference risk. With these discussions, a dynamic update method of the trust network is proposed to determine the real-time weights of DMs and subgroups. In addition, a two-stage feedback adjustment mechanism for individuals and subgroups is designed. In the end, a numerical example and comparative analysis are provided to illustrate the feasibility and superiority of the proposed method.

The consistency and consensus analysis for group decision-making with incomplete linguistic interval-valued intuitionistic fuzzy preference relations

The consistency and consensus analysis for group decision-making with incomplete linguistic interval-valued intuitionistic fuzzy preference relations

Spatial Bounded Consistency of Intuitionistic Fuzzy Preference Relations

The consistency of intuitionistic fuzzy preference relations (IFPRs) is an important requirement in handling the decision-making problems modeled with IFPRs. Multiplicative consistency and additive consistency are two common types of consistency of IFPRs. These types of consistency of IFPRs are developed in the form of mathematical formulas to satisfy the perfect rationality of decision makers. In real decision-making, the decision makers are generally of bounded rationality rather than perfect rationality due to their own preferences. In consideration of the decision-makers’ preferences, this article proposes a new type of consistency of IFPRs, which is named spatial bounded consistency. A spatial framework is constructed to characterize the relations of three IFPRs among three alternatives. The spatial transitivity of IFPRs is defined based on the restricted max-max transitivity of IFPRs. By following the spatial transitivity of IFPRs, the preferences of decision makers contained in IFPRs are described in two situations. Under the assumption that the preferences of a decision maker are according in handling similar decision-making problems, the historical IFPRs satisfying spatial transitivity are collected to represent decision-makers’ preferences. On this basis, the spatial bounded consistency of IFPRs is then developed. A multicriteria group decision-making (MCGDM) method is designed based on the spatial bounded consistency. A problem of selecting the supplier of breast puncture needle is analyzed to demonstrate the applicability and effectiveness of the developed MCGDM method.

An advanced stratified decision-making strategy to explore viable plastic waste-to-energy method: A step towards sustainable dumped wastes management

Dumping waste and dumping sites pose significant environmental issues with serious implications for human health, the environment, and wildlife. Dumping grounds can also cause difficulties such as leaching, which occurs when waste chemicals seep into the soil and damage groundwater resources. The vast quantity of dumped waste plastic is a major source of energy in the form of gas, fuel, and electricity. The selection of the most appropriate waste-to-energy (WtE) technology affects the dumped waste because it allows for reduced greenhouse gas emissions, diverts dumpsites, generates energy, supports the circular economy, and lowers post-recycling pollution. This complex selection problem requires careful consideration of uncertainties from multi-perspective analysis, vague information, and imprecision in decisions. The stratified fuzzy multi-criteria decision making approach is suitable for addressing different states of events, uncertain data, and sustainable choice selection. Hence, we improved the intuitionistic analytical hierarchical process with a stratified targeting concept for multi-level criteria importance and coupled it with weighted aggregated sum product assessment for ranking WtE techniques. The preferences of experts are characterized using intuitionistic fuzzy preference relations. An empirical study on dumped plastic waste and dumpsite management discovered that plasma technology becomes a more feasible option by satisfying stratification and is more effective in clearing landfills by recovering energy. The comparative analysis, sensitive analysis, and Spearman’s rank correlation validate the proposed methodology, and this method seems to be a new dimension to handle ecological issues.

A dynamic trust consensus model considering individual overconfidence

In the consensus reaching process (CRP) under the dynamic trust network, decision-makers’ (DMs’) self-confidence can be regarded as the psychological expression of self-estimation. However, their overconfidence usually has a negative impact on the CRP, even leading to the failure of group decision-making (GDM). To address the issue, we propose a dynamic trust consensus model considering overconfidence under the hesitant intuitionistic fuzzy preference relations (HIFPRs). To determine dynamic trust relationships between multi-attribute DMs, an interactive evaluation-based method is proposed, and thereafter, DMs’ weights are allocated based on the trust degree. In the CRP considering overconfidence, DM’s self-confidence level is defined to detect overconfidence, and feedback mechanisms are constructed for different cases. If overconfident DMs are identified, their trust relationships and self-confidence levels will be adjusted to facilitate the CRP; otherwise, DMs’ HIFPRs will be adjusted. A numerical example, comparative analysis, and discussions are used to illustrate the validity of the proposed model. Comparisons reveal that managing overconfidence by adjusting DMs’ interactive evaluation and self-confidence levels in the dynamic trust network can effectively improve the group consensus degree.

Regression coefficient measure of intuitionistic fuzzy graphs with application to soil selection for the best paddy crop

<abstract><p>According to United Nations forecasts, India is now expected to pass China as the most populous country in the world in 2023. This is due to the fact that in 2022, China saw its first population decline in over 60 years. In order to keep pace with the rapid rise in its population, India will need to significantly raise food production in the future. Specific soil selection can help in achieving expected food production. In this article, we use Laplacian energy and regression coefficient measurements to face decision-making issues based on intuitionistic fuzzy preference relations (IFPRs). We present a novel statistical measure for evaluating the appropriate position weights of authority by computing the fuzzy evidence of IFPRs and the specific similarity grade among one distinct intuitionistic preference connection to the others. This new way of thinking bases decisions on evidence from both external and internal authorities. We evolved a statistical (regression coefficient measure) approach to determine the importance of alternatives and the best of the alternatives after integrating the weights of authority into IFPRs. This statistical analysis can be put to good use to choose the best soil for different crops to provide food for India's rapidly growing population in the future. To show how useful and realistic the suggested statistical measure is, a good example from real life is given. Additionally, we discovered how correlation and regression coefficient measurements are related to one another in intuitionistic fuzzy graphs.</p></abstract>

Correlation Coefficient Measure of Intuitionistic Fuzzy Graphs with Application in Money Investing Schemes

Intuitionistic fuzzy graphs are extensions of fuzzy graphs that preserve the dualism characteristics of fuzzy graphs and have a stronger capacity to describe ambiguity in actual decision-making issues than fuzzy graphs. In this research paper, the Laplacian energy and correlation coefficient of intuitionistic fuzzy graphs are computed for finding group decision-making problems that are supported by intuitionistic fuzzy preference relations. We propose a novel method for calculating establishments' comparative position loads by manipulating the undecided corroboration of IFPR and the correlation coefficient of one personality IFPR to the other items. As a result, we comprehend a large number of establishments in the detailed IFPR and devise a correlation coefficient process to investigate the significance of alternatives and the best of the alternatives. Finally, we present a collaborative decision-making technique in a money-investing scheme, and that idea may be devised in disparate beneficial investing schemes.

Interactively Iterative Group Decision-Making Method with Interval-Valued Intuitionistic Fuzzy Preference Relations Based on a New Additive Consistent Concept

Interactively Iterative Group Decision-Making Method with Interval-Valued Intuitionistic Fuzzy Preference Relations Based on a New Additive Consistent Concept

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.

Hierarchical multi-criteria decision making with group voting information: New Tanino’s additive consistency intuitionistic fuzzy translation and utility vector acquisition

The frame of intuitionistic fuzzy preference relations (IFPRs) is an effective tool of representing pairwise preference order based group voting information. However, existing intuitionistic fuzzy translations of Tanino’s additive consistency and previous methods of acquiring utility vectors from IFPRs are often unable to achieve a satisfactory solution for hierarchical multi-criteria decision making (HMCDM) with IFPRs. This study analyzes existing notions of additively consistent IFPRs (ACIFPRs) and shows their shortages. A novel intuitionistic fuzzy translation of Tanino’s additive consistency is developed and an index computational formula is provided to measure additive inconsistency of IFPRs. A new approach is offered to generate ACIFPRs from vectors with intuitionistic fuzzy elements and a frame is put forward to normalize intuitionistic fuzzy vectors. Subsequently, a closed-form solution based method is presented to secure normalized intuitionistic fuzzy utility vectors from ACIFPRs and a linear program is built to acquire an optimal and normalized intuitionistic fuzzy utility vector from any IFPR. An approach is proposed to tackle HMCDM problems with pairwise preference order based group voting information. The reasonability and performance of the models developed are validated by an illustrative example and a case study about outstanding teacher recommendation based on large-scale group votes on teaching satisfaction.

A New Consensus Model Based on Trust Interactive Weights for Intuitionistic Group Decision Making in Social Networks

A promising feature for group decision making (GDM) lies in the study of the interaction between individuals. In conventional GDM research, experts are independent. This is reflected in the setting of preferences and weights. Nevertheless, each expert's role is played through communication, collaboration, and cooperation with other individuals. The interaction from others may affect the power of an expert as well as his/her opinion. Furthermore, it is noted that a link path with the highest degree of trust is the most efficient information transmission channel. Inspired by these findings, an optimal trust-induced consensus process is designed with the usage of intuitionistic fuzzy preference relation. The comprehensive weight of each expert is decomposed into two portions, namely: 1) the individual weights and 2) interactive weights. Three optimization models are constructed to achieve weight parameters under different decision situations, where the weight parameters are represented through a 2-order additive fuzzy measure and the Shapley value. To reflect the interaction, the Choquet integral is employed for aggregating opinions, and a novel distance measure is adopted for accomplishing a consensus index. An illustrative example and comparison are put in practice to show the effectiveness and improvements of the proposed method.

Consistency threshold- and score function-based multi-attribute decision-making with Q-rung orthopair fuzzy preference relations

As a general form of intuitionistic fuzzy preference relations (IFPRs) and Pythagorean fuzzy preference relations (PFPRs), q-rung orthopair fuzzy preference relations (q-ROFPRs) provide a more flexible information representation for decision makers (DMs) to express their vagueness and uncertainty. However, there have been only a few studies conducted on q-ROFPRs. Therefore, in the context of multi-attribute decision-making (MADM), a decision framework for MADM with q-ROFPRs is proposed. First, a novel score function is proposed to compare two different q‐rung orthopair fuzzy numbers (q‐ROFNs). Subsequently, an algorithm is developed to check and improve the multiplicative consistency of q-ROFPRs. Moreover, to consider the rationality of the threshold determination, an objective method for determining the threshold of q-ROFPRs is developed considering the number of alternatives and rung q. Finally, a new method for determining the weights of attributes is discussed. In addition, an illustrative example involving the brand evaluation of new energy vehicles is used to verify the applicability of the above methods. The rationality and superiority of the proposed methods are highlighted by a comparative analysis with existing studies.

Operation mode selection of public-funded private-run elderly care agencies based on triangular intuitionistic fuzzy preference relations group decision-making

Operation mode selection of public-funded private-run elderly care agencies based on triangular intuitionistic fuzzy preference relations group decision-making