Intuitionistic Fuzzy Values Research Articles

Engineered nanomaterials reduce metal(loid) accumulation and enhance staple food production for sustainable agriculture.

Metal(loid) contaminants in food pose a global health concern. This study offers a global analysis of the impact of nanomaterials (NMs) on crop responses to metal(loid) stresses. Our findings reveal that NMs have a positive effect on the biomass production of staple crops (22.8%), while showing inhibitory effects on metal(loid) accumulation in plants (-38.3%) and oxidative damage (-21.6%) under metal(loid) stress conditions. These effects are influenced by various factors such as NM dose, exposure duration, size and composition. Here we introduce a method using interval-valued intuitionistic fuzzy values by integrating the technique for order preference by similarity to an ideal solution and entropy weights to compare the effectiveness of different NM application patterns. These results offer practical insights for the application of NMs in similar multi-criteria decision-making scenarios, contributing to sustainable agriculture and global food safety.

Dynamic Flow Algorithm with Intermediate Storage for Emergency Evacuation Allowing Lane Reversal based on Incomplete Intuitionistic Fuzzy Preference Relation

Background Evacuation in case of disasters is of the greatest importance because of significant occurrences of natural and artificial disasters worldwide, which is why a reliable evacuation plan is always needed. However, evacuation models are difficult to develop due to various uncertain aspects that need to be considered, multiple and often conflicting criteria for evaluation and as lack of expertise regarding a specific preference of alternatives. Objective This study aims to transport the maximum number of evacuees in a dynamic network with lane reversal by a safe pattern of transportation, i.e., allowing storage at intermediate nodes. The optimal order of shelters and intermediate nodes for a reliable evacuation plan will be defined by incomplete intuitionistic fuzzy preference relation. Methods The illustrated method incorporates multiple and often conflicting criteria into a process of emergency decision-making. When evaluating evacuation alternatives, a decision-maker may hesitate and be unsure which alternative is better or not have sufficient expertise to evaluate a pair of alternatives. To model uncertainty and hesitation, intuitionistic fuzzy values are used to describe alternatives in more detail. This study relies on flow models and graph theory to simulate the movement of evacuees to safe destinations. Furthermore, fuzzy methods and their recent modifications are applied to determine the effective priority order of shelters. A case study which simulates the evacuation of aggrieved to safe destinations is presented. Results A method of evaluating the shelters and intermediate nodes for evacuation based on incomplete intuitionistic fuzzy preference relation is proposed. The method allows the missed values of experts’ assessments to be filled in regarding the evacuation alternatives and deals with intuitionistic fuzzy values, which describe experts’ hesitation. The dynamic character of flow distribution enables transit arc capacities and time factors to be processed. The contraflow technique, which is a powerful tool to decrease traffic jams and congestion on roads by reversing the movement along the unused segments, is applied to maximize the number of survivors. Conclusion The results of the method were compared to those of existing methods, and their consistency was proved. In the future, we intend to apply interval-valued intuitionistic preference relations and iterative algorithms to improve the consistency of intuitionistic preference relations to the tasks of transporting the maximum possible number of aggrieved to safe locations.

A New Method of Distance Measure Between Intuitionistic Fuzzy Sets and its Application in Admission Procedure

Sundry complex real-world problems involving decision-making have been resolved using the idea of distance measures between intuitionistic fuzzy sets (IFSs). Several distance measuring techniques between IFSs have been developed, but it is only the work of Xie et al. that considered the tendency coefficients of the intuitionistic fuzzy parameters (IFPs), namely, membership grade, nonmembership grade and hesitation grade. Albeit, Xie et al.’s technique uses assumed tendency coefficients for IFPs, which is defective for a reliable result. Sequel to this setback, we develop a new distance measure between IFSs which includes tendency coefficients of the IFPs, where the tendency coefficients are computed from the intuitionistic fuzzy values to enhance reliable results. In addition, the new distance measure between IFSs is applied to discuss students’ admission process to ascertain the most eligible candidate based on academic performance in an entry examination. The application is carried out using two techniques, namely, the recognition principle and the multiple criteria decision-making approach, respectively. Finally, the superiority of the newly developed distance measure between IFSs is shown comparatively with respect to the existing approaches between IFSs. This new distance measure can be applied to clustering analysis, multiple attributes decision-making (MADM), a technique for order preference by similarity to ideal solution (TOPSIS), etc. in future research.

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.

Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems

In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.

Strict intuitionistic fuzzy distance/similarity measures based on Jensen-Shannon divergence

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance “1” can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets.

Evaluation method of e-government audit information based on big data analysis

Abstract In order to improve the problems of low efficiency of intelligent auditing and long approval cycles in the evaluation of e-government audit information, this paper proposes a model for the evaluation of e-government audit information. The model covers the acquisition of audit information, evaluation rules, and e-government auditing. The intuitionistic fuzzy roughness model is applied to determine the distinguishing relationship between objects based on the intuitionistic fuzzy values of different objects and to determine the evaluation rules for audit information. An e-government auditing approach based on big data analysis is also proposed, and a genetic algorithm is used to optimize the relevant parameters of a convolutional neural network to enhance the stability of the e-government auditing model. Audit information evaluation activities are carried out at Changchun Housing Provident Fund Center in Jilin Province, China, whose shared approval information data failure records in 2023 accounted for as high as 70.54% of all documents, with low stability. The number of cases and closure of the provident fund center accepting the extranet from 2017 to 2023 only accounted for 4.57% and 3.99% of the whole. In the audit information evaluation indicators, nine secondary indicators, such as credit management and indirect income, have an evaluation value of more than 0.5 in the “medium” evaluation level, and many indicators have an evaluation value of more than 0 in the “poor” evaluation level, so there are many shortcomings in the business.

An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws

The intuitionistic fuzzy soft set (IFSS) is a vital technique for tackling uncertainty while the collection of information with the help of the membership function having values from unit interval. Moreover, the Aczel-Alsina t-norm (AATNRM) and Aczel-Alsina t-conorm (AATCRM) are the most generalized and flexible operational laws to operate the information which is the part of the unit intervals. The purpose of this article is to provide a number of aggregation operations (AOs) for information represented by intuitionistic fuzzy soft values (IFSVs) based on AATRM and AATCRM. Therefore, some new operational laws are developed by using on the AATRM and AATCRM for the development of the sum and product laws for IFSVs. Then, intuitionistic fuzzy soft Aczel-Alsina weighted averaging (IFSAAWA) and geometric (IFSAAWG) operators are purposed based on these operational laws. Additionally, some of their characteristics are examined, and the difference of the proposed and existing operators is investigated. Moreover, the proposed approach is applied to the problem of multi-attribute decision-making (MADM) for significance.

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.

Diagnosis of Alzheimer’s disease via Intuitionistic fuzzy least squares twin SVM

Neurodegenerative disorders like Alzheimer’s disease (AD) are irreversible and show atrophies in the area of the cerebral cortex of brain. AD leads to loss of memory and other cognitive impairments. The AD subjects are evaluated based on magnetic resonance imaging scans. The data may have the problem of class imbalance, noise and outliers which is a great challenge for classification. Support vector machines and twin support vector machine-based classifiers may not effectively deal with these problems as both these models assume that all the samples are equally important for the separating hyperplane. To overcome these issues, we propose intuitionistic fuzzy least square twin support vector machine for class imbalance problems (IFLSTSVM) and class specific-IFLSTSVM (CS-IFLSTSVM). To minimize the effects of class imbalance, the samples are appropriately weighted to minimize their effect on the optimal hyperplane. Moreover, we use intuitionistic fuzzy scores to overcome the issues of noise and outliers. Intuitionistic fuzzy score values generate appropriate weights by considering both the distance of the samples from the class centroid as well as the heterogeneity of the samples. The proposed models IFLSTSVM and CS-IFLSTSVM are efficient as they need to solve a system of linear equations. In Alzheimer’s disease diagnosis, the proposed IFLSTSVM and CS-IFLSTSVM models showed better performance in MCI_vs_AD and CN_vs_MCI cases, respectively. Moreover, the proposed models showed better performance in the diagnosis of breast cancer classification. The statistical analysis carried out over KEEL and UCI data leads to the superiority of the proposed models. The source code of the proposed model is available at https://github.com/mtanveer1/Diagnosis-of-Alzheimer-s-disease-via-Intuitionistic-fuzzy-least-squares-twin-SVM.

An extended EDAS method with circular intuitionistic fuzzy value features and its application to multi-criteria decision-making process

An extended EDAS method with circular intuitionistic fuzzy value features and its application to multi-criteria decision-making process

Post Evaluation of Rural Road Renovation and Upgrading Plans in Low Mountain and Hilly Areas Based on IF-VE Method

Currently, China is vigorously promoting the construction of "Four Good Rural Roads", and the planning and construction layout of urban and rural transportation, especially rural roads, can effectively promote the rapid integration of urban and rural areas and the coordinated development of small towns. However, there are still problems in the current planning and construction of rural roads, such as large inventory, low level, and chaotic layout. Post evaluation of rural road renovation and upgrading, analysis and evaluation of the effectiveness of the plan, can provide strong support for the subsequent adjustment of regional comprehensive transportation system construction. Based on various national, provincial, and municipal transportation development guidelines, this article analyzes the factors related to the planning and evaluation of rural roads in low mountain and hilly areas. Based on the IF-VE method formed by intuitionistic fuzzy theory and value engineering theory, a post evaluation study is conducted on a rural road renovation and upgrading project plan. The application results indicate that the indicator system and model constructed in the article have certain feasibility and applicability.

A Decision-Making Method for Design Schemes Based on Intuitionistic Fuzzy Sets and Prospect Theory

Conceptual design is a key link in the process of complex product design, and it is very important to select the appropriate design scheme; however, there are many types and inaccuracies of the evaluation data, and there is a problem of mutual influence between the evaluation criteria, which leads to unreliable decision making of the optimal solution. In order to solve this problem, a decision-making method based on intuitionistic fuzzy sets (IFS) and prospect theory is proposed. This method can be used for symmetric and asymmetric evaluation data. The evaluation data are classified according to different expression types and unified using intuitionistic fuzzy numbers. The intuitionistic fuzzy prospect value of decision information is calculated using prospect theory, and the prospect transformation of decision information is completed. At the same time, the Gray Relational Analysis (GRA) method and the Criteria Importance Though Intercriteria Correlation (CRITIC) method are used to calculate the subjective and objective weights of the technical and economic evaluation indexes of the product, and the combination weights are given; then, based on the evidence theory, the basic probability distribution of the evidence chain of all conceptual design schemes is synthesized, and the comprehensive prospect evaluation results of the schemes are obtained to complete the optimization of the conceptual design schemes. Finally, the effectiveness of the proposed method is verified by the conceptual design of the chip removal system of the deep hole machining machine tool. This work provides a promising method for decision makers to optimize the design scheme and provides insights into multi-objective decision-making problems.

Multiattribute decision making based on nonlinear programming methodology, the Euclidean distance between IVIFVs, and new score function of IVIFVs

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming methodology, the Euclidean distance between interval-valued intuitionistic fuzzy values (IVIFVs), and the proposed score function of IVIFVs. Firstly, a new score function of IVIFVs is proposed to overcome the shortcomings of the existing score functions of IVIFVs. Then, we construct the score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, a nonlinear programming model is proposed based on the Euclidean distance between IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we solve the proposed nonlinear programming model to obtain the optimal weights of the attributes. Then, the weighted score of each alternative is calculated based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores of the alternatives. The MADM method proposed in this paper can conquer the shortcomings of the existing MADM methods in the environments of IVIFVs.

RETRACTED: Multiattribute decision making based on nonlinear programming methodology, novel score function of interval-valued intuitionistic fuzzy values, and the standard deviations of the score values in the score matrix

In this paper, we propose a new multiattribute decision making (MADM) method using the proposed nonlinear programming (NLP) model, the proposed score function (SCF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the standard deviation of the score values appeared in each column of the constructed score matrix (SX). The proposed SCF of IVIFVs can overcome the shortcomings of the existing SCFs of IVIFVs. Firstly, we construct the SX using the decision matrix given by the decision maker and the proposed SCF of IVIFVs. Then, we construct a NLP model using the obtained SX, the standard deviation of the score values appeared in each column of the SX, the interval-valued intuitionistic fuzzy weights of the attributes, the largest ranges of IVIFVs, and the concept of deviation variables. Then, we solve the NLP model to get the optimal weights of the attributes, respectively. Then, based on the constructed SX and the obtained optimal weights of the attributes, we calculate the weighted score of each alternative. Finally, we rank the alternatives according to the obtained weighted scores. The proposed MADM method can overcome the drawbacks of the existing MADM methods.

RETRACTED: Multiple attribute decision making based on novel nonlinear programming model, the distance between score values, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a novel multiple attribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the distance between the score values appeared in the constructed score matrix (SCMX), and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), where the NLP model is used to get the optimal weights (OWs) of the attributes. Firstly, we propose a novel SF to conquer the shortcomings of the existing SFs of IVIFVs. Then, we use the proposed SF to construct the SCMX from the decision matrix (DM) given by the decision maker (DK). Then, we propose a NLP model to obtain the OWs of the attributes based on the distance between the score values appeared in the constructed SCMX, the interval-valued intuitionistic fuzzy weights (IVIFWs) of the attributes provided by the DK, the concept of deviation variables, and the largest range of the IVIFW of each attribute. Then, we calculate the weighted score (WS) of each alternative based on the obtained SCMX and the obtained OWs of the attributes. Finally, we rank the alternatives according to the WSs of the alternatives. The proposed MADM method can conquer the shortcomings of the existing MADM methods.

RETRACTED: Multiattribute decision making method based on nonlinear programming model, cosine similarity measure, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the cosine similarity measure of IVIFVs, and the proposed nonlinear programming (NLP) model. The proposed SF of IVIFVs overcomes some shortcomings of the existing SFs of IVIFVs. The proposed MADM method overcomes some shortcomings of the existing MADM methods based on IVIFVs. Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of some existing SFs of IVIFVs. Then, we construct a score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, we build a NLP model based on the cosine similarity measure of IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes. Then, we solve the NLP model to obtain the optimal weights (OWs) of the attributes, respectively. Based on the obtained OWs of the attributes and the constructed score matrix, we compute the weighted scores (WSs) of the alternatives, respectively. Finally, we rank the alternatives based on the obtained WSs. The proposed MADM method provides us a very useful approach for MADM in the interval-valued intuitionistic fuzzy context.

Multiattribute decision making based on nonlinear programming methodology, score function of interval-valued intuitionistic fuzzy values, and the dispersion degree of score values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the dispersion degree of the score values appeared in each column of the score matrix (SMX). Firstly, we propose a new SF of IVIFVs to construct the SMX. The proposed SF of IVIFVs can overcome the drawbacks of the existing SFs of IVIFVs. Then, we calculate the dispersion degree of the score values appeared at each column of the SMX. Then, we construct a NLP model to get the optimal weight (OW) of each attribute based on the obtained SMX, the dispersion degree of the score values appeared at each column of the SMX, and the interval-valued intuitionistic fuzzy weights of the attributes given by the decision maker. Then, we calculate the weighted score (WS) of each alternative based on the obtained SMX and the obtained OWs of the attributes. Finally, we get the preference order (PFO) of the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the drawbacks of some existing MADM methods in an interval-valued intuitionistic fuzzy setting.

The Impact of the Intuitionistic Fuzzy Entropy-Based Weights on the Results of Subjective Quality of Life Measurement Using Intuitionistic Fuzzy Synthetic Measure.

In this paper, an extended Intuitionistic Fuzzy Synthetic Measure (IFSM) with intuitionistic fuzzy (IF) entropy-based weights is presented. This method can be implemented in a ranking problem where the assessments of the criteria are expressed in the form of intuitionistic fuzzy values and the information about the importance criteria is unknown. One example of such a problem is measuring the subjective quality of life in cities. We join the debate on the determination of weights for the analysis of the quality of life problem using multi-criteria methods. To handle this problem, four different IF entropy-based weight methods were applied. Their performances were compared and analyzed based on the questionnaires from the survey concerning the quality of life in European cities. The studies show very similar weighting systems obtained by different IF entropy-based approaches, resulting in almost the same city rankings acquired through IFSM by using those weights. The differences in rankings obtained through the IFSM measure (and only by one position) concern the six cities included in the analysis. Our results support the assumption of the equal importance of the criteria in measuring this complex phenomenon.

RETRACTED: Multiattribute decision making based on nonlinear programming model, the Gini coefficient, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the Gini coefficient, and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of the existing SFs of IVIFVs. Then, we construct a score matrix (SMX) based on the proposed SF of IVIFVs and the decision matrix given by the decision maker (DMK). Then, we construct a NLP model based on the constructed SMX, the Gini coefficient, and the interval-valued intuitionistic fuzzy (IVIF) weights of the attributes given by the DMK. After solving the constructed NLP model, we obtain the optimal weight (OW) of each attribute. Then, we compute the weighted score (WS) of each alternative based on the constructed SMX and the obtained OWs of the attributes. Finally, we rank the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods in IVIF environments.