Intuitionistic Fuzzy Environment Research Articles

EXTRACTING AND PRIORITIZING THE ATTRACTIVENESS PARAMETERS OF SHOPPING CENTERS UNDER INTUITIONISTIC FUZZY NUMBERS

Shopping center plays an important role in distribution system and marketing. These canters provide an appropriate atmosphere for customers; so that, the customers achieve the best service within a short time. However, there is an intense competition among shopping centers to attract more customers for increasing the profit. Therefore, a powerful model assists authorities in identifying the critical competitive aspects and directing their efforts toward performance improvement. However, a number of strategies have been developed to identify the most relevant components. The Delphi technique under intuitionistic fuzzy environment, called intuitionistic fuzzy Delphi method (IFDM) study, is a group-based technique that can simply formulate the uncertainty imposed by decision making circle. On the other hand, multi criteria decision making (MCDM) method such as analytical network process (ANP) is a mathematical tool for taking into account mutual relationships in order to rank a number of criteria. Nonetheless, the ANP is unable to account for the uncertainty involved in the decision-making process. Similarly, the intuitionistic fuzzy set (IFS) can express ambiguity and vagueness by utilizing the given scale. Because the IFS is robust in dealing with complexity and ambiguity, the IFS-GANP (an integrated model of the IFS and ANP methods under group decision) can result in a more specific description of the situation. As a result, the IFS-GANP approach outperforms both conventional ANP and fuzzy ANP. To demonstrate the model’s feasibility, a case study rating the essential aspects impacting the attractiveness of retail centers is shown. The result demonstrates factor C31 (Location) with value of 0.202 plays the greatest role in attracting customers.

An intuitionistic fuzzy approach for prey–predator harvesting system with toxicity and time delay

This study presents an intuitionistic fuzzy prey–predator model with time delay, where several toxic substances from external sources contaminate the prey and predator species. The system consists of one prey and one predator, with the logistic growth of prey species and predation terms proportional to prey density. This system incorporates Holling type-II functional response and introduces a time delay in harvesting prey species over a precise size or age. The primary focus of this work is to investigate the impact of age or size-selective delay on the system’s stability within the intuitionistic fuzzy environment. The model employs triangular intuitionistic fuzzy numbers to account for imprecise biological parameters, and it is converted into an intuitionistic fuzzy model using the Hukuhara derivative. The fuzziness of the model is then resolved using Yager’s Ranking method. Without delay, the paper delves into the system’s dynamics, examining local and global stability and bionomic considerations. Numerical simulations are performed using MATLAB to validate the theoretical findings.

A mathematical approach to optimizing brand school placement via intuitionistic Sombor indices

The property of fuzziness is advantageous for any setting where a problem prediction and solution are intended. In comparison to the classical approach (crisp set), fuzzy graphs are beneficial as they provide greater precision and flexibility. Intuitionistic fuzzy graphs (IFGs) are generalizations of fuzzy graphs, in which each vertex is allocated an ordered pair whose first coordinate represents the membership value and whose second coordinate gives the non-membership value. Sombor indices are recently invented indices and are prime indices in describing the topology of a graph. They have demonstrated strong prediction ability in mathematical chemistry. The main aim of this research draft is to define two milestones, the fifth and sixth versions of Sombor indices in an intuitionistic fuzzy environment, IFGs are much more generalized and universal as compared to crisp graph theory, so we converted these two topological indices in this environment and then formulae for some fundamental families of graphs such as path graph, cycle graph, complete graph etc. are being derived. Our manuscript presents a novel application of opening a chain of schools of a popular brand in a certain vicinity, including the cluster center of the chain and applying intuitionistic fuzzy-based topological indices to assess their performance. With the help of this application, we highlight the practical implications and benefits of employing intuitionistic fuzzy-based techniques on the performance of schools through a comparative analysis. We checked the importance of intuitionistic fuzzy Sombor indices by presenting the application and concluded these indices can be applied to decision-making problems. With the help of the application, the efficiency of both of the intuitionistic fuzzy Sombor indices is also characterized, which must be a future efficacious tool in decision-making issues.

Multi-attribute three-way decision making based on interval-valued intuitionistic fuzzy sets

In the interval-valued intuitionistic fuzzy environment, a new multi-attribute three-way decision-making model is proposed to address the problems that the relative loss function in the existing multi-attribute three-way decision-making model does not consider the degree of hesitancy, and the alternative conditional probabilities are given subjectively by the authors, which lacks objectivity. First, three types of ideal solutions are introduced, and the correlation coefficients between the evaluated values and ideal solutions are utilized to construct alternative relative loss functions. Second, the ELECTRE-I method is generalized to the interval-valued intuitionistic fuzzy environment to establish the outranking relation and a method for estimating the conditional probability of alternatives is given. Finally, the model is used to experimentally analyze examples to illustrate the effectiveness and rationality of the model.

Selecting an optimal approach to reduce energy crises under interval-valued intuitionistic fuzzy environment

The concept of interval-valued intuitionistic fuzzy sets is intellectually stimulating and holds significant utility in the representation and analysis of real-world problems. The development of similarity measures within the class of interval-valued intuitionistic fuzzy sets possesses significant importance across various academic disciplines, particularly in the fields of decision-making and pattern recognition. The utilization of similarity measures is of utmost importance in the decision-making process when implementing interval-valued intuitionistic fuzzy sets. This is due to its inherent capability to quantitatively assess the level of resemblance or similarity between two interval-valued intuitionistic fuzzy sets. In this article, the drawbacks of the existing similarity measures in the context of an interval-valued intuitionistic fuzzy environment are addressed, and a novel similarity measure is presented. Many fundamental properties of this new interval-valued intuitionistic fuzzy similarity measure are also established, and the effectiveness of this similarity measure is illustrated by presenting a useful example. Moreover, a comparison is given to demonstrate the validity of the newly proposed similarity measure within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment. In addition, an algorithm is designed to solve multi-criteria decision making problems by means of the proposed measure in the interval-valued intuitionistic fuzzy setting. Furthermore, this newly defined similarity measure is successfully applied to select an optimal renewable energy source to reduce energy crises. Finally, we conduct a comparative study to showcase the authenticity of the recently defined technique within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment.

Shared manufacturing service evaluation based on intuitionistic fuzzy VIKOR

With the rise of the concept of sharing economy, the shared manufacturing model has gained widespread attention. The VIKOR shared manufacturing service evaluation approach is presented based on an intuitionistic fuzzy environment, which enables users to filter out acceptable shared manufacturing services from a wide pool of shared manufacturing services with similar functional qualities. Firstly, considering the QOS multi-indicator comprehensive evaluation of services by multiple stakeholders under the fundamental characteristics of shared manufacturing, the QOS evaluation index system is built from the two aspects of online and offline, which includes 2 first-level indicators and 10 second-level indicators. The paper also constructs a service recommendation model considering supply and demand constraints. Secondly, the intuitionistic fuzzy numbers are introduced to define the non-quantitative indexes, and the G1-method and variable-precision rough set theory are used for the assignment, and the maximum entropy theory is utilized to integrate the assignment method to obtain the combination weights. Thirdly, the VIKOR method based on intuitionistic fuzzy sets is used to evaluate and rank the shared manufacturing candidate services, in which the combined benefits and minimum regret values of the groups are solved based on the intuitionistic fuzzy number similarity. Finally, the reliability and feasibility of the algorithm are verified with a real case.

Evaluating and Selecting a Supplier in a Healthcare Supply Chain Using the Technique for Order Performance by Similarity to Ideal Solution Under Intuitionistic Fuzzy Environment

Evaluating and Selecting a Supplier in a Healthcare Supply Chain Using the Technique for Order Performance by Similarity to Ideal Solution Under Intuitionistic Fuzzy Environment

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.

A new energy vehicle battery supplier selection using SWARA-MEREC-MARCOS approach under probabilistic triangular intuitionistic hesitant fuzzy environment

In this manuscript, we construct a Multi-Criteria Decision-Making (MCDM) model to study the new energy vehicle (NEV) battery supplier selection problem. Firstly, we select criteria to build an evaluation index system. Secondly, SAWARA and MEREC methods are used to calculate subjective and objective weights in the ranking process, respectively, and PTIHFS (Probabilistic Triangular Intuitionistic Hesitant Fuzzy Set) is employed to describe the decision maker’s accurate preferences in performing the calculation of subjective weights. Then, the game theory is used to find the satisfactory weights. We use TFNs to describe the original information in the MARCOS method to obtain the optimal alternative. Finally, a correlation calculation using Spearman coefficients is carried out to compare with existing methods and prove the model’s validity.

Two-sided matching decision method and application based on subject differences in interval intuitionistic fuzzy environment

In this paper, a two-sided matching decision model based on interval-valued intuitionistic fuzzy environment is proposed to maximize the demand of individual differences. Firstly, the attribute feature table and weight matrix of both agents are constructed, and a formula for calculating the comprehensive advantage in the interval-valued intuitionistic fuzzy environment is given, namely the interval-valued intuitionistic fuzzy comprehensive advantage aggregation operator (IIFCAAO); Secondly, the interval-valued intuitionistic fuzzy decision matrix of both agents is calculated by using the comprehensive advantage aggregation operator, and the interval-valued intuitionistic fuzzy decision matrix is transformed into a score function matrix by using a score function formula; Thirdly, the two-sided matching model is established to maximize the score; Finally, the scientificity and practicability of the model are verified by an example of college students changing their majors.

Sustainable selection of microwave absorbing materials: A green evaluation under interval-valued intuitionistic fuzzy environment

Environmentally friendly technology is being used by industries all over the world, and engineers in the manufacturing and materials industry are embracing sustainable business models. In this paradigm, materials are processed using economically and environmentally sound methods. The use of microwave-absorbing materials (MAMs) in low-altitude observatory aircraft and the rise in electromagnetic pollution have brought them to light. The main aim of this study is to select an ideal MAM with excellent physical, electromagnetic, chemical, and thermal properties, which also fulfills sustainability aspects based on expert judgments. In this regard, we have proposed a new hybrid framework consisting of Modified Digital Logic (MDL), a subjective weighting method in combination with the measurement of alternatives and ranking according to compromise solution (MARCOS) under an interval-valued intuitionistic fuzzy (IVIF) environment to select an optimum MAM. Furthermore, this research work contributes to streamlining the selection process by consolidating the plethora of work available in the literature on the synthesis and characterization of MAMs. A database is created for 160 potential candidate materials in C, S, X, and Ku bands for carbon-based materials, including carbon nanotubes (CNT), graphene, reduced graphene oxide (rGO), carbon fibers, and biomass-derived materials. These materials are then passed through successive screening stages to shortlist 14 materials, which are ranked subsequently over a set of 15 crisp and ambiguous criteria. This comprehensive study simultaneously caters to quantitative and qualitative information extracted from experimental work, material resource packs, or expert evaluations. The findings highlight CNT/Fe (20 wt%, E) (Al1) as the most suitable candidate for MAM application with outstanding electromagnetic properties. Finally, the results are compared with extant approaches to check the reliability of the proposed framework. In addition, sensitivity analysis is carried out to establish the feasibility and robustness of the obtained results.

A novel method for weighting decision makers for failure mode and effect analysis under intuitionistic fuzzy environment

AbstractThis study introduces an innovative method to implement Failure Mode and Effect Analysis (FMEA) in an Intuitionistic Fuzzy (IF) environment and targets inherent limitations of traditional FMEA, particularly its reliance on precise numerical values that can lead to human subjectivity and compromise accuracy of analysis. The primary aim is to increase the objectivity in evaluating Failure Modes (FMs) in industrial settings, thus enhancing safety and quality assessments. The novel approach integrates the Measurement Alternatives and Ranking according to the Compromise Solution (MARCOS) method within an IF framework. An implementation at a defense industry company is performed for evaluation of the FMs by four Decision Makers (DMs), each possessing different levels of experience and system knowledge. A key innovation of this study is the unique weighting methodology applied to DMs, based on predefined rules, which acknowledges and quantifies their varied expertise and insights. Our methodology significantly contributes to the study's practicality and significance in ranking FMs, emphasizing its effectiveness, robustness, and accuracy. The findings reveal that this method greatly reduces the subjectivity found in traditional FMEA, also providing a more detailed and reliable assessment. This is achieved by adapting the analysis to the specific knowledge levels of the DMs, leading to more dependable and objective quality evaluations in industrial processes. The application of this method in the real‐world setting demonstrates its practical relevance and potential for wider adoption.

A novel generalized similarity measure under intuitionistic fuzzy environment and its applications to criminal investigation

In our contemporary world, where crime prevails, the expeditious conduct of criminal investigations stands as an essential pillar of law and order. However, these inquiries often grapple with intricate complexities, particularly uncertainties stemming from the scarcity of reliable evidence, which can significantly hinder progress. To surmount these challenges, the invaluable tools of crime linkage and psychological profiling of offenders have come to the forefront. The advent of Intuitionistic Fuzzy Sets (IFS) has proven pivotal in navigating these uncertain terrains of decision-making, and at the heart of this lies the concept of similarity measure-an indispensable tool for unraveling intricate problems of choice. While a multitude of similarity measures exists for gauging the likeness between IFSs, our study introduces a novel generalized similarity measure firmly rooted in the IFS framework, poised to surpass existing methods with enhanced accuracy and applicability. We then extend the horizon of practicality by employing this pioneering similarity measure in the domain of clustering for crime prediction-a paramount application within the realm of law enforcement. Furthermore, we venture into the domain of psychological profiling, a potent avenue that has the potential to significantly fortify the arsenal of crime investigations. Through the application of our proposed similarity measure, we usher in a new era of efficacy and insight in the pursuit of justice. In sum, this study not only unveils a groundbreaking similarity measure within the context of an Intuitionistic fuzzy environment but also showcases its compelling applications in the arena of criminal investigation, marking a significant stride toward swifter and more informed decisions in the realm of law and order.

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.

Optimization of grinding processes using multi-criteria decision making methods in intuitionistic fuzzy environment

Optimization of grinding processes using multi-criteria decision making methods in intuitionistic fuzzy environment

On solving a healthcare supplier selection problem using MCDM methods in intuitionistic fuzzy environment

On solving a healthcare supplier selection problem using MCDM methods in intuitionistic fuzzy environment

Triangular intuitionistic fuzzy linear system of equations with applications: an analytical approach

This study extended an existing semi-analytical technique, the Homotopy Perturbation Method, to the Block Homotopy Modified Perturbation Method by solving two n × n crisp triangular intuitionistic fuzzy (TIF) systems of linear equations. In the original system, the coefficient matrix is considered as real crisp, while the unknown variable vector and right hand side vector are regarded as triangular intuitionistic fuzzy numbers. The Block Homotopy Modified Perturbation Method is found to be efficient and practical to solve n × n TIF linear systems as it only requires the non-singularity of the n × n TIF linear system's coefficient matrix, whereas the point Homotopy Perturbation Method and other classical numerical iterative methods typically require non-zero diagonal entries in the coefficient matrix. A set of theorems relevant to this study are presented and demonstrated. We solve an engineering application, i.e. a current flow circuit problem that is represented in terms of a triangular intuitionistic fuzzy environment, using the suggested method. The unknown current is then obtained as a triangle intuitionistic fuzzy number. The proposed semi-analytic method is used to solve some numerical test problems in order to validate their performance and efficiency in comparison to other existing techniques. The numerical results of the example are displayed on graphs with different degrees of uncertainty. The efficiency and accuracy of the proposed method are further demonstrated by comparisons to block Jacobi, Adomain Decomposition method, Successive Over-Relaxation method and the classical Gauss-Seidel numerical method.

VIKOR-based Method for Assessing the Degree of Development of Film and Television City Tourism Resources in An Intuitively Fuzzy Environment

This paper proposes a multi-attribute decision-making method based on VIKOR in an intuitionistic fuzzy environment to evaluate the extent conducted tourism resources development in film and television cities. Firstly, the decision matrix is normalized; secondly, the VIKOR method is introduced into the performance assessment to calculate the individual regret value and group utility value, and the evaluation objects are ranked in a meritocratic way; finally, the effectiveness and scientificity of the method are proved by example analysis.

Fuzzy clustering based on distance metric under intuitionistic fuzzy environment

Fuzzy clustering based on distance metric under intuitionistic fuzzy environment

Version [1.1]- [Handling decision-making in intuitionistic fuzzy environment: PyIFDM package

The paper introduces the update of the Python Intuitionistic Fuzzy Decision Making (PyIFDM) package, emphasizing its focus on Multi-Criteria Decision Analysis (MCDA) with uncertain data modeled as Intuitionistic Fuzzy Sets (IFS). The update enhances PyIFDM’s capabilities, introducing five new IF-MCDA methods and basic mathematical operations on IFS. The update includes the implementation of Max normalization, a Hausdorff measure-based Euclidean distance, and a module for IFS-similarity measures. The release contributes to a significant library upgrade, providing advanced tools for modeling fuzzy data in and outside the MCDA space. PyIFDM now supports a greater variety of popular IF-MCDA methods, offering flexibility and applicability in decision-making scenarios. The added visualization module facilitates the graphical representation of IFS, aiding the interpretation of complex decision models involving intuitionistic fuzzy data. The enhanced version of the PyIFDM library expands its applicability in research methodologies, making it a more efficient tool for conducting multi-criteria decision analysis in an intuitionistic fuzzy environment.