Intuitionistic Fuzzy Approach Research Articles

A new Fermatean fuzzy multi‐objective indefinite quadratic transportation problem with an application to sustainable transportation

AbstractIn this work, a Fermatean fuzzy (FF) multi‐objective indefinite quadratic transportation problem (TP) is introduced. Due to some unavoidable reasons, real‐life transportation parameters such as supply, demand and costs are indeterminate in nature and cannot be expressed in crisp terms. We represent these parameters using FF numbers, an extension of fuzzy numbers, which are capable of representing indeterminacy efficiently. A multi‐objective indefinite quadratic TP where each objective is a product of two linear factors (cost functions) is considered. Defuzzification of FF numbers is accomplished by the introduction of ‐cut for the first time. The obtained crisp TP is solved using the intuitionistic fuzzy programming approach and FF programming approach to arrive at a compromise solution. To substantiate the work, solution methodology based on defuzzification using the ranking function is also deliberated. The applicability of the model is demonstrated through a sustainable TP, which simultaneously minimizes transportation cost with depreciation cost and packaging cost with wastage cost. The resulting value of the objective functions and the aspiration levels are compared to depict the efficacy of the proposed method over the ranking function method. The concluding section summarizes the work, and future avenues along with some limitations of the work are also specified.

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.

Identifying and prioritizing the barriers to green innovation in SMEs and the strategies to counteract the barriers: An interval-valued intuitionistic fuzzy approach

Increasing environmental burdens and the importance of innovation in the presently competitive environment have encouraged small- and mid-size enterprises (SMEs) to adopt and implement green innovation practices. This process, however, is faced with many limitations and obstacles. The purpose of this study is to propose a framework to identify barriers to green innovation in SMEs and to provide solutions/strategies to overcome such barriers. Using the systematic literature review (SLR) method and the opinions of 20 experts, the study primarily identified 29 sub-categories of barriers falling under seven main categories including “management”, “organization”, “human resources”, “financial resources”, “external cooperation”, “customers, markets or competitors”, and “the external environment.” Similarly, 22 strategies were discovered that could help to counteract the barriers identified. To determine the weights of the barriers, the Intuitionistic Fuzzy Multiplicative Best-Worst Method (IFMBWM) was used. The strategies, too, were ranked through the Interval-Valued Intuitionistic Fuzzy MULTIMOORA (IVIF-MULTIMOORA) method. Then, a sensitivity analysis and a comparative analysis were applied to confirm the robustness of the proposed method and ensure the consistency of the obtained ranking of alternatives. As the results revealed, the optimal and effective solutions that could be used by policy-makers/managers to overcome the barriers to green innovation were “simplifying authorization and licensing procedures”, “effective environmental laws and regulations”, “shared responsibility throughout the supply chain”, “a supportive organizational culture”, and “merit-based selection of managers.”

Compromise optimum allocation in neutrosophic multi-character survey under stratified random sampling using neutrosophic fuzzy programming

Survey sampling has wide range of applications in social and scientific investigation to draw inference about the unknown parameter of interest. In complex surveys, the sample information about the study variable cannot be expressed by a precise number under uncertain environment due fuzziness and indeterminacy. Therefore, this information is expressed by neutrosophic numbers rather than the classical numbers. The neutrosophic statistics, which is generalization of classical statistics, deals with the neutrosophic data that has some degree of indeterminacy and fuzziness. In this study, we investigate the compromise optimum allocation problem for estimating the population means of the neutrosophic study variables in a multi-character stratified random sampling under uncertain per unit measurement cost. We proposed the intuitionistic fuzzy cost function, modeling the fuzzy uncertainty in stratum per unit measurement cost. The compromise optimum allocation problem is formulated as a multi-objective intuitionistic fuzzy optimization problem. The solution methodology is suggested using neutrosophic fuzzy programming and intuitionistic fuzzy programming approaches. A numerical study includes the means estimation of atmospheric variables is presented to explore the real-life application, explain the mathematical formulation, and efficiency comparison with some existing methods. The results show that the suggested methods produce more precise estimates with less utilization of survey resources as compared to some existing methods. The Python is used for statistical analysis, graphical designing and numerical optimization problems are solved using GAMS.

Modelling the critical success factors of software development freelancing using an intuitionistic fuzzy DEMATEL approach

Modelling the critical success factors of software development freelancing using an intuitionistic fuzzy DEMATEL approach

An intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model

Intuitionistic fuzzy sets cannot consider the degree of indeterminacy (i.e., the degree of hesitation). This study presents an intuitionistic fuzzy differential equation approach for the lake water and sediment phosphorus model. We examine the proposed model by assuming generalized trapezoidal intuitionistic fuzzy numbers for the initial condition. Feasible equilibrium points, along with their stability criteria, are evaluated. We describe the characteristics of intuitionistic fuzzy solutions and clarify the difference between strong and weak intuitionistic fuzzy solutions. Numerical simulations are performed in MATLAB to validate the model results.

Multi-Source T-S Target Recognition via an Intuitionistic Fuzzy Method

To realize aerial target recognition in a complex environment, we propose a multi-source Takagi–Sugeno (T-S) intuitionistic fuzzy rules method (MTS-IFRM). In the proposed method, to improve the robustness of the training process of the model, the features of the aerial targets are classified as the input results of the corresponding T-S target recognition model. The intuitionistic fuzzy approach and ridge regression method are used in the consequent identification, which constructs a regression model. To train the premise parameter and reduce the influence of data noise, novel intuitionistic fuzzy C-regression clustering based on dynamic optimization is proposed. Moreover, a modified adaptive weight algorithm is presented to obtain the final outputs, which improves the classification accuracy of the corresponding model. Finally, the experimental results show that the proposed method can effectively recognize the typical aerial targets in error-free and error-prone environments, and that its performance is better than other methods proposed for aerial target recognition.

A trapezoidal intuitionistic fuzzy optimization approach for crashing a budget constrained project

While the classical fuzzy applications have gained popularity in many different areas, intuitionistic fuzzy set theory emerged as an advancement to better identify various complex circumstances such as the hesitancy of a decision maker under uncertainty. In this study, we propose a project scheduling model in which the allocated budget for crashing is treated as an intuitionistic fuzzy number. With the intuitionistic fuzzy approach, the uncertainty inherent in the project completion time as well as the hesitancy of a decision maker in using the budget amount are integrated into decision making process. The proposed model numerically provides more information than that of the classical ones and better represents the complexity of decision making related to time and cost in project management. Decision makers are provided not only with an optimal schedule but also with a determined degree of satisfaction/dissatisfaction related to the budget and project completion time. Our experimental results show that the decision makers can substantially save money with some delays in the project completion time. Thus, a broader perspective encompassing the satisfaction/dissatisfaction level of a decision maker is presented to schedule a project under uncertain conditions.

Discovering effect of intuitionistic fuzzy transformation in multi-layer perceptron for heart disease prediction: a study

Cardiovascular disease (CVD) is the one of the most fatal diseases in the world we have seen in last two decades. For heart disease detection, imprecision in clinical parameters may occur due to error in taking readings or in measuring devices or environmental conditions etc. Hence, introducing fuzzy set theory in feature engineering may give better results as it deals with uncertainty. But in fuzzy set theory, only one uncertainty is considered, which is membership degree or degree of belongingness. Intuitionistic fuzzy set (IFS) considers two uncertainties - membership degree and non-membership degree and so IFS may provide efficient results. To reduce the risk of heart disease, an advanced deep learning algorithm will play a significant role in heart disease prediction that will help physicians to diagnose early. In this paper, we have established a transformation of patient features using i) intuitionistic fuzzy parameters, where Sugeno-type fuzzy complement is used and ii) fuzzy parameters, where gamma membership function is used. These transformed attributes are applied on Deep Learning prediction algorithm as Multi-layer Perceptron (MLP). The novelty of the paper lies from feature transformation to deep learning. It is observed that intuitionistic fuzzy transformation approach, keeping model parameters intact, significantly outperforms non-fuzzy method and gammy fuzzy Transformation, which is reflected in evaluation mechanisms.

Statistical Fuzzy Reliability Analysis: An Explanation with Generalized Intuitionistic Fuzzy Lomax Distribution

To illustrate data uncertainty, intuitionistic fuzzy sets simply use membership and non-membership degrees. However, in some cases, a more complex strategy is required to deal with imprecise data. One of these techniques is generalized intuitionistic fuzzy sets (GIFSs), which provide a comprehensive framework by adding extra factors that provide a more realistic explanation for uncertainty. GIFSs contain generalized membership, non-membership, and hesitation degrees for establishing symmetry around a reference point. In this paper, we applied a generalized intuitionistic fuzzy set approach to investigate ambiguity in the parameter of the Lomax life distribution, seeking a more symmetric assessment of the reliability measurements. Several reliability measurements and associated cut sets for a novel L-R type fuzzy sets are derived after establishing the scale parameter as a generalized intuitionistic fuzzy number. Additionally, the study includes a range of reliability measurements, such as odds, hazards, reliability functions, etc., that are designed for the Lomax distribution within the framework of generalized intuitionistic fuzzy sets. These reliability measurements are an essential tool for evaluating the reliability characteristics of various types of complex systems. For the purpose of interpretation and application, the results are visually displayed and compared across different cut set values using a numerical example.

An Intuitionistic Fuzzy Decision Support for Agile Project Selection Problem

In the early 1990s, organizations started to use information technology and software engineering, which encouraged the companies for employing project management methodologies to survive and then advance in competitive technologic environment. Use of project management methodologies provides efficient planning, budgeting and scheduling processes and high management quality for companies. A lot of different methodologies were developed and used to reach better ways of defining the project requirements, analyzing the problem, and implementing it in a systematic manner. In 2001, agile project management methodology came forward in response to cope with waterfall project methodology’s limitations that arise from unpredictability of technology evolution, customer requirements, and unstable business environments. In this study, intuitionistic fuzzy COPRAS method, which aims to obtain a solution relative to the ideal solution, is used to rank agile project alternatives and identify the best performing one among them. Intuitionistic fuzzy sets are used to deal with loss of information and hesitation in data that may occur in operations with fuzzy numbers. The application of the proposed intuitionistic fuzzy decision-making approach is illustrated by conducting a case study.

A stable matching method for technology trading with intuitionistic fuzzy multi-attribute information

Technology trading matching facilitates quicker solution-finding for technology demanders and expedites the transformation of scientific and technological achievements. Yet, unstable matchings often lead traders to renounce existing contracts, sidestep trading intermediaries, and resort to private transactions. This results in inefficient trading mechanisms and market disarray. To ensure a stable and mutually satisfactory match for both suppliers and demanders, we propose a stable two-sided matching decision-making method that incorporates intuitionistic fuzzy multi-attribute information. Initially, we introduce an intuitionistic fuzzy TOPSIS approach to compute the comprehensive satisfaction of both suppliers and demanders by aggregating intuitionistic fuzzy information across various attributes. Subsequently, we design a multi-objective optimization model that weighs both stability and satisfaction to determine the ideal technology trading pairs. We conclude with a real-world example that demonstrates the proposed method’s application, and its effectiveness is corroborated through sensitivity and comparative analyses.

A new intuitionistic fuzzy correlation coefficient approach with applications in multi-criteria decision-making

The Intuitionistic Fuzzy Set (IFS) is a powerful extension of Fuzzy Set (FS) used to handle vagueness and uncertainty. The correlation coefficient is an established tool for finding the strength of relationships between two IFSs. This study proposes a new approach for finding a correlation coefficient to compare with the existing approach and show its superiority over the existing approach. In many counter-intuitive cases, existing approaches fail to handle the problem appropriately by giving indeterminate form, incorrect and inaccurate results. We demonstrate the reliability and efficiency of the proposed approach in handling these concerns. We also present the application of the proposed approach in pattern detection, medical illness diagnosis, clustering, and Multi-Criteria Decision-Making (MCDM) to further exhibit its practicability and effectiveness.

Intuitionistic fuzzy multi-objective transportation model during pandemic COVID-19

The given paper discusses an intuitionistic fuzzy discrete time-space optimization model while taking into account the COVID-19 pandemic. The novelty of this study is characterized by the proposal of a distinctive multi-objective intuitionistic fuzzy transportation model in which the demand function varies with time as the number of infected, exposed and susceptible persons increase. Forecasting of demand is executed using the epidemic diffusion model. Also, a new approach to defuzzify triangular intuitionistic fuzzy numbers, depending upon the concept of the golden ratio, is presented. Intuitionistic fuzzy programming approach is used to obtain the pareto-optimal solution. A real-life numerical illustration is explained using the proposed methodology to examine its practical suitability. Outperforming the existing traditional method of solving a transportation problem verifies its proficiency.

Modelling the interrelationships of critical success factors of humanitarian supply chain: an intuitionistic fuzzy DEMATEL approach

PurposeAmid increasing frequency of disaster across the globe, humanitarian supply chain (HSC) has gained significant attention in recent times. This work aims to contribute towards improving the decision-making capabilities of relief organisations by offering more comprehensive understanding of the critical success factors (CSFs) concerning HSC. Hence, the current work attempts to classify CSFs as cause-and-effect factors and explore their relative importance in the stated significance.Design/methodology/approachCurrent work takes an explorative and deductive approach. It uses literature and experts' input to identify the CSFs for HSC and to develop a structural model for assessing these factors. Intuitionistic fuzzy DEMATEL (IF-D) is employed for modelling and analysing the cause-effect linkages among the CSFs. IF-D method is chosen as it is robust to vagueness of data and small samples.FindingsThe findings indicate that “motivated and committed employees” is the most influencing causal factor followed by “IT infrastructure”, and among effect factors, “physical network” carries the most significance followed by “anticipation capabilities.”Practical implicationsRelief organisations and stakeholders at various levels may put more emphasis on cause group factors with more influence on most critical effect factors to build more efficient and effective HSC to execute more impactful relief programs.Originality/valueCurrent work explores the cause–effect relationships among the CSFs concerning HSC by implementing IF-D, which can be considered as the original contribution.

A novel interactive intuitionistic fuzzy approach to find satisfactory Pareto-optimal solutions for general bilevel multi-followers programming

This paper focuses on the approach for solving the satisfactory Pareto-optimal solutions of the general form of bilevel multi-followers programming(BMFP), including the BMFP with partial shared variables among followers, the so-called referential-uncooperative BMFP, the uncooperative BMFP, and the cooperative BMFP. Without losing generality, the BMFP with partial shared variables among followers will be taken as a representative to explain the universal applicability of the proposed generic interactive intuitionistic fuzzy method. Based on the theory of intuitionistic fuzzy set, the new definition of satisfactory Pareto-optimal solutions is introduced by means of membership function, non-membership function, and score function. In order to obtain satisfactory Pareto-optimal solutions of BMFP with partial shared variables among followers, a prior minimization optimization problem and a series of corresponding auxiliary maximization optimization problems are formulated, and we strictly prove that the optimal solution of the prior minimization optimization problem is not necessarily the satisfactory Pareto-optimal solutions, but at least one satisfactory Pareto optimal solution can be derived by further solving these auxiliary maximization optimization problems. Then, a detailed interactive intuitionistic fuzzy algorithm framework that consider both the balance of satisfactory degree between the leader and the followers and the balance of satisfactory degree among all followers is proposed. In the part of numerical experiments, four examples(including a linear BMFP problem with partial shared variables among followers, a BMFP model of a road network problem, an uncooperative BMFP problem, and a nonlinear BMFP problem with partial shared variables among followers) are illustrated to demonstrate the applicability, effectiveness and superior performance of the proposed technique.

An Intuitionistic Fuzzy Decision Aid for Neuromarketing Technology Selection Problem

Neuromarketing, which uses neuroimaging technologies for marketing initiatives, is represented as the application of neuroscientific methods for analysing and understanding consumer behaviour with regard to marketing objectives. Medical diagnostic devices for brain imaging are used by marketers as neuromarketing technologies. In this study, the intuitionistic fuzzy COPRAS method, which aims to obtain a solution relative to the ideal solution, is used to rank neuromarketing technology alternatives and identify the best-performing one among them. Intuitionistic fuzzy sets are used to deal with the loss of information and hesitation in data that may occur in operations with fuzzy numbers. The application of the proposed intuitionistic fuzzy decision-making approach is illustrated by conducting a case study

Renewable energy generation forecasting in Turkey via intuitionistic fuzzy time series approach

Recently, renewable energy generation (REG) forecasting has become a challenging task for effective energy management. To date, a number of time-series models utilizing physical models, statistical techniques, and artificial intelligence algorithms have been proposed to deal with this problem. Fuzzy time series (FTS) models stand out among these methods since they do not need extensive historical data or some statistical assumptions like the normal distribution. Because intuitionistic fuzzy sets incorporate non-membership values in addition to membership values, they provide more information than conventional fuzzy sets do. In this regard, this paper recommends a hybrid methodology that combines the intuitionistic FTS method with the intuitionistic fuzzy c-means method for REG forecasting of Turkey between the years 2000–2020. According to the empirical results, it can be concluded that the presented integrated model showed good performance in terms of accuracy. The suggested framework is a useful tool not only for REG forecasting but also for other time series forecasting problems.

Modified total Bregman divergence driven picture fuzzy clustering with local information for brain MRI image segmentation

This research work discusses a noise-robust picture fuzzy clustering method with an application to the MRI image segmentation problem. The MRI images suffer from the problem of noise and non-linear structures. Although there are many variants of fuzzy set theory and intuitionistic fuzzy set theory-based clustering approaches to handle the problem of noise and non-linearity present in the image during the segmentation process, still they lack in achieving accurate segmentation. To overcome this problem, we have suggested using the picture fuzzy set theoretic approach which enhances the representational capability of the data and helps in handling the non-linear structures present in the image, and in our proposed work, the picture fuzzy Euclidean distance is replaced with modified picture fuzzy total Bregman divergence using the spatial neighborhood information around the sample. Squared Euclidean distance is itself a special case of Bregman Divergence, hence Bregman divergence helps to explore the details in a better way thus resulting in noise suppression. Furthermore, the proposed algorithm proves to be robust in preserving the image details using picture fuzzy set theory and is free from any parameter selection due to the incorporation of a local information factor. The algorithm was performed on a synthetic image corrupted with “Gaussian”, “salt and pepper”, “mixture of Gaussian and salt and pepper noise” of different intensities, “Brainweb” datasets corrupted with noise, six real “IBSR” datasets along with seven “MRbrainS18” datasets. Performance measures used were partition coefficient, partition entropy, dice score (DS), average segmentation accuracy (ASA), and XB index, and the proposed method was robust when compared to a series of algorithms stated in the literature.

Intuitionistic fuzzy approach to reliability assessment of multi-state systems

One of the major problems that one encounters within an engineering system is the assessment of its quality, or in other words, reliability. However, conventional reliability tends to ignore the fuzziness in the system, i.e., the lack of precision, vagueness, inaccuracy, or inadequacy in the information obtained. As a result, the integration of fuzzy sets into reliability theory has proven to be incredibly vital. Similarly, the universal generating function (UGF) technique has also been an asset in reliability assessment ever since its inception due to its simplicity. Here, a novel technique involving the intuitionistic fuzzy sets (IFS), specifically using the triangular intuitionistic fuzzy numbers (TIFN) and the UGF method, has been created for the reliability assessment of a fuzzy multi-state system (FMSS). This method is then applied to a system of wireless communication and its intuitionistic fuzzy reliability and availability are evaluated where each performance state and its probability are characterized by a TIFN. The obtained results are also represented graphically for better insights. This work is helpful in getting a clear picture of FMSS and thus, making them more reliable.