Intuitionistic Fuzzy Set Theory Research Articles

An Intuitionistic Fuzzy C-Means and Local Information-Based DCT Filtering for Fast Brain MRI Segmentation.

Structural and photometric anomalies in the brain magnetic resonance images (MRIs) affect the segmentation performance. Moreover, a sudden change in intensity between two boundaries of the brain tissues makes it prone to data uncertainty, resulting in the misclassification of the pixels lying near the cluster boundaries. The discrete cosine transform (DCT) domain-based filtering is an effective way to deal with structural and photometric anomalies, while the intuitionistic fuzzy C-means (IFCM) clustering can handle the uncertainty using the intuitionistic fuzzy set (IFS) theory. In this background, we propose two novel approaches, namely, the DCT-based intuitionistic fuzzy C-means (DCT-IFCM) and the DCT-based local information IFCM (DCT-LIFCM), which effectively deal with the Rician and Gaussian noises and also handle the data uncertainty problem to provide high segmentation accuracy. The DCT-IFCM approach performs the histogram-based segmentation, while the DCT-LIFCM uses the pixel-wise computation to include the spatial information. Although the DCT-LIFCM delivers slightly better performance than the DCT-IFCM, the latter is very fast in providing equally high segmentation accuracy. An exhaustive performance analysis is provided to demonstrate the superior performance of the proposed algorithms compared with the state-of-the-art algorithms, including those based on the DCT-based filtering approach and the IFS theory.

Interval-valued intuitionistic fuzzy AROMAN method and its application in sustainable wastewater treatment technology selection

In the theory of interval-valued intuitionistic fuzzy set (IVIFS), the rating/grade of an element is the subset of the closed interval [0, 1], therefore the IVIFS doctrine is more useful for the decision expert to present their judgments in terms of intervals rather than the crisp values. The present work develops an integrated decision-making methodology for evaluating sustainable wastewater treatment technologies within the context of IVIFS. The proposed decision-making framework is divided into three stages. First, some Yager weighted aggregation operators and their axioms are developed to combine the interval-valued intuitionistic fuzzy information. These operators can offer us a flexible way to solve the realistic multi-criteria decision-making problems under IVIFS context. Second, an extension of Symmetry Point of Criterion model is introduced to determine the criteria weights under IVIFS environment. Third, an integrated alternative ranking order model accounting for two-step normalization (AROMAN) approach is proposed from IVIF information perspective. Next, the practicability and efficacy of the developed model is proven by implementing it on a case study of sustainable wastewater treatment technologies evaluation problem with multiple criteria and decision experts. Finally, comparative analysis is discussed to illustrate the consistency and robustness of the obtained outcomes.

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.

Higher-order circular intuitionistic fuzzy time series forecasting methodology: Application of stock change index

Abstract This article presents a higher-order circular intuitionistic fuzzy time series forecasting method for predicting the stock change index, which is shown to be an improvement over traditional time series forecasting methods. The method is based on the principles of circular intuitionistic fuzzy set theory. It uses both positive and negative membership values and a circular radius to handle uncertainty and imprecision in the data. The circularity of the time series is also taken into consideration, leading to more accurate and robust forecasts. The higher-order forecasting capability of this method provides more comprehensive predictions compared to previous methods. One of the key challenges we face when using the amount featured as a case study in our article to project the future value of ratings is the influence of the stock market index. Through rigorous experiments and comparison with traditional time series forecasting methods, the results of the study demonstrate that the proposed higher-order circular intuitionistic fuzzy time series forecasting method is a superior approach for predicting the stock change index.

Neutrosophic Fuzzy Numbers and its Impact on Transportation Problem

The neutrosophic fuzzy set offers us a broad outline for combining several existing sets into one. Indeterminate and unpredictable data cannot be dealt with by either the fuzzy set theory or intuitionistic fuzzy set theory. The computing techniques of neutrosophic sets are valid for software development for many uses. The transportation problem profoundly depends on the neutrosophic fuzzy set. Most of the time, the data provided is indeterminate and inconsistent. At this point of time, we cannot make use of the fuzzy set and intutionistic fuzzy set to get deal with this indeterminacy. Here, we have solved numerically to reflect the impact of neutrosophic pentagonal numbers and neutrosophic octagonal numbers. The efficiency of the method is applied is also compared with the other methods.

Innovative approaches to solar cell selection under complex intuitionistic fuzzy dynamic settings

<abstract> <p>The need to meet current energy demands while protecting the interests of future generations has driven people to adopt regulatory frameworks that promote the careful use of limited resources. Among these resources, the sun is an everlasting source of energy. Solar energy stands out as a prime example of a renewable and environmentally friendly energy source. An imperative requirement exists for precise and dependable decision-making methods for the selection of the most efficacious solar cell. We aimed to address this particular issue. The theory of complex intuitionistic fuzzy sets (CIFS) adeptly tackles ambiguity, encompassing complex problem formulations characterized by both intuitionistic uncertainty and periodicity. We introduced two aggregation operators: The complex intuitionistic fuzzy dynamic ordered weighted averaging (CIFDOWA) operator and the complex intuitionistic fuzzy dynamic ordered weighted geometric (CIFDOWG) operator. Noteworthy features of these operators were stated, and significant special cases were meticulously outlined. An updated score function was devised to address the deficiencies, identified in the current score function within the context of CIF knowledge. In addition, we devised a methodical strategy for managing multiple attribute decision-making (MADM) problems that involve CIF data by implementing the proposed operators. To demonstrate the efficacy of the formulated algorithm, we presented a numerical example involving the selection of solar cells together with a comparative analysis with several well-established methodologies.</p> </abstract>

On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces

The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intuitionistic fuzzy neutrosophic soft topologies is introduced and some equivalent conditions concerning, this topic are established here.

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.

New similarity measures and TOPSIS method for multi stage decision analysis with cubic intuitionistic fuzzy information

This research work proposes a novel approach for multi stage decision analysis (MSDA) using innovative concepts of cubic intuitionistic fuzzy set (CIFS) theory. The paper introduces CIF-technique for order preference by similarity to ideal solution (TOPSIS) as a robust method for MSDA problems, particularly for the diagnosis of epilepsy disorders. To achieve this goal, new similarity measures (SMs) are developed for CIFS, including the Cosine angle between two vectors, a new distance measure, and the Cosine function, presented as three different types of Cosine similarity measures. The proposed CIF-TOPSIS approach is found to be suitable for precise value performance ratings and is expected to be a viable approach for case studies in the diagnosis of epilepsy disorders. The efficiency and reliability of the proposed MSDA methods is efficiently carried through numerical examples and comparative analysis.

Selection of Optimal Approach for Cardiovascular Disease Diagnosis under Complex Intuitionistic Fuzzy Dynamic Environment

Cardiovascular disease (CVD) is a leading global health concern. There is a critical need for accurate and reliable decision-making tools to select the optimal approach for diagnosing cardiovascular disease (CVD). In this study, we have addressed this pressing issue. Complex intuitionistic fuzzy set (CIFS) theory is adept at encapsulating vagueness due to its capability to encompass comprehensive problem specifications characterized by both intuitionistic uncertainty and periodicity. Within the scope of this article, we present two novel aggregation operators: the complex intuitionistic fuzzy dynamic weighted averaging (CIFDWA) operator and the complex intuitionistic fuzzy dynamic weighted geometric (CIFDWG) operator. Some intriguing characteristics of these operators are elucidated, and important special cases are also defined in detail. We devise an enhanced score function to rectify the deficiencies observed in the existing score function under complex intuitionistic fuzzy knowledge. Furthermore, these operators are employed in the development of a systematic approach for the handling of multiple attribute decision-making (MADM) scenarios involving complex intuitionistic fuzzy data. Moreover, we undertake the resolution of an MADM problem, wherein we ascertain the optimal approach for diagnosing cardiovascular disease (CVD) through the utilization of the proposed operators, thereby substantiating their utility in decision-making processes. Finally, we conduct a comprehensive comparative analysis, pitting the presented operators against an array of existing counterparts, in order to demonstrate the reliability and stability inherent in the derived methodologies.

A hybrid incomplete decision system using fuzzy sets and rough set theory with varying object sets and values

Researchers in science and engineering face various obstacles due to a lack of specific and full data. Many different approaches have been devised to deal with these restrictive requirements, but two notable schools of thought are the fuzzy set (FS) theory and the rough set (RS) theory, both of which have spawned many extensions and hybridizations. Although RS theory originated from an indiscernibility relation (also known as an equivalence relation in mathematics), emphasis rapidly shifted to similarity or coverings (and their fuzzy analogues). Many other hybrid schemes were suggested with this goal in mind. The gap between those concepts shrank because to this thorough analysis. Fuzzy set theory is a legitimate way to convey the ambiguity of assessment data, yet it is still inadequate for dealing with certain intricate problems in the actual world. In reality, decision makers will undoubtedly provide different kinds of ambiguous and nuanced assessments. Atanassov’s intuitionistic fuzzy set theory broadened the application of fuzzy set theory by imbuing it with an element of uncertainty. Sometimes in real life, you have to deal with a neutral element on top of the indeterminate one. Picture fuzzy sets were developed specifically for this purpose. Membership roles may be positive, neutral, or negative/refusal. In contrast, hesitant fuzzy sets and its hybrid models are useful when decision makers are on the fence about which option to choose. As a binary relation on a set, a graph is symmetric. It is a staple in mathematical modelling and is used in almost every scientific and technological discipline. Graph theory has been essential in the mathematical modelling and subsequent resolution of several real-world situations. Information about connections between things is often best represented using graph theory, which uses vertices to stand in for the items and edges for the relationships between them. The suggested dynamic algorithm is better to the static approach in dealing with the multidimensional dynamic changes of the hybrid incomplete decision system, according to a series of experiments carried out on nine UCI datasets.

Schweizer–Sklar Power Aggregation Operators Based on Complex Interval-Valued Intuitionistic Fuzzy Information for Multi-attribute Decision-Making

This manuscript proposes the concept of Schweizer–Sklar operational laws under the consideration of the complex interval-valued intuitionistic fuzzy (CIVIF) set theory, where the Schweizer–Sklar norms are the essential and valuable modification of many norms, such as algebraic, Hamacher, and Lukasiewicz norms. Moreover, keeping the dominancy of the presented laws, we derive the concept of CIVIF Schweizer–Sklar power averaging (CIVIFSSPA), CIVIF Schweizer–Sklar power ordered averaging (CIVIFSSPOA), CIVIF Schweizer–Sklar power geometric (CIVIFSSPG), and CIVIF Schweizer–Sklar power ordered geometric (CIVIFSSPOG) operators, which are the combination of the three different structures for evaluating three different problems. Further, some reliable and feasible properties and results for derived work are also invented. Additionally, we also illustrate an application, called multi-attribute decision-making (MADM) scenario for evaluating some real-world problems with the help of discovered operators for showing the reliability and stability of the evaluated operators. Finally, we compare our mentioned operators with various prevailing operators for enhancing the worth and stability of the evaluated approaches.

TOPSIS based Renewable-Energy-Source-Selection using Moderator Intuitionistic Fuzzy Set

Many criteria must be taken into account while selecting the best renewable energy source (RES), which necessitates a sophisticated multi-criteria decision-making (MCDM) procedure. Conflicting norms, as well as insufficient and inaccurate information, make this endeavour challenging. The theory of moderator intuitionistic fuzzy set (MIFS), a generalization of intuitionistic fuzzy sets (IFSs) has been developed to handle these uncertainties. The MIFS also helps to get a higher degree of precision in the uncertain behaviours due to the moderator parameter. In this paper, first some distance measures are presented for MIFSs, and then, on the basis of the proposed distances, we suggest a TOPSIS technique for choosing the best RES inside MIFS architecture. The efficacy of the proposed MIFS-based TOPSIS technique is put to the test by comparing different wind generating systems in a case study. The findings of the study are then compared in order to demonstrate that the suggested method is superior to the existing ones.

Picture fuzzy VIKOR-TOPSIS approach based on knowledge and accuracy measures for suitable adsorbent decision making

In contrast to a fuzzy and intuitionistic fuzzy (IF) set, a picture fuzzy (PF) set may be taken as an effective tool to tackle decision-making problems. Fuzzy and intuitionistic fuzzy set theory can be extended to PF-set theory. As per our knowledge, there is no PF-knowledge measure has been proposed by any researcher so far. A novel picture fuzzy knowledge measure is proposed in the present manuscript. Its mathematical properties are investigated along with its validation. Its performance is evaluated using four distinct examples. Besides this, the newly presented PF-knowledge measure is used to derive a new PF-Accuracy measure. The derived PF-accuracy measure is checked for its validation and its properties are explained. The applications of the derived PF-accuracy measure are given in pattern recognition. Furthermore, a VIKOR-TOPSIS approach based on the proposed PF-knowledge and accuracy measure is designed. Finally, the suggested approach is utilized to identify an appropriate adsorbent for extracting hexavalent chromium from wastewater.

A novel approach for brain MRI segmentation and image restoration under intensity inhomogeneity and noisy conditions

Brain magnetic resonance (MR) images are vulnerable to many photometric artifacts such as noise, and intensity inhomogeneity (IH). Furthermore, they contain brain-related intrinsic structural complexities such as edges, corners, and other fine structures. These artifacts and structural complexities pose several challenges for the segmentation process of brain MR images which is needed for the proper diagnosis of brain related diseases. We develop a segmentation framework which deals with noise, IH, uncertainty, and other structural complexities present in the brain MR images in unison. The noise is dealt with by incorporating the local spatial and gray level information in the form of a local parameter-free fuzzy factor. This factor also preserves the fine structural details that are present in abundance in the brain MR images. A recently introduced approach for dealing with the IH is incorporated, and integrated with the local information. The problem pertaining to uncertainty in assigning membership to the pixels lying near the boundaries of different tissues is solved by representing the various components of the information such as intensity, cluster centers, and IH, using the intuitionistic fuzzy set theory. Further, a procedure is developed to obtain artifact-free image which could be useful for its comparison with the input image for the better analysis of the MR images by the experts. Thus, an integrated approach is presented to segment and restore the MR images. Experimental results demonstrate the superiority of the proposed approach over the state-of-the-art approaches about segmentation accuracy and robustness to the various imaging artifacts.

Analysis of distance measures in intuitionistic fuzzy set theory: A line integral perspective

Analysis of distance measures in intuitionistic fuzzy set theory: A line integral perspective

A Novel Dual-Center-Based Intuitionistic Fuzzy Twin Bounded Large Margin Distribution Machines

Intuitionistic fuzzy (IF) set theory combined with twin support vector machines (TSVM) has shown highly advantageous performance in robust and fast classification. However, the existing methods have some inherent flaws: i) The inaccurate confidence caused by the single-center based IF strategy degrades the classification performance of the model. ii) The non-membership degree is time-consuming and the threshold is difficult to determine, as it depends on sample's local neighborhood set. iii) Recent theoretical studies have demonstrated that optimizing the margin distribution achieve better generalization performance than maximizing the minimum margin in SVM-based models (SVMs). In view of the aforementioned shortcomings, we propose a novel dual-center based IF (DC-IF) function, and introduce the margin distribution into IFTSVM, forming a DC-IF twin bounded large margin distribution machines (DC-IFTBLDM). Initially, the DC-IF strategy references the contribution of one sample to both categories, which is time efficient and more accurately reflects the credibility of the samples. Moreover, the margin mean and variance are used to optimize the margin distribution, and a regularization term is utilized to minimize structural risk. Therefore, DC-IFTBLDM has a good performance in noise immunity and classification capability. Comparative experiments based on synthetic datasets, UCI benchmark datasets, and datasets with different noise ratios verify the effectiveness of the proposed model. The parameter sensitivity analysis further proves the high accuracy and stability of IFTBLDM.

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.

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.

Choquet Integral-Based Aczel–Alsina Aggregation Operators for Interval-Valued Intuitionistic Fuzzy Information and Their Application to Human Activity Recognition

Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, we concentrate on studying the problem of HAR; for this, we use the proposed theory of Aczel and Alsina, such as Aczel–Alsina (AA) norms, and the derived theory of Choquet, such as the Choquet integral in the presence of Atanassov interval-valued intuitionistic fuzzy (AIVIF) set theory for evaluating the novel concept of AIVIF Choquet integral AA averaging (AIVIFC-IAAA), AIVIF Choquet integral AA ordered averaging (AIVIFC-IAAOA), AIVIF Choquet integral AA hybrid averaging (AIVIFC-IAAHA), AIVIF Choquet integral AA geometric (AIVIFC-IAAG), AIVIF Choquet integral AA ordered geometric (AIVIFC-IAAOG), and AIVIF Choquet integral AA hybrid geometric (AIVIFC-IAAHG) operators. Many essential characteristics of the presented techniques are shown, and we also identify their properties with some results. Additionally, we take advantage of the above techniques to produce a technique to evaluate the HAR multiattribute decision-making complications. We derive a functional model for HAR problems to justify the evaluated approaches and to demonstrate their supremacy and practicality. Finally, we conduct a comparison between the proposed and prevailing techniques for the legitimacy of the invented methodologies.