Type-2 Sets Research Articles

MultiFuzzTOPS: A Fuzzy Multi-Criteria Decision-Making Model Using Type-2 Soft Sets and TOPSIS

Effective and optimal decision-making can enhance system performance, potentially leading to a positive reputation and financial gains. Multi-criteria decision-making (MCDM) is an important research topic widely applied to practical decision-making problems. Using the basic idea of symmetry to balance the arrangement where elements or features have an equality or similarity in distribution, MCDM provides robust decisions in such multi-dimensional complex issues. This study proposes MultiFuzzTOPS, a decision-making model to deal with complexity of multi-criteria decision-making. The proposed MultiFuzzTOPS leverages the fuzzy logic and soft sets such as type-2 soft sets (T2SS) and technique for order preference by similarity to ideal solution (TOPSIS) for decision-making. We validate the proposed model by implementing it to solve the pesticide selection problem in food science by considering various criteria for the selection of pesticides. Our proposed MultiFuzzTOPS recommends the best pesticide compared with its counterparts because it covers the maximum information for the selection of the best alternative. Results are ranked on the basis of the Hamming distance and similarity coefficient. We also validate the effectiveness by performing the sensitivity analysis, and the validation shows the reliability and effectiveness of our proposed model.

Crips sets, type-1, and type-2 fuzzy sets in the context of linguistic variables and rule-based systems for cognitive computing

The computing with words is an approach that has unique characteristics and advantages to model cognitive processes, this article explains the relationship and difference between type-1 and type-2 fuzzy sets in the definition of linguistic values. Here, we perform a compressive review and justify because type-2 sets are more appropriate in modeling linguistic values, and a heuristic procedure by examples is carried out to define linguistic values on a continuous variable. A visual comparison of a rule-based system, when linguistic values use crips, type-1, and type-2 fuzzy sets in modeling a cognitive system.

Sine function similarity-based multi-attribute decision making technique of type-2 neutrosophic number sets and application to computer software quality evaluation

With the rapid development of information technology, software products are playing an increasingly important role in people’s production and life, and have penetrated into many industries. Software quality is the degree to which the software meets the specified requirements, and is an important indicator to evaluate the quality of the products used. At present, the scale of software is increasing, and the complexity is increasing. It is an urgent problem to reasonably grasp and ensure the product quality. The measurement and evaluation of Software quality characteristics is an effective means to improve Software quality. Faced with the complex system of software, there are many factors that affect product quality. Current research mainly measures software product quality from a qualitative perspective. The computer software quality evaluation is a classical multi-attribute group decision making (MAGDM). Type-2 Neutrosophic Numbers (T2NNs) is a popular set in the field of MAGDM and many scholars have expanded the traditional MAGDM to this T2NNs in recent years. In this paper, two new similarity measures based on sine function for T2NN is proposed under T2NNs. These two new methods are built for MAGDM based on the sine similarity measures for T2NN (SST) and sine similarity weighted measures for T2NN (SSWT). At the end of this paper, Finally, a practical case study for computer software quality evaluation is constructed to validate the proposed method and some comparative studies are constructed to verify the applicability. Thus, the main research contribution of this work is constructed: (1) two new similarity measures based on sine function for T2NN is proposed under T2NNs; (2) These two new methods are built for MAGDM based on the sine similarity measures for T2NN (SST) and sine similarity weighted measures for T2NN (SSWT); (3) an example for computer software quality evaluation is employed to verify the constructed techniques and several decision comparative analysis are employed to verify the constructed techniques.

A decision support mechanism in the determination of organic waste collection and recycling center location: A sample application for Turkiye

The location problem of organic waste collection and recycling plants is a significant concern for policy makers in developing countries. Factors such as rapid population growth, unplanned urbanization, and limited resources pose challenges to the efficient management of organic waste. Inadequate waste disposal practices not only endanger the environment and human health but also hinder the development of sustainable and livable cities. Therefore, it is crucial to address the specific challenges associated with locating organic waste collection and recycling facilities to ensure effective waste management and promote environmental sustainability. This study aims to identify the most appropriate location for an organic waste collection and recycling facility for compost production. This study involves identifying the most influential aspects of organic waste collection and recycling center location selection through a literature review and expert opinion. The Analytical Hierarchy Process (AHP) methodology with fuzzy interval type-2 (T2F) sets is employed to weight the criteria. The COmbinative Distance-based Assessment (CODAS) approach is extended in a T2F environment to better reflect the uncertainty and evaluate the alternative locations. The study concludes by revealing the optimal location for the food waste collection center for Trabzon city in Turkiye. To verify the validity and reliability of the proposed integrated methodology, a comparative analysis was also performed using various decision-making methods.

Analytical Studies of the Application Aspects of Fuzzy Intuitionistic and Fuzzy Type 2 Set

The main aim of this paper is to introduce the definition of intuitionistic fuzzy set and operations on it that will prove fruitful to conclude to a solution on problems of real life and how fuzzy logic and Graphics Processing unit can be used together to solve different domain problems for faster responses. Various comprehensive survey of Type-2 fuzzy set and the intuitionistic fuzzy set theories have been described here. IFS is nothing but a simple extension of the fuzzy set defined in the domain of discourse. Graphics Processing Unit (GPU) has been used to enhance the speed of execution. The intuitionistic fuzzy set is utilized as a proper element for representing the degree of hesitation concerning both the non-membership and membership degrees of an element of a set. Recent trends show how GPU is used for various computational applications that are run parallel to reduce overall execution time. Both the fuzzy domains seek application in tackling of the situation of vagueness with their respective characteristic feature sets to the fields concerned to different engineering domains of interdisciplines. This paper highlights the overview of the two eminent fuzzy categories like Fuzzy type 2 and intuitionistic fuzzy theory along with their application on greater scale.

Type-2 Neutrosophic Set and Their Applications in Medical Databases Deadlock Resolution

Electronic patient data gives many advantages, but also new difficulties. Deadlocks may delay procedures like acquiring patient information. Distributed deadlock resolution solutions introduce uncertainty due to inaccurate transaction properties. Soft computing-based solutions have been developed to solve this challenge. In a single framework, ambiguous, vague, incomplete, and inconsistent transaction attribute information has received minimal attention. The work presented in this paper employed type-2 neutrosophic logic, an extension of type-1 neutrosophic logic, to handle uncertainty in real-time deadlock-resolving systems. The proposed method is structured to reflect multiple types of knowledge and relations among transactions’ features that include validation factor degree, slackness degree, degree of deadline-missed transaction based on the degree of membership of truthiness, degree of membership of indeterminacy, and degree of membership of falsity. Here, the footprint of uncertainty (FOU) for truth, indeterminacy, and falsity represents the level of uncertainty that exists in the value of a grade of membership. We employed a distributed real-time transaction processing simulator (DRTTPS) to conduct the simulations and conducted experiments using the benchmark Pima Indians diabetes dataset (PIDD). As the results showed, there is an increase in detection rate and a large drop in rollback rate when this new strategy is used. The performance of Type-2 neutrosophic-based resolution is better than the Type-1 neutrosophic-based approach on the execution ratio scale. The improvement rate has reached 10% to 20%, depending on the number of arrived transactions.

An incremental type-2 fuzzy classifier for stock trend prediction

Due to its complex and unstable nature, stock market prediction is one of the most challenging problems. Lots of research has tried to explore the possibility of predicting stock trends using numerous machine learning methods. However, little effort has been made to predict the future trend online. In this paper, we propose an incremental type-2 fuzzy rule-base classifier capable of considering a high amount of uncertainty in stock data in addition to self-adaptation in an online manner. In this approach, interval type-2 fuzzy sets are built by combining type-1 sets that are directly extracted from the data. The proposed classifier can dynamically modify its parameters in order to react to the alteration of concepts without re-training the model. The efficiency of the proposed method is tested on some market indexes such as SP500, TAIEX, etc. and compared to various incremental methods. Moreover, to show the effectiveness of the proposed technique even in offline mode, we have compared it against some outstanding offline approaches, including deep neural networks. The obtained results demonstrate that our proposed method performs well under different settings.

Ternary soft sets based on the (complete) informal context

In this paper, the ternary soft set is discussed based on the soft triadic (complete) formal context. The ternary soft set is a generalization of Molodsov’s soft set, which can characterize the objects universe more clearly by the attributes set, and different from type-2 soft set. The definitions of the ternary soft set and ternary formal context are given and illustrated with some examples. A mindmap is used to show the idea of ternary soft set visually. The usage of bijective soft set enables fast decision making process by our work. We demonstrate the idea with a flowchart and a case study. Meanwhile, the soft operations among the ternary soft sets are defined and their properties are studied.

A Novel Approach to Type-Reduction and Design of Interval Type-2 Fuzzy Logic Systems

Abstract Fuzzy logic systems, unlike black-box models, are known as transparent artificial intelligence systems that have explainable rules of reasoning. Type 2 fuzzy systems extend the field of application to tasks that require the introduction of uncertainty in the rules, e.g. for handling corrupted data. Most practical implementations use interval type-2 sets and process interval membership grades. The key role in the design of type-2 interval fuzzy logic systems is played by the type-2 inference defuzzification method. In type-2 systems this generally takes place in two steps: type-reduction first, then standard defuzzification. The only precise type-reduction method is the iterative method known as Karnik-Mendel (KM) algorithm with its enhancement modifications. The known non-iterative methods deliver only an approximation of the boundaries of a type-reduced set and, in special cases, they diminish the profits that result from the use of type-2 fuzzy logic systems. In this paper, we propose a novel type-reduction method based on a smooth approximation of maximum/minimum, and we call this method a smooth type-reduction. Replacing the iterative KM algorithm by the smooth type-reduction, we obtain a structure of an adaptive interval type-2 fuzzy logic which is non-iterative and as close to an approximation of the KM algorithm as we like.

Enhanced COVID-19 X-ray image preprocessing schema using type-2 neutrosophic set

In this study, we introduce a new medical image enhancement approach depending on a type-2 neutrosophic set (T2NS) and α-mean and β- enhancement operations. This new approach obtains a good enhancement result by defining the uncertainties within the image in a six-degree membership. To show the real case study of this proposed technique, a novel enhancement approach for COVID-19 in X-ray is introduced. The X-ray image suffers from poor contrast and inconsistencies in its gray levels. The proposed method tackles this issue by obtaining a neutrosophic domain for gray level images depending on six membership functions. Through enhancement operations, T2NS entropy is obtained to evaluate the change in the gray level of X-ray images. The proposed approach can improve chest X-ray images by reducing the entropy values to minimize the uncertainty within the image. An image de-neutrosophication operation is obtained on the enhanced images to convert them from the neutrosophic set (NS) domain to the grayscale image. Finally, output images are compared with the enhanced images achieved under a single-valued neutrosophic set (SVNS) domain.

Properties of interval type-2 fuzzy sets in decision support systems

Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.

Performance Analysis of PI, T1NFC, and T2NFC of Indirect Vector Control-Based Induction Motor Using DSpace-2812

A type 2 Neuro-Fuzzy torque controller for indirect vector control (IVC) based induction motor (IM) driving is presented in this work. In various operating modes, a linear fixed-gain proportional-integral (PI) based speed controller is employed in indirect vector control of an IM drive (IMD). To achieve high performance, the PI controller (PIC) requires precise and accurate gain parameters. The PIC gain values have been tuned for a specific operating point and may not perform satisfactorily when the load torque and operating point change. To enhance dynamic performance over a wide speed range and reduce load torque ripple, the PIC is replaced by a Type-1 neuro-fuzzy logic controller (T1NFC). The T1FLC is simple, easy to use, and successful at dealing with nonlinear control systems without the use of complex mathematical equations. Instead, it relies on simple logical rules that are decided by an expert. The T1NFC is replaced by a Type-2 neuro-fuzzy logic controller to enhance controller performance. Owing to the availability of three-dimensional control with type-reduction technique (i.e. Type-2 fuzzy sets and Type-2 reducer set) in the defuzzification process, the T2NFC effectively handles the large footprint of uncertainties compared to the T1NFC, whereas the T1NFC have only Type-1 fuzzy sets and a single membership function. The T2NFC using MATLAB Simulink is used to observe the induction motor performance characteristics like, stator phasor current, torque, and speed under various operating situations. T2NFC controllers provide better driving performance characteristics than PI and T1NFC controllers. When associated to the PI and T1NFC controllers, the suggested T2NFC greatly reduce the amount of ripple in the torque and stator current of the IM drive. Practical validation is also performed with a 3.7 KW IM drive and a DSP 2812 controller for real-time examination of the drive parameters.

Risks of water and wastewater PPP projects: an investors’ perspective

PurposeWater and wastewater (WW) projects are gaining attention in Iran because of shortages of water resources. However, these projects are lengthy and they are accompanied by numerous risks, such as lack of sufficient financial resources. Public–private partnerships (PPPs) are taken into account as a constructive approach to deal with the problem of insufficient government funds and they are increasingly being implemented to construct the required infrastructures in different countries. Although WW projects in PPPs can reduce the government’s debt, investors are still uncertain about this approach. Hence, this study aims to identify and evaluate the risk of all parties involved in WW-PPP projects, from the viewpoint of investor.Design/methodology/approachFirst, the risk factors which are involved in WW projects are identified by interviewing experts and reviewing the literature by means of fault tree analysis (FTA) tool. Second, the probability and effects of the risky factors which are related to specific event are evaluated and analyzed by hybridization of interval fuzzy Type-2 sets (IT2FS) and risk score formulation. Finally, some solutions are proposed to deal with the most challenging risks.FindingsSix gate events, namely, risks which are related to investors such as investor’s consultant-related risks, risky conditions from engineering, procurement, and construction (EPC) contractors’ point of view, risk factors which public sector takes into account, public sector’s consultant-related risks which public sector’s consultant consider challenging and external factors were defined according to the literature. From FTA tool and by interviewing the experts, 94 basic events were identified. Finally, from hybridization of IT2FSs and risk score formulation, top five risks are determined as “Difficulty of injecting financial resources into the project,” “Fluctuation in inflation rate,” “Poor decision-making process” in public sector, “Difficulty of importing the equipment which are required for the project (such as pumps, grain catchers, garbage collectors, etc.) from other countries” and “Impact of risky conditions in other projects on operation of PPP project.”Originality/valueIn the absence of a constructive approach for risk identification and a reliable model for evaluating the identified risks in PPP projects, this research project is one of the first research studies which used FTA for identifying risks and hybridization of IT2FSs and risk score formulation for evaluating the risks.

Graphical Representation of Type-2 Neutrosophic sets

Neutrosophic set is the universality of the fuzzy and intuitionistic fuzzy sets. If the value of grade of membership contains uncertainty then that problems or situations can be dealt by type-2 fuzzy and intuitionistic fuzzy sets. It is not possible to work in enigmatic and uncertain situations and indeterminate situations as well. This present study introduces, graphical representation of type-2 neutrosophic set (T2NS) to deal the level of uncertainty in truth, indeterminate and false part of the information from footprint of uncertainty (FOU). This graphical representation helps as a learning strategy of type-2 neutrosophic sets. Also discussed the advantage of T2NS.

A type-2 neutrosophic-entropy-fusion based multiple thresholding method for the brain tumor tissue structures segmentation

In this paper, we introduce an extension theory of the neutrosophic set (NS) called type-2 neutrosophic set (T2NS). This new theory provides a granular representation of features and helps to model uncertainties with six different memberships very effectively. To demonstrate the real-time application of this theory, a new segmentation method for brain tumor tissue structures in magnetic resonance imaging (MRI) is presented. There are inconsistencies in the gray levels observed in MRIs due to their low illumination. The proposed theory addressed this problem by performing neutrosophication operation on gray levels based on six different membership functions called type-2 neutrosophic membership functions. During segmentation, a concept of T2NS entropy is used to quantify each gray level of MRIs. The proposed method is able to select multiple adaptive thresholds for segmentation of brain tumor tissue structures in MRIs from the locations of maximum entropy values of gray levels. Finally, an image fusion operation is performed on the segmented images with different thresholds to include all features and identify the location of brain tumor. The fusion images are compared with the segmented images obtained by five different methods, including fuzzy c-means algorithm, modified fuzzy c-means algorithm, fuzzy-K-means clustering algorithm, kernel intuitionistic fuzzy entropy c-means and neutrosophic entropy-based adaptive thresholding method. The proposed method achieves Jaccard similarity coefficients of 97.07%, 97.92% and 97.13% in the case of three different sets of MRIs, namely Set I, Set II and Set III, respectively. The proposed method exhibits correlation coefficients of 0.9638, 0.9698 and 0.9610 for the Set I, Set II and Set III of MRIs, respectively. Similarly, the proposed method shows uniformity measures of 0.9624, 0.9633 and 0.9660 for the Set I, Set II and Set III of MRIs, respectively. These three performance evaluation metrics show the effectiveness of the proposed method compared to the existing methods.

Decision-Making Approach with Fuzzy Type-2 Soft Graphs

Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, regular fuzzy type-2 soft graphs, irregular fuzzy type-2 soft graphs, fuzzy type-2 soft trees, and fuzzy type-2 soft cycles. We construct some operations such as union, intersection, AND, and OR on fuzzy type-2 soft graphs and discuss these concepts with numerical examples. The fuzzy type-2 soft graph is an efficient model for dealing with uncertainty occurring in vertex-neighbors structure and is applicable in computational analysis, applied intelligence, and decision-making problems. We study the importance of fuzzy type-2 soft graphs in chemical digestion and national engineering services.

A Parameterized Intuitionistic Type-2 Fuzzy Inference System with Particle Swarm Optimization

The aim of this study was to develop a novel intuitionistic Type-2 fuzzy inference system (IT-2 FIS) which adopts a parameterized Yager-generating function and particle swarm optimization (PSO). In IT-2 FIS, the intuitionistic Type-2 is set as a fuzzy symmetrical triangular number in which the hesitation degree adopts the Yager-generating function, and the parameters of the proposed IT-2 FIS adopting the PSO are tuned. The intuitionistic and Type-2 fuzzy sets have been proven to be the most effective for handling more uncertainty. Therefore, this study proposes an intuitionistic Type-2 set with a Yager-generating function to enhance the conventional fuzzy inference system. Moreover, PSO can improve the fuzzy inference system by searching for the optimal parameters of IT-2 FIS. In this study, linguistic variables were represented by triangular fuzzy numbers (TFS). Two numerical examples were examined: capacity-planning and medical diagnosis problems. An approaching capacity-loadings example was used to verify that the proposed IT-2 FIS could effectively estimate the results of the capacity loadings. In the medical diagnosis problem, IT-2 FIS could obtain a higher correct rate by revealing experts’ knowledge. In both examples, the proposed IT-2 FIS provided more objective estimated values than traditional fuzzy inference systems (FIS) and Type-2 FIS.

Type-2 single-valued neutrosophic sets and their applications in multi-criteria group decision making based on TOPSIS method

Type-2 fuzzy set and type-2 intuitionistic fuzzy set are important tools for dealing with problems involving uncertainty and linguistic variables. However, it is sometimes difficult to model problems involving inconsistent data by using these approaches. In this paper, the concept of type-2 single-valued neutrosophic sets is defined in order to cope with this difficulty. Also, some distance measure methods for type-2 single-valued neutrosophic sets based on Hausdorff, Hamming and Euclidean distances are introduced and some properties of them are investigated. Furthermore, a multi-criteria group decision-making method is developed based on TOPSIS approach under the type-2 single-valued neutrosophic environment. Finally, an illustrative example is given in order to show the validity and process of the proposed method.

Tilting-Pad Journal Bearing Subjected to Fuzzy Type-2 Uncertain Parameters

Abstract This paper evaluates the effects of uncertainties on the load capacity of a four-pad tilting-pad journal bearing, in which the pad radius, oil viscosity, and radial clearance are considered as uncertain information. The hydrodynamic supporting forces at the bearing pads are obtained by solving the Reynolds equation. In this case, the uncertain parameters are modeled as fuzzy type-2 variables. Fuzzy type-2 sets have been widely used due to their ability to model higher orders of uncertainties as compared with the fuzzy type-1 approach. They allow for inaccurate knowledge to be included in the membership functions used to describe the uncertain parameters. In the present contribution, the so-called α-level optimization was associated with the fuzzy type-2 technique for uncertainty analysis purposes. A sensitivity analysis was also carried out as an additional assessment of the considered uncertain parameters. The numerical results allowed to understand how the uncertain parameters affect the bearing supporting forces for three shaft speeds, namely, 3000, 9000, and 15,000 rpm. It was demonstrated that the effect of the uncertain parameters on the supporting forces increases according to the shaft speed. Additionally, the load capacity revealed to be more sensitive to variations on the oil viscosity and radial clearance than to the pad radius concerning the adopted uncertain interval. Consequently, the obtained results can provide suitable information for the design, manufacturing, and maintenance of tilting-pad journal bearings.

A novel WASPAS approach for multi-criteria physician selection problem with intuitionistic fuzzy type-2 sets

Due to innovative and practical technology, the selection of a right physician is an important issue for patients. However, uncertainty and vagueness frequently arise during the process of selecting physicians. Intuitionistic fuzzy type-2 sets (IFT2Ss) (recently named as Pythagorean fuzzy sets) provide an important tool to handle the uncertainty arises in real-life decision-making problems. This paper presents an extended weighted aggregated sum product assessment (WASPAS) method based on novel information measures (entropy and divergence measures) and operators under IFT2Ss context. In the proposed WASPAS method, entropy and divergence measure-based formula is developed to find the criteria weights. For this, several intuitionistic fuzzy entropy and divergence measures are developed for IFT2Ss. To increase the stability of the proposed methodology, the criteria’s weights are calculated in the form of objective and subjective weights. Further, to reveal the applicability and effectiveness of proposed method, an uncertain multi-criteria decision-making problem of physician selection is executed with intuitionistic fuzzy information of second type. Finally, the validity of the proposed method is implemented by comparison with existing methods and sensitivity analysis and also proves that the proposed method is valid and feasible in the physician selection processes with information given in intuitionistic fuzzy type-2 numbers (IFT2Ns).