Concept Of Fuzzy Sets Research Articles

Intuitionistic Fuzzy Ordered Subalgebras in Ordered BCI-algebras

In this paper, we apply the concept of an intuitionistic fuzzy set to ordered subalgebras in ordered BCI-algebras in the sense of intuitionistic fuzzy point. We introduce the notion of an intuitionistic fuzzy (ordered) subalgebra in ordered BCI-algebras, and investigate some related properties. We provide relations between an intuitionistic fuzzy ordered subalgebra and an intuitionistic fuzzy subalgebra. We give characterizations of an intuitionistic fuzzy (ordered) subalgebra. Finally, we provide relations between a $q_{(t,s)}$-level set of intuitionistic fuzzy set and an intuitionistic fuzzy ordered subalgebra.

Homomorphism on bipolar-valued fuzzy sub-bigroup of a bigroup for secured data transmission over WSN

Cryptography field, which enables secure communication between civilians, governmental organizations, military forces, and many more, addresses security, confidentiality, and integrity of information being conveyed regardless of the medium used. Protection of priceless information resources on intranets, the Internet, and the cloud has become a vital demand of contemporary electronic security systems. In this paper, we deploy homomorphic data encryption (HDE) technique on Bipolar-valued Fuzzy Sub-Bigroups (BVFSB). Intuitionistic Fuzzy Sets were presented by Atanassov in 1986, as a modification of Fuzzy Sets, by taking into consideration the grade of membership value and non-membership value for each element in the universe. A fuzzy algebraic structure known as Bipolar-valued Fuzzy sub-bigroup of a bigroup has been established by applying the concept of bipolar-valued Fuzzy sets to bigroups. Some of the theorems related to homomorphism and anti-homomorphism, are stated and proved.

Characteristic Picture Fuzzy Sets and Level Subsets in UP (BCC)-Algebras

The eight new concepts of picture fuzzy sets in UP (BCC)-algebras are introduced by Kankaew et al. in 2022. This idea is extended to the lower and upper level subsets of picture fuzzy sets in UP (BCC)-algebras. Moreover, we define a picture fuzzy set in the same way as a characteristic function and study its characterizations from the related subset.

An Approach Toward Pattern Recognition and Decision-Making Using the Concept of Bipolar T-Spherical Fuzzy Sets

An Approach Toward Pattern Recognition and Decision-Making Using the Concept of Bipolar T-Spherical Fuzzy Sets

Strait fuzzy sets, strait fuzzy rough sets and their similarity measures-based decision making systems

In this paper, a new uncertainty modelling concept called strait fuzzy set is introduced, which brings new perspectives to both theoretical and practical advances in fuzzy mathematics. This set type allows objects/points to be graded with fuzzy membership intervals that are partitions of [0,1] (so that the union of these partitions is [0,1] and their intersection is empty) instead of fuzzy membership degrees represented as exact values in [0,1]. Moreover, some basic operations and properties of strait fuzzy sets are studied in detail. The concept of strait fuzzy rough set is put forward and its theoretical aspects are discussed. In addition, two different similarity approaches are proposed for strait fuzzy sets and strait fuzzy rough sets, and applied to measure the similarity rates of vaccines against influenza viruses.

Interval-Valued Topology on Soft Sets

In this paper, we study the concept of interval-valued fuzzy set on the family SSX,E of all soft sets over X with the set of parameters E and examine its basic properties. Later, we define the concept of interval-valued fuzzy topology (cotopology) τ on SSX,E. We obtain that each interval-valued fuzzy topology is a descending family of soft topologies. In addition, we study some topological structures such as interval-valued fuzzy neighborhood system of a soft point, base and subbase of τ and investigate some relationships among them. Finally, we give some concepts such as direct sum, open mapping and continuous mapping and consider connections between them. A few examples support the presented results.

Fuzzy Differential Subordination and Superordination Results for Fractional Integral Associated with Dziok-Srivastava Operator

Fuzzy set theory, introduced by Zadeh, gives an adaptable and logical solution to the provocation of introducing, evaluating, and opposing numerous sustainability scenarios. The results described in this article use the fuzzy set concept embedded into the theories of differential subordination and superordination from the geometric function theory. In 2011, fuzzy differential subordination was defined as an extension of the classical notion of differential subordination, and in 2017, the dual concept of fuzzy differential superordination appeared. These dual notions are applied in this paper regarding the fractional integral applied to Dziok–Srivastava operator. New fuzzy differential subordinations are proved using known lemmas, and the fuzzy best dominants are established for the obtained fuzzy differential subordinations. Dual results regarding fuzzy differential superordinations are proved for which the fuzzy best subordinates are shown. These are the first results that link the fractional integral applied to Dziok–Srivastava operator to fuzzy theory.

CO2 emission based GDP prediction using intuitionistic fuzzy transfer learning

The industrialization has been the primary cause of the economic boom in almost all countries. However, this happened at the cost of the environment, as industrialization also caused carbon emissions to increase exponentially. According to the established literature, Gross Domestic Product (GDP) is related to carbon emissions (CO2) which could be optimally employed to precisely estimate a country's GDP. However, the scarcity of data is a significant bottleneck that could be handled using transfer learning (TL) which uses previously learned information to resolve new tasks, more specifically, related tasks. Notably, TL is highly vulnerable to performance degradation due to the deficiency of suitable information and hesitancy in decision-making. Therefore, this paper proposes ‘Intuitionistic Fuzzy Transfer Learning (IFTL)’, which is trained to use CO2 emission data of developed nations and is tested for its prediction of GDP in a developing nation. IFTL exploits the concepts of intuitionistic fuzzy sets (IFSs) and a newly introduced function called the modified Hausdorff distance function. The proposed IFTL is investigated to demonstrate its actual capabilities for TL in modeling hesitancy. To further emphasize the role of hesitancy modelled with IFSs, we propose an ordinary fuzzy set (FS) based transfer learning. The prediction accuracy of the IFTL is further compared with widely used machine learning approaches, extreme learning machines, support vector regression, and generalized regression neural networks. It is observed that IFTL capably ensured significant improvements in the prediction accuracy over other existing approaches whenever training and testing data have huge data distribution differences. Moreover, the proposed IFTL is deterministic in nature and presents a novel way for mathematically computing the intuitionistic hesitation degree.

Bilateral fuzzy sets and their three-way decisions: a new perspective of fuzzy logic

Fuzzy sets provide an effective method for dealing with uncertain and imprecise problems. For data of intermediate fuzzy distribution, membership degrees of objects whose attribute values are larger or smaller than the normal value would be the same and carried out the same decision. However, objects with different values mean that the information they contain is different for the decision-making problem. The decision process of calculating membership degrees in fuzzy set will lose the information of data itself. Therefore, bilateral fuzzy sets and their three-way decisions are proposed. First, the deviation degree is proposed in order to distinguish these objects. Compared with the membership degree, the deviation degree extends the mapping range from [0, 1] to [- 1, 1]. For six typical membership functions, their corresponding deviation functions are discussed and deduced. Second, the concept of bilateral fuzzy sets is proposed and the corresponding operation rules are analyzed and proved. Then, three-way decisions and approximations based on bilateral fuzzy sets are constructed. Next, for the optimization of threshold, principle of least cost is extended to the three-way decisions model based on bilateral fuzzy sets, and theoretical derivation is carried out. Finally, based on probability statistics, the principle based on confidence interval is proposed, which provides a new perspective for threshold calculation.

Similarity measures of neutrosophic fuzzy soft set and its application to decision making

ABSTRACT Complex data analysis should be done in the most accurate way in order to express the uncertain environments in the most ideal way. In addition, mathematical models that can best express the membership degrees that represent the objects are preferred for these data analyses. Taking these situations into account, this study proposes the concept of single-valued neutrosophic fuzzy soft set, which can be expressed with four different membership degrees of each object that provides a parameter, with the contribution of the parameterisation tool. Some important results are obtained by examining some single-valued neutrosophic fuzzy soft set-based theoretical operations. In addition, distance measures between two single-valued neutrosophic fuzzy soft sets. Then, similarity measurements based on these distance measurements are studied. In this way, a determination has been made for the analysis of the decision-making processes for the determination of the interaction between two single-valued neutrosophic fuzzy soft sets.

Development and Optimization of a Novel Soft Sensor Modeling Method for Fermentation Process of Pichia pastoris.

This paper introduces a novel soft sensor modeling method based on BDA-IPSO-LSSVM designed to address the issue of model failure caused by varying fermentation data distributions resulting from different operating conditions during the fermentation of different batches of Pichia pastoris. First, the problem of significant differences in data distribution among different batches of the fermentation process is addressed by adopting the balanced distribution adaptation (BDA) method from transfer learning. This method reduces the data distribution differences among batches of the fermentation process, while the fuzzy set concept is employed to improve the BDA method by transforming the classification problem into a regression prediction problem for the fermentation process. Second, the soft sensor model for the fermentation process is developed using the least squares support vector machine (LSSVM). The model parameters are optimized by an improved particle swarm optimization (IPSO) algorithm based on individual differences. Finally, the data obtained from the Pichia pastoris fermentation experiment are used for simulation, and the developed soft sensor model is applied to predict the cell concentration and product concentration during the fermentation process of Pichia pastoris. Simulation results demonstrate that the IPSO algorithm has good convergence performance and optimization performance compared with other algorithms. The improved BDA algorithm can make the soft sensor model adapt to different operating conditions, and the proposed soft sensor method outperforms existing methods, exhibiting higher prediction accuracy and the ability to accurately predict the fermentation process of Pichia pastoris under different operating conditions.

An approach to multi-attribute decision making based on intuitionistic fuzzy rough Aczel-Alsina aggregation operators

A concept of intuitionistic fuzzy rough set based on approximations plays a vital role in coping with uncertainty. Aczel-Alsina t-norm and t-conorm are the most flexible operational laws based on the parameter for fuzzy frameworks. In multi-attribute group decision-making (MAGDM), the aim of this article is to develop some tools based on norm operations for the information fusion. In this article, intuitionistic fuzzy rough Aczel-Alsina weighted geometric operators are developed and studied their properties. Based on these operators, MAGDM algorithm is presented. The developed aggregation operators (AOs) are compared with some existing AOs, and their significance is discussed.

Borderline scenarios of outranking classification based on α-cut variation in fuzzy intervals: Application in police investigations

This paper presents a new method for classifying actions called α-FlowSort, which uses sections of the fuzzy interval to allow vertical and horizontal decision strategies, which consider the decision-maker’s levels of certainty and optimism. α-FlowSort adds to the traditional MCDA FlowSort method the concepts of fuzzy sets with α-cut variation techniques and identification of outranking relations between fuzzy numbers, thus providing the decision-maker with scenarios for adjusting the decision, to add subjective elements at the time of assignment or to use a global recommendation. The decision maker is offered visual evaluation options that enable better identification and definition of the attribution of actions that in a single analysis would be positioned on the border between categories, in addition to which, by aggregating multiple simultaneous evaluations, a single recommendation is offered in a more robust way, even in a fuzzy environment. To demonstrate the results, an application of the new method is presented in the context of distributing resources to support criminal investigations, the results of which were compared with those obtained with the FlowSort and F-FlowSort methods. Simulations and comparisons between the methods were also carried out, using a thousand random alternatives.

Performance Evaluation of Healthcare Supply Chain in Industry 4.0 with Linear Diophantine Fuzzy Sine-Trigonometric Aggregation Operations

The concept of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and data-driven multi-criteria decision making (MCDM). The sine-trigonometric function (STF) has two significant features, periodicity and symmetry about the origin that are very useful tools for information analysis. Keeping in view the characteristics of both STF and LDFS theory, this article introduces the sine-trigonometric operations for linear Diophantine fuzzy numbers (LDFNs). These operational laws lay a foundation for developing new linear Diophantine fuzzy sine-trigonometric aggregation operators (LDFSTAOs). The integration of Industry 4.0 technology into healthcare has the potential to revolutionize patient care. One of the most challenging tasks is the selection of efficient suppliers for the healthcare supply chain (HSC). The traditional suppliers are not efficient in accordance with Industry 4.0, with particular uncertainties. A new MCDM framework is presented based on LDFSTAOs to examine the HSC performance in industry 4.0. A credibility test, sensitivity analysis and comparative analysis are performed to express the novelty, reliability, and efficiency of the proposed methodology.

New Applications of Fuzzy Set Concept in the Geometric Theory of Analytic Functions

Zadeh’s fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use the fuzzy set concept embedded into the theories of differential subordination and superordination established and developed in geometric function theory. As an extension of the classical concept of differential subordination, fuzzy differential subordination was first introduced in geometric function theory in 2011. In order to generalize the idea of fuzzy differential superordination, the dual notion of fuzzy differential superordination was developed later, in 2017. The two dual concepts are applied in this article making use of the previously introduced operator defined as the convolution product of the generalized Sălgean operator and the Ruscheweyh derivative. Using this operator, a new subclass of functions, normalized analytic in U, is defined and investigated. It is proved that this class is convex, and new fuzzy differential subordinations are established by applying known lemmas and using the functions from the new class and the aforementioned operator. When possible, the fuzzy best dominants are also indicated for the fuzzy differential subordinations. Furthermore, dual results involving the theory of fuzzy differential superordinations and the convolution operator are established for which the best subordinants are also given. Certain corollaries obtained by using particular convex functions as fuzzy best dominants or fuzzy best subordinants in the proved theorems and the numerous examples constructed both for the fuzzy differential subordinations and for the fuzzy differential superordinations prove the applicability of the new theoretical results presented in this study.

Quaternionic Fuzzy Sets

A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, intersection, and aggregation of QFSs, are presented. Quaternionic fuzzy relations and their composition are also investigated. QFS is designed to maintain the advantages of traditional FS and CFS, while benefiting from the properties of quaternions. Cuts of QFSs and rotational invariance of quaternionic fuzzy operations demonstrate the particularity of quaternion-valued grades of membership.

Mathematical Modeling and Multi-Criteria Optimization of Design Parameters for the Gyratory Crusher

There are a sufficient number of works devoted to modeling crushing machines. Nevertheless, the fact that there are a large number of working conditions, and the ongoing development of science and technology, require continuous improvement and specification of the models intended for crushing processes and those of the devices concerned. However, there are few studies related to single-roll gyratory crushers. Such crushers are promising for use in mines to crush rocks laid in the developed space. Mathematical modeling and optimization of the design parameters of the working chamber and the executive body (roll) of a single-roll gyratory shaft crusher, designed for crushing strong rocks, was performed in this paper. A differential equation was derived. As a result of its solution, the rational shape of the working chamber cheek of the single-roll gyratory crusher was established, representing a logarithmic spiral arc. Analytical expressions were derived to determine the rational rotation speed and productivity of the crusher under consideration. Expressions for calculating the kinematic load components acting on the roll were formulated. They are the periodic functions of the shaft rotation angle. The Fourier series expansion showed that the loads contained harmonics of the first, second, third and fourth orders. Using the concept of fuzzy sets, a multi-criteria optimization of the design parameters of the working chamber was performed, including the values of the eccentricity and the central angle of the beginning of the cheek profile. The variation coefficients of the kinematic components of the loads acting on the working body reduced, due to the optimal choice of the working chamber profile and the angular coordinates of the installation of the fixed cheeks. The torque reduced 1.67 times, while the radial load decreased 1.2 times.

Early infectious diseases identification based on complex probabilistic hesitant fuzzy N-soft information.

This paper aims to assess and deal with the challenges experienced by medical professionals caring for infectious diseases. In Pakistan, public health is still a serious concern and the main contributor to morbidity and mortality is infectious diseases. The major issue is a resemblance in the clinical symptoms of infectious diseases such as tuberculosis, hepatitis, COVID-19, dengue, and malaria. Early detection of infectious disease is crucial in order to start treatment with counseling and medication. This can only be done if several infections with similar clinical traits can be diagnosed depending on several criteria, including the availability of various kits, the ability to carry out diagnostic procedures, money, and technical staff. But woefully Pakistan's economy is badly battered due to several circumstances. Therefore, we are unable to provide patients with enough diagnostic testing kits and broadly accessible therapy choices, which makes diagnosis more difficult and create hesitancy with fuzziness and randomness. For this purpose, we introduced the new concept of the complex probabilistic hesitant fuzzy N-soft set. We defined its fundamental operations (like restricted and extended union, restricted and extended intersection, weak, top and bottom weak complements, as well as soft max-AND or soft min-OR) with examples. We also discussed their many properties with their proofs and theorems. Furthermore, we developed the algorithms for decision-making where doctors use the complex probabilistic hesitant fuzzy N-soft information to identify a particular disease. Furthermore, we explained numerical illustration of two case studies. Moreover, a sensitive and comparative analysis is discussed. In the last, we conclude the whole study.

Perbandingan Uji Akurasi Fuzzy Time Series Model Cheng Dan Lee Dalam Memprediksi Perkembangan Harga Cabai Rawit

Fuzzy Time Series is a method used to predict data. Fuzzy Time Series is a development of time series analysis, where Fuzzy Time Series uses the concept of fuzzy sets as the basis for its calculations. In addition, Fuzzy Time Series has various methods such as Cheng and Lee Fuzzy Time Series. In this study, Fuzzy Time Series is used to predict data on the price development of cayenne pepper in Indonesia. By using these two methods, an analysis of the level of accuracy is then carried out using several methods. So that the results obtained in this study are the MAE value of the Cheng method 669,162 and the Lee method 502,285, the MSE value of the Cheng method 1.261.393 and the Lee method 699.030.1, the MPE value of the Cheng method 0,01% and the Lee method -0,02%, and The MAPE value of the Cheng method is 1,24% and the Lee method is 0.92%. The Lee method has a smaller error value than the Cheng method, so that the Lee method is declared to be better than the Cheng method.

Nonlinear distance measures under the framework of Pythagorean fuzzy sets with applications in problems of pattern recognition, medical diagnosis, and COVID-19 medicine selection

BackgroundThe concept of Pythagorean fuzzy sets (PFSs) is an utmost valuable mathematical framework, which handles the ambiguity generally arising in decision-making problems. Three parameters, namely membership degree, non-membership degree, and indeterminate (hesitancy) degree, characterize a PFS, where the sum of the square of each of the parameters equals one. PFSs have the unique ability to handle indeterminate or inconsistent information at ease, and which demonstrates its wider scope of applicability over intuitionistic fuzzy sets.ResultsIn the present article, we opt to define two nonlinear distances, namely generalized chordal distance and non-Archimedean chordal distance for PFSs. Most of the established measures possess linearity, and we cannot incorporate them to approximate the nonlinear nature of information as it might lead to counter-intuitive results. Moreover, the concept of non-Archimedean normed space theory plays a significant role in numerous research domains. The proficiency of our proposed measures to overcome the impediments of the existing measures is demonstrated utilizing twelve different sets of fuzzy numbers, supported by a diligent comparative analysis. Numerical examples of pattern recognition and medical diagnosis have been considered where we depict the validity and applicability of our newly constructed distances. In addition, we also demonstrate a problem of suitable medicine selection for COVID-19 so that the transmission rate of the prevailing viral pandemic could be minimized and more lives could be saved.ConclusionsAlthough the issues concerning the COVID-19 pandemic are very much challenging, yet it is the current need of the hour to save the human race. Furthermore, the justifiable structure of our proposed distances and also their feasible nature suggest that their applications are not only limited to some specific research domains, but decision-makers from other spheres as well shall hugely benefit from them and possibly come up with some further extensions of the ideas.