General Fuzzy Research Articles

Multilattice as the set of truth values for fuzzy rough sets

Radzikowska and Kerre developed L-fuzzy rough set as a fuzzy generalisation of the notion of rough sets. Specifically, they have taken a residuated lattice L as the underlying set of truth degrees. However, in real life, we may encounter situations where truth degrees are not always linear, or where the existence of the least upper bound of two elements is no longer required. Instead, there may be the possibility of having minimal upper bounds, and dually, maximal lower bounds, multilattices have become a suitable algebraic structure for addressing such cases. Our aim is to extend Radzikowska and Kerre's work by replacing a residuated lattice with a multilattice M, thereby obtaining a more flexible structure. We define M-fuzzy rough sets using operators derived from adjoint pairs within the multilattice M. For a tolerance and an equivalence M-fuzzy relation, we define an appropriate M-fuzzy rough set and investigate its properties.

Novel complex fuzzy distance measures with hesitance values and their applications in complex decision-making problems

A complex fuzzy distance measure (CFDMs) plays a significant role in applications involving complex or high-dimensional data where traditional distance measures may not adequately capture the nuances of the data relationships. The significance of CFDMs lies in their ability to handle uncertainty, imprecision, and complexity in various domains. Numerous researchers introduced different concepts of CFDMs, yet these CFDMs fails to convey any information regarding the hesitancy degree associated with an element. The main objective of this paper is to introduce some new distance measures based on complex fuzzy sets, called complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure, which is the generalization of complex fuzzy normalized Hamming distance measure and complex fuzzy Euclidean distance measure. Some new operations and primay results are discussed in the environment of proposed CFDMs and complex fuzzy operations. Moreover, we discussed the applications of the proposed CFDMs in addressing decision-making problems. We introduced a new decision-making algorithm that integrates CFDMs into decision-making processes, providing a robust methodology for handling real-world complexities. Further, the comparative study of the proposed CFDMs is discussed with some existing CFDMs.

Classification of Fritillaria using a portable near-infrared spectrometer and fuzzy generalized singular value decomposition

Fritillaria is a popular Chinese medicinal crop known for its medicinal value. However, the chemical composition and medicinal value of Fritillaria can vary significantly depending on the variety and origin. Therefore, there is a need for a more efficient and accurate method to identify Fritillaria of different varieties and origins. This study employed a portable near-infrared (NIR) spectrometer to collect NIR spectral data on six kinds of Fritillaria and classify them by using different feature extraction methods. In order to circumvent the limitations of Linear Discriminant Analysis (LDA) in small-sample size problem and improve the classification accuracy, Fuzzy Generalized Singular Value Decomposition (FGSVD) was proposed for feature extraction from NIR spectra. The original NIR data were first pre-processed by the Savitzky-Golay (SG) filtering, and then their dimensionality was reduced by Principal Component Analysis (PCA). After that, Generalized Singular Value Decomposition (GSVD) and FGSVD were performed for feature extraction, respectively. In the end, the spectral data were classified into six categories using the k-Nearest Neighbour (KNN) classifier and Extreme Learning Machines (ELM). The results of the study showed that FGSVD had the highest classification accuracy when using the KNN classifier and was able to achieve 100 % classification accuracy. At the same time, GSVD and LDA were able to achieve 97.5 % and 92.5 % classification accuracy respectively. The classification accuracy obtained by FGSVD was also higher than GSVD and LDA when ELM was used. The highest classification accuracies obtained by FGSVD, GSVD and LDA were 96.9 %, 94.2 % and 92.3 % respectively. Thus, the KNN classifier outperformed ELM in classification. Consequently, the portable near-infrared spectrometer coupled with PCA+FGSVD is a novel strategy for rapid and non-destructive classification of Fritillaria.

Coupling of Rough Set Theory and Predictive Power of SVM Towards Mining of Missing Data

Rough set theory offers a novel approach to identifying structural correlations amidst imprecise or noisy data, particularly applicable to variables with diverse values. It presents a promising avenue for handling fuzzy, conflicting, and uncertain data, with recent models incorporating various fuzzy generalizations. This technique stands out as a popular solution within artificial intelligence, particularly in data analysis and processing tasks. In the medical domain, where missing data poses a significant challenge, leveraging rough set theory alongside machine learning algorithms for disease prediction is common. This paper proposes a model that effectively predicts missing values using rough set theory, addressing the prevalent issue of incomplete data. By providing a systematic approach and robust algorithm, the model demonstrates the adaptability and potential of rough set theory in contemporary data analysis scenarios. Classification of the predicted data set using supervised Learning Model (SVM) results in accuracy of 82.1% while the F1 score is 82.6%. Through validation with reallife medical datasets using supervised classification techniques, the paper underscores the accuracy and applicability of the proposed algorithm, offering a valuable tool for researchers and practitioners grappling with the complexities of modern data analysis.

Intuitionistic Fuzzy Generalized Conformable Fractional Derivative

Intuitionistic Fuzzy Generalized Conformable Fractional Derivative

A Comprehensive Study of Picture Fuzzy Planar Graphs with Real-World Applications

Picture fuzzy planar graph is a generalization of fuzzy and intuitionistic fuzzy planar graph. There are some real-life problems which cannot be handled by a fuzzy planar graph but such types of problems can efficiently be handled by a picture fuzzy planar graph. Motivated by this point of view, we consider the picture fuzzy planar graph in our research study. In this paper, we introduce picture fuzzy planar graphs, picture fuzzy dual graphs and their important properties. Also, we introduce a new concept of planarity value which satisfies the picture fuzzy criteria. An algorithm for testing the planarity of a picture fuzzy graph is also designed. Also, we provide a flowchart of the corresponding algorithm. Besides this, we propose an application for ranking the essentiality of flyover or underpass in street junctions and select the most essential street junctions where flyover or underpass is needed in a smart city.

Domain fuzzy generalization networks for semi-supervised intelligent fault diagnosis under unseen working conditions

In recent years, domain adaptation methods have made remarkable achievements in fault diagnosis under variable working conditions. However, the methods usually fail when target data are unavailable for model training. Confronting with the problem of intelligent fault diagnosis for unseen working conditions, domain generalization methods have been gradually explored. Most existing domain generalization fault diagnosis methods are supervised learning models that require multiple fully labeled source domains. Few studies have been done on semi-supervised domain generalization when only partial source domains have class labels, which is generally a practical industrial scenario because labeling industrial data is a laborious work and requires scarce domain experts. Consequently, this paper proposes a novel semi-supervised domain generalization framework, named domain fuzzy generalization networks (DFGN), for intelligent fault diagnosis under unseen working conditions. The main idea of the DFGN is to enhance the capabilities of learning domain-invariant and discriminative features by proposing domain fuzzy and metric learning strategies. First, the traditional domain discriminator outputting one-dimensional domain probability is innovatively substituted by a domain classifier that predicts the domain probabilities belonging to all the source domains. Then, the domain fuzzy strategy is established in domain-adversarial training to extract the domain-invariant features with fine-grained distribution alignment. Finally, the metric learning is embedded in feature extractor to extract the discriminative features from a class-level optimization perspective. Benefited from the extracted domain-invariant and discriminative features, the proposed DFGN model exhibits strong generalization ability that can be effectively applied to intelligent fault diagnosis under unseen working conditions. The advantages and superiority of the proposed method over state-of-the-art semi-supervised domain generalization methods are confirmed by extensive generalization experiments on two bearing datasets.

Multi-Area Load Frequency Control in Power System Integrated With Wind Farms Using Fuzzy Generalized Predictive Control Method

Frequency security is critical for the power systems’ stability and reliability. The integration of renewable energy resources brings new challenges to the frequency security of power systems. To provide a more robust control method for controlling the frequency and tie-line power flow of an interconnected power system integrated with wind farms (IPSWF), a load frequency control (LFC) controller of generalized predictive control (GPC) based on the Takagi-Sugeno (T–S) fuzzy model (fuzzy-GPC) is proposed in this paper. First, the T–S fuzzy model of the IPSWF is constructed. Then, the GPC is used to design the controller. Lastly, to validate the proposed scheme, an LFC strategy is established for a two-area interconnected power system integrated with a wind farm in power systems computer aided design (PSCAD). The control performance of proportional-integral, GPC, and fuzzy-GPC controller are compared under two faulty operating conditions. The simulation results show that the performance indicators and the dynamic behavior when the fuzzy-GPC controller is used are better than the performance when the PI controller and GPC controller are used. The proposed fuzzy-GPC used in the LFC of the IPSWF can regulate the frequency deviation and tie-line power deviation adaptively and achieve minimum frequency deviation and tie-line power deviation in a multi-area IPSWF.

Regular and Intra-Regular Ternary Semirings in Terms of m-Polar Fuzzy Ideals

In practical applications, the basic fuzzy set is used via symmetric uncertainty variables. In the research field, it is comparatively rare to discuss two-fold uncertainty due to its complication. To deal with the multi-polar uncertainty in real life problems, m-polar (multi-polar) fuzzy (m-PF) sets are put forward. The main objective of this paper is to explore the idea of m-PF sets, which is a generalization of bipolar fuzzy (BPF) sets, in ternary semirings. The major aspects and novel distinctions of this work are that it builds any multi-person, multi-period, multi-criteria, and complex hierarchical problems. The main focus of this study is to confine generalization of some important results of BPF sets to the results of m-PF sets. In this research, the notions of m-polar fuzzy ternary subsemiring (m-PFSS), m-polar fuzzy ideal (m-PFI), m-polar fuzzy generalized bi-ideal (m-PFGBI), m-polar fuzzy bi-ideal (m-PFBI), and m-polar fuzzy quasi-ideal (m-PFQI) in ternary semirings are introduced. Moreover, this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular ternary semiring in terms of these ideals.

Feature Subset Selection With Multi-Scale Fuzzy Granulation

As a typical multigranularity data analysis model, multi-scale rough sets have attracted considerable attention in recent years. However, classical multi-scale rough sets and most of its extended models can only deal with discrete data, which limits its popularization and application. To overcome this problem, we investigate the fuzzy generalization of multi-scale rough sets as well as their application in feature selection for continuous data. To this end, a new type of decision systems, i.e., multi-scale fuzzy decision systems, is formalized to represent knowledge at different scales. Scaled fuzzy granules in terms of a family of scaled fuzzy relations are introduced, using which the granular structures of fuzzy lower and upper approximations are presented. A heuristic lattice-based optimal scale selection algorithm is then put forward from the viewpoint of maintaining the consistency of decision systems. Decision rules with strong generalization ability can be obtained by selecting appropriate scales. Finally, a forward feature selection algorithm was developed by means of the optimal scale to reduce redundant fuzzy relations. Extensive numerical experiments are further conducted to compare the proposed algorithm with some state-of-the-art algorithms. The experimental results show that our model can improve the generalization ability of fuzzy rough set, so as to be more feasible and effective.

Some fixed point results for fuzzy generalizations of Nadler's contraction in b-metric spaces

<abstract> <p>The main purpose of this study is to examine the existence of fuzzy fixed points of fuzzy mappings meeting the criteria of some generalized contractions of Nadler's type in the framework of complete b-metric spaces. From the pertinent literature, there are additional previous observations that are provided as corollaries. Our study expands and incorporates several implications that are apparent in this mode and are addressed in considerable literature.</p> </abstract>

A study on the Heronian mean operators for managing complex picture fuzzy uncertain linguistic settings and their application in decision making

The major influence of this manuscript is to diagnose a valuable and considerable technique of Complex Picture Fuzzy Uncertain Linguistic setting and described its useful and valuable operational laws. The theory of Complex Picture Fuzzy Uncertain Linguistic information is massive modified and generalized than the Complex intuitionistic Fuzzy Uncertain Linguistic, Complex Fuzzy Uncertain Linguistic, Fuzzy Uncertain Linguistic and Uncertain Linguistic information. Keeping the supremacy and dominancy of the Complex Picture Fuzzy Uncertain Linguistic information, we investigated the Complex Picture Fuzzy Uncertain Linguistic Arithmetic Heronian Mean, Complex Picture Fuzzy Uncertain Linguistic Weighted Arithmetic Heronian Mean, Complex Picture Fuzzy Uncertain Linguistic Geometric Heronian Mean and Complex Picture Fuzzy Uncertain Linguistic Weighted Geometric Heronian Mean operators. The property of idempotency, boundedness, monotonicity, and various well-known results with certain specific cases of the invented work are also deliberated. Furthermore, in the availability of the above-proposed analysis, we constructed a multi-attribute decision-making technique by considering the diagnosed operators for complex picture fuzzy uncertain linguistic information to enhance the worth and rationality of the invented theory. Finally, we illustrated the merits and restrictions of the novel operators by comparing them with certain prevailing operators based on fuzzy generalization. Finally, in the presence of evaluated examples, we compared the pioneered operators with various existing operators to enhance the feasibility and worth of the invented operators.

Best Proximity Point Theorems without Fuzzy P-Property for Several (ψ − ϕ)-Weak Contractions in Non-Archimedean Fuzzy Metric Spaces

This paper addresses a problem of global optimization in a non-Archimedean fuzzy metric space context without fuzzy P-property. Specifically, it concerns the determination of the fuzzy distance between two subsets of a non-Archimedean fuzzy metric space. Our approach to solving this problem is to find an optimal approximate solution to a fixed point equation. This approach has been well studied within a category of problems called proximity point problems. We explore some new types of (ψ−ϕ)-weak proximal contractions and investigate the existence of the unique best proximity point for such kinds of mappings. Subsequently, some fixed point results for corresponding contractions are proved, and some illustrative examples are presented to support the validity of the main results. Moreover, an interesting application in computer science, particularly in the domain of words has been provided. Our work is a fuzzy generalization of the proximity point problem by means of fuzzy fixed point method.

Stability analysis with general fuzzy measure: An application to social security organizations.

An effective method for evaluating the efficiency of peer decision-making units (DMUs) is data envelope analysis (DEA). In engineering sciences and real-world management problems, uncertainty in input and output data always exists. To achieve reliable results, uncertainties must be taken into account. In this research, a General Fuzzy (GF) approach is designed to cope with uncertainty in the presence of fuzzy observations for categorizing and specifying stability radius and alterations ranges of efficient and inefficient DMUs, which is applicable to real-world decision-making problems. For this purpose, a DEA sensitivity analysis model is presented, which will be modeled by fuzzy sets. Then, by applying the General Fuzzy (GF) approach, the fuzzy DEA sensitivity analysis model is transformed into the equivalent crisp form of fuzzy chance constraints according to specific confidence levels. Finally, a numerical example and a case study of branches of the social security organization are presented to illustrate sensitivity and stability analysis in the presence of fuzzy data. The obtained results provide the input and output changes of the evaluated units according to the attitude and preference of the decision maker with different confidence levels so that the data changes in the fuzzy environment do not change the units’ classification from efficient to inefficient and vice versa.

Fuzzy Halpern and Shoham's interval temporal logics

The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.

Fuzzy Kakutani-Fan-Glicksberg fixed point theorem and existence of Nash equilibria for fuzzy games

In this paper, we give fuzzy generalizations to the well-known Brouwer fixed point theorem and Kakutani-Fan-Glicksberg fixed point theorem. As applications, we apply the fuzzy Kakutani-Fan-Glicksberg fixed point theorem to derive an existence theorem for Nash equilibria in generalized fuzzy games with locally convex Hausdorff topological vector spaces for strategy spaces and/or discontinuous payoff functions which generalizes existence theorems for Nash equilibria in generalized games.

Multivariate Control Chart based on Neutrosophic Hotelling T2 Statistics and Its Application

Under classical statistics Hotelling 〖 T〗^2 control chart is applied when the observations of quality characteristics are precise, exact, or crips data. However, in reality, under uncertain conditions, the observations are not necessarily precise, exact, or indeterminacy. As a consequence, the classical Hotelling〖 T〗^2control chart is not appropriate to monitor the process for this condition. To tackle this situation, we proposed new Hotelling 〖 T〗^2 monitoring scheme based on a fuzzy neutrosophic concept. Neutrosophic is the generalization of fuzzy. It is used to handle uncertainty using indeterminacy. The combination of statistics based on neutrosophic Hotelling 〖 T〗^2 and classical Hotelling 〖 T〗^2 control chart will be proposed to tackle indeterminacy observations. The proposed Hotelling 〖 T〗^2 statistics, its call neutrosophic Hotelling 〖 T〗^2 (T_N^2 ) control chart. This chart involves the indeterminacy of observations, its call neutrosophic data and will be expressed in the indeterminacy interval. T_N^2 control charts consist T_N^2 lower chart and T_N^2 upper chart. In this paper, the neutrosophic Hotelling T^2will be applied to individual observations of glass production and will be compared by using classical Hotelling T^2 control chart. Based on T_N^2 control charts of glass production, nine points fall outside of 〖UCL〗_N of lower control chart and 24 points outside from 〖UCL〗_N of upper control chart. Whereas using classical Hotelling T^2 control chart, just one point outside frim UCL. From the comparison, it concluded that the neutrosophic Hotelling T^2 control chart is more suitable for the indeterminacy of observations.

Network Analysis for Projects with High Risk Levels in Uncertain Environments

The critical path method is one of the oldest and most important techniques used for planning and scheduling projects. The main objective of project management science is to determine the critical path through a network representation of projects. The critical path through a network can be determined by many algorithms and is useful for managing, monitoring, and controlling the time and cost of an entire project. The essential problem in this case is that activity durations are uncertain; time presents considerable uncertainty because the time of an activity is not always easily or accurately estimated. This issue increases the need to use neutrosophic theory to solve the critical path problem. Real-world problems are characterized by a lack of precision, consistency, and completeness. The concept of neutrosophic sets has been introduced as a generalization of fuzzy, intuitionistic fuzzy, and crisp sets to overcome the ambiguity surrounding real-world problems. Truth-, falsity-, and indeterminacy-membership functions are used to express neutrosophic elements. This study was performed to examine a neutrosophic event-oriented algorithm for determining the critical path in activity-on-arc networks. The activity time estimates are presented as trapezoidal neutrosophic numbers, and score and accuracy functions are used to obtain a crisp model of the problem. An appropriate numerical example is then used to explain the proposed method.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy So Set with Their Application to Solve Multi-Attribute Group Decision Making Problem

Interval-valued Pythagorean fuzzy so set (IVPFSS) is a generalization of the interval-valued intuitionistic fuzzy so set (IVIFSS) and interval-valued Pythagorean fuzzy set (IVPFS). The IVPFSS handled more uncertainty comparative to IVIFSS; it is the most signicant technique for explaining fuzzy information in the decision-making process. In this work, some novel operational laws for IVPFSS have been proposed. Based on presented operational laws, two innovative aggregation operators (AOs) have been developed such as interval-valued Pythagorean fuzzy so weighted average (IVPFSWA) and interval-valued Pythagorean fuzzy so weighted geometric (IVPFSWG) operators with their fundamental properties. A multi-attribute group decision-making (MAGDM) approach has been established utilizing our developed operators. A numerical example has been presented to ensure the validity of the proposed MAGDM technique. Finally, comparative studies have been given between the proposed approach and some existing studies. The obtained results through comparative studies show that the proposed technique is more credible and reliable than existing approaches.

A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough studies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets.