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This paper is dedicated to defining and studying for the first time a two-fold algebra over the neutrosophic real number ring by merging the fuzzy set mapping with the algebraic operations of the neutrosophic real number ring. Also, we study the elementary algebraic properties of the defined two-fold algebra through its algebraic operations and substructures such as homomorphisms and ideals. [ABSTRACT FROM AUTHOR]

There is some uncertainty in the nature of tunnel excavation operations and this is an important part of the uncertainty due to unknown geological and geotechnical conditions. This paper proposes a risk assessment approach for problems which may arise during tunneling operations. A new model has been developed for the risk management of line 3 of the Mashhad subway (Iran’s second biggest city) applying a hybridization of game theory and fuzzy theory. Using questionnaires, appropriate responses to key risks are suggested based on modelling of game theory and categorized and ranked by importance. Linear programming problems are introduced to compute the average, optimistic, and pessimistic game values and their corresponding optimal strategies. This is the first work in this field to discuss geological and geotechnical risks in a hierarchy fashion. Hierarchy means that the ranking is done at different levels and each level has its own importance. The results indicate that providing the engineering geological profile along the route using obtained information and changing the excavation parameters based on it, is the most significant risk response. Using geophysical methods for subsurface studies and Excavating trenches for shallow investigations on the tunnel excavation route is ranked at the next level of importance. [ABSTRACT FROM AUTHOR]

This study analyzed data from the Korea Welfare Panel Study to identify changing patterns in social exclusion among South Korean youth and determine the influencing factors. The study examined 345 youth from 2012 to 2021. A fuzzy set theory and growth mixture model was used to measure social exclusion and identify patterns and the associated factors during this timeframe. The main findings are as follows. First, the social exclusion gap among South Korean youth that emerged a decade ago has continued, with high, middle, and low levels of exclusion identified. Second, the analysis revealed that looking at the demographics, being female, having less education and lower personal and household income increased the likelihood of falling into a relatively higher level of social exclusion. Based on the results, policy recommendations are suggested to mitigate the social exclusion gap among Korean youth. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TSVM) is an effective machine learning tool for classification problems. However, TSVM classifier works on empirical risk principle only and also while training, each sample contributes equally, even if it is a noise or an outlier. It does not incorporate the uncertainties associated with data into modeling and hence its generalization ability declines. To address these issues, intuitionistic fuzzy regularized least square twin support vector machine having intuitionistic fuzzy network has been proposed in this paper. The non-parallel classifiers are obtained by solving two systems of linear equations only rather than the solution of two quadratic programming problems as in TSVM, which leads to speed up the training process. Moreover, the method follows both structural risk and empirical risk minimization principles. In order to de-escalate the effect of pollutant patterns, their contribution of the patterns into learning the decision function has been made according to their importance in the classification. The significance of the training patterns is measured in terms of intuitionistic fuzzy numbers based on their geometrical locations and surroundings. The method is further extended to find non-parallel decision planes in the feature space using nonlinear kernel function, which also gives rise to the solution of two systems of linear equations. To show the efficacy of the proposed method, computer simulations on fourteen standard and six big UCI datasets using linear and Gaussian kernels are performed and their results have been compared with well-established methods in the literature. The experimental results are represented in terms of accuracy, computational time, F-measure, sensitivity and specificity rates. The outcomes demonstrate that the proposed method outperforms the existing methods and is also feasible for big datasets. The comparison and statistical inferences using two non-parametric: Friedman and Nemenyi tests, conclude that the proposed approach is fast and yields better generalization. [ABSTRACT FROM AUTHOR]

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of cubic soft (CS) algebra, CS o-subalgebra, and CS ideals within the framework of B-algebra. We provide comprehensive characterizations of these new structures, elucidating their unique properties and interrelationships. Specifically, we present detailed conditions under which a CS subalgebra can be classified as a closed CS ideal. Our analysis explores the intricate relationships among closed cubic soft ideals, cubic soft subalgebras, and cubic soft o-subalgebras. By doing so, we aim to provide a deeper understanding of how these structures interact and coexist within the broader context of B-algebra The findings offer significant insights into the application and theoretical underpinnings of cubic soft sets in algebraic systems, contributing to the ongoing evolution of fuzzy set theory and its applications in various mathematical domains. Our work not only broadens the scope of B-algebra but also enhances its utility in solving complex problems where traditional algebraic approaches may fall short. Through this exploration, we seek to advance the field and open new avenues for research and practical applications in mathematical sciences. [ABSTRACT FROM AUTHOR]

This paper's findings are related to geometric function theory (GFT). We employ one of the most recent methods in this area, the fuzzy admissible functions methodology, which is based on fuzzy differential subordination, to produce them. To do this, the relevant fuzzy admissible function classes must first be defined. This work deals with fuzzy differential subordinations, ideas borrowed from fuzzy set theory and applied to complex analysis. This work examines the characteristics of analytic functions and presents a class of operators in the open unit disk J η , ς κ (a , e , x) for ς > − 1 , η > 0 , such that a , e ∈ R , (e − a) ≥ 0 , a > − x . The fuzzy differential subordination results are obtained using (GFT) concepts outside the field of complex analysis because of the operator's compositional structure, and some relevant classes of admissible functions are studied by utilizing fuzzy differential subordination. [ABSTRACT FROM AUTHOR]

Quality of Life (QoL) is a multifaceted concept encompassing economic, social, environmental, psychological, and physical dimensions of an individual’s life, including personal living conditions, happiness, well-being, and life satisfaction. As a vital criterion for sustainable development and active social policy in countries, QoL has been significantly influenced by the dynamic technological evolution of social media. However, the comprehensive impact of social media, including its role in disseminating disinformation – a major social and socio-economic concern – on QoL remains underexplored. This research aims to develop a novel fuzzy model to assess the level of disinformation on digital platforms and its correlation with the population’s QoL. Employing a mathematical approach rooted in expert evaluation, this study leverages intellectual knowledge analysis and fuzzy set theory. Grounded in data from real respondents and knowledge-based models, this study pioneers an information model to evaluate inhabitants’ QoL, incorporating factors such as financial concerns, perception of disinformation, and its influence on digital platforms. The fuzzy estimation model, verified with data from 3,036 respondents, quantitatively assesses citizens’ QoL. An illustrative application of the model demonstrates its effectiveness. The findings are particularly valuable for policymakers, experts in economic and innovative development, aiding the creation of regulatory and monitoring mechanisms to foster sustainable economic growth and devise effective development strategies. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to identify different combinations of causal conditions (celebrity attributes) that explain our outcome: destination image. More specifically, three main research questions guide our work: (1) Which attributes should an outstanding sportsperson have to enhance the image of his/her country as a destination image? (2) Are these the same for different product categories? (3) Do tourists and residents differ? Design/methodology/approach: To this end, the fuzzy-set Qualitative Comparative Analysis (fsQCA) was used with a sample of 187 participants (105 tourists and 82 residents). Findings: Results show that some attributes of a sports celebrity are more critical than others in enhancing destination image. Those attributes of sports celebrities appearing in the intermediate and parsimonious analysis should be prioritized. This is the case of trustworthiness. Second, experience is a peripheral requirement (only appeared in the intermediate analysis). Third, attractiveness is unnecessary and an even and undesired attribute in many solutions. Fourth, when comparing tourists and residents, both groups value the role of football players, while residents also appreciate the role of marathon runners. Tennis players are the less relevant sports celebrities to build Spain's destination image. Originality/value: First, a new statistical analysis in the marketing discipline, QCA, has been used. The use of qualitative approaches to investigate destination images has been scarce. Second, the study of the role of sports celebrity endorsement on brand–place attachment has yet to be investigated. Third, studies about the role of residents in the image of a tourism destination/city are scarce. Tourists and residents must be investigated because they can benefit from sports celebrities' activities. [ABSTRACT FROM AUTHOR]

The best way to deal with complicated life scenarios that accompany the decision-making process is to update previous concepts constantly. Therefore, researchers must constantly discover powerful mathematical tools that suit the accompanying circumstances. In this regard, we combine both soft set, neutrosophic set, and interval setting under Q-two-dimensional universal information to introduce a new hybrid innovative model called interval valued-Q-neutrosophic soft sets. The core goal of this model is to keep the features of previous models like soft sets, neutrosophic sets, and Q-Fuzzy sets in dealing with the lack of uncertainty and neutrality associated with real-life issues. This new approach allows decisionmakers to employ interval-valued form with Q-two-dimensional universal information, which provides them with more stability and feasibility in describing uncertain information more completely and accurately. Under the our propose model, we discuss effectively set-theory operations such as subset, union, intersection, complement, AND operation, and OR operation for interval valued-Q-neutrosophic soft sets, as well as some special operations like the necessity and possibility operations of an interval valued-Q-neutrosophic soft sets. In addition, we presented many properties supported by numerical examples that explain how they work. Finally, this new model has been successfully tested in dealing with one of the medical diagnostic problems based on hypothetical data for a respiratory disease. Building an algorithm based on the aggregation operator for interval valued-Q-neutrosophic soft set data solved this issue (i.e., selecting the optimal alternative). [ABSTRACT FROM AUTHOR]

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of (∈, ∈) and (∈, ∈ ∨ q)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of (α, β)-fuzzy subalgebras and (α, β)-fuzzy ideals on equality algebras. Also, by using the notion of (∈, ∈)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of X, and we proved that the set of all classes of X by these order is a poset. [ABSTRACT FROM AUTHOR]

Let $ (X, f) $ (X , f) be a dynamical system, i.e. X is a compact metric space and f is a continuous self-map on X and let $ K(X) $ K (X) , $ M(X) $ M (X) and $ \mathbb {F}(X) $ F (X) be the sets of all non-empty compact subsets of X, Borel probability measures on X and upper semi-continuous fuzzy sets on X, respectively. Then $ K(X) $ K (X) , $ M(X) $ M (X) and $ \mathbb {F}(X) $ F (X) are metric spaces under Hausdorff metric, prohorov metric and level-wise metric, respectively. Therefore, $ (X, f) $ (X , f) naturally induces three new systems $ (K(X), \bar {f}) $ (K (X) , f ¯) , $ (M(X), \hat {f}) $ (M (X) , f ^) and $ (\mathbb {F}(X), \tilde {f}) $ (F (X) , f ~). In this article, we investigate the connection of $ (r,s) $ (r , s) -sensitivity, $ (r,s) $ (r , s) -asymptotic sensitivity, $ (r,s) $ (r , s) -Li-Yorke sensitivity and Δ-transitivity of $ (X, f) $ (X , f) and its induced systems $ (K(X),\bar {f}) $ (K (X) , f ¯) , $ (M(X),\hat {f}) $ (M (X) , f ^) and $ (\mathbb {F}(X),\tilde {f}) $ (F (X) , f ~) and we obtain some desired results. For instance, we prove that $ (K(X),\bar {f}) $ (K (X) , f ¯) is $ (r,s) $ (r , s) -sensitive ⇔ $ (\mathbb {F}^{1}(X),\widetilde {f_{g}}) $ (F 1 (X) , f g ~) is $ (r,s) $ (r , s) -sensitive for each $ g\in D_{m}(I) $ g ∈ D m (I) satisfying $ g^{-1}(1)=\{1\} $ g − 1 (1) = { 1 } ; $ (X,f) $ (X , f) is Δ-transitive ⇔ $ (K(X),\bar {f}) $ (K (X) , f ¯) is Δ-transitive ⇔ $ (M(X),\hat {f}) $ (M (X) , f ^) is Δ-transitive $ \Leftrightarrow \,(\mathbb {F}^{1}(X),\tilde {f}) $ ⇔ (F 1 (X) , f ~) is Δ-transitive. [ABSTRACT FROM AUTHOR]

In this manuscript we demonstrate interval-valued bipolar complex fuzzy set (IVBCFS) and then interval-valued bipolar complex fuzzy soft set (IVBCFSS), as a generalization of fuzzy set, interval-valued fuzzy set, bipolar fuzzy set, complex fuzzy set and soft set. We also initiate operational laws and basic results and properties for IVBCFS and IVBCFSS. Further explanation is given for the basic algebraic operations like complement, extended union, extended intersection, restricted union, and restricted intersection, AND product and OR product for IVBCFSS. Moreover, we demonstrate some fundamental aggregation operators like IVBCFS average aggregation, IVBCFS geometric and as well as their properties. To emphasize the usefulness and application of the system, we also develop the decision-making method and joint instances of the IVBCFSS (set-ups 1 and 2). In order to describe the effectiveness and influence of the approaching novel work, this study uses a comparative analysis of the new creating concept with prevailing ideas. [ABSTRACT FROM AUTHOR]

Monitoring equipment wear is an important problem that requires constant attention, since this process can lead to a decrease in its efficiency, accidents or breakdown. The problem of replacing equipment is a production problem, in which it is necessary to consider many factors that influence the efficiency of the enterprise itself. This paper examines various formulations of the equipment replacement problem: in the classical formulation of dynamic programming, in the stochastic formulation and fuzzy graph representation. The idea to solve the problem using periodic fuzzy graphs is proposed. We also consider the age of equipment when determining the wear coefficient, determined by the degree of belonging to a particular class of parameters defined in the formulation of the problem. Periodic fuzzy graphs allow considering the problem of replacing equipment not for one type of equipment, but for a complex of machines, which ensures the scalability of the classical dynamic programming problem under uncertain initial data. When determining the membership function, it is possible to consider those factors that may influence the solution of the optimization production problem. Setting the problem in a fuzzy form makes it possible to forecast and plan the activities of an enterprise for future periods. [ABSTRACT FROM AUTHOR]

Rough Set (RS) theory is a useful mathematical strategy to handle uncertainty. In 1982, Pawlak presented the idea, and numerous authors have undertaken in-depth studies on RS in both ordinary cases and fuzzy situations. In terms of both the theoretical investigations and the practical applications, progress in this field of RS theory has yielded favorable outcomes over the last three decades and it is typically considered to be an extension of classical sets. A universe in RS is separated by two subsets known as lower and upper approximations. Upper approximations are nonempty intersections of equivalence classes, whereas lower approximations are subsets of the set. In this study, rough sets are examined when the universe set has a ring structure. The main contribution of this study is to focus on rough fuzzy prime and semi-prime ideals of the gamma ring structure and explain certain respects of its upper and lower approximations. The goal of this research is to investigate some of the characterizations of prime and semi-prime ideals and prove some related results. Moreover, the study discusses rough fuzzy ideals (RFI) in Γ Residue class and gives some findings. [ABSTRACT FROM AUTHOR]

This study aims to examine sustainable portfolio selection for conservative investors. In this context, a two-stage approach is proposed. In the first stage, the sustainability scores of stocks are obtained by utilizing expert knowledge through a fuzzy multicriteria decision-making (FMCDM) approach abbreviated as R-FES. In the second stage, a robust optimization problem that takes into account the sustainability score vector, the sample mean vector and the sample covariance matrix is formulated. Moreover, the analytical solution of this problem is given under certain assumptions. In order to introduce the proposed robust theoretical approach, an application on BIST participation sustainability index stocks is made. In the application, it is seen that sustainable investment may not cause performance loss. In addition, the constraint of not taking short positions is found to improve performance while reducing risk and return. [ABSTRACT FROM AUTHOR]

This work has explored spectral analysis to view the relationship between the time series of surface temperature and total ozone concentration (TOC) over New Delhi from 1995 to 2005. The time series has a discernible spectral density when analysed using harmonic analysis. Between the surface temperature and TOC, a common cycle of period of 10 months has been noted for the years under investigation. In addition, a binary fuzzy relation method has been used to examine the relationship between surface temperature and TOC using membership matrices produced by max-min composition. Overall, a fuzzy set theoretic approach has established a connectivity between surface temperature and TOC, and a spectral analysis approach which falls under the category of frequency domain approach has established the existence of a common cycle between these two time series. [ABSTRACT FROM AUTHOR]

This article delves into the engagement of Afghans in Europe in diaspora organizations (DOs) and examines the factors influencing the varying levels of transnational involvement aiming Afghan DOs (ADOs). Through a fuzzy set qualitative comparative analysis (fsQCA) of 85 ADOs across Austria, Denmark, Germany, the Netherlands, Sweden and the United Kingdom, this study explores intricate configurations leading to transnational activities. Drawing from a diverse range of qualitative data sources, this study deciphers different causal pathways underlying diasporic transnational activities. The results show that although individual conditions do not singularly drive transnational activities, the analysis identifies specific configurations where external funding notably shapes these transnational activities. Particularly, the research reveals that organizations in Germany and the Netherlands have stronger transnational ties to their country of origin compared to ADOs in Austria and Sweden, which focus primarily on local activities. [ABSTRACT FROM AUTHOR]

We introduce soft v-ideals, soft s-ideals and soft vs-ideals over a Menger algebra of rank n. Moreover, we investigate several properties of each of the types of soft ideals. Furthermore, we prove that the collection of all soft vs-ideals forms a distributive lattice. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The significance of studying voting behaviour is underscored by its ability to gauge the continuity or divergence of electoral politics from historical trends, elucidating the real impact of the transformative ballot box, and contributing to the examination of democracy as a value among both masses and elites. Additionally, it aids in comprehending the intricate process of political socialization. Methods: An inherent strength of the rough set lies in its reliance solely on raw data, devoid of external inputs. The decision-theoretic rough set framework, an evolution of the rough set, has garnered widespread application across diverse domains, serving as a proficient tool for acquiring knowledge, particularly in navigating situations marked by vagueness and uncertainty. Despite the proliferation of mathematical models designed to discern people's voting behavior, a decision-based rough set recommendation remains noticeably absent in existing literature. This paper introduces an innovative three-way decision approach grounded in linguistic information for identifying voting behavior. The proposed approach is based on a hybrid probabilistic rough fuzzy model incorporating linguistic information and providing insights into voting patterns. Results: The three-way decision hybrid models are tested on people and a highly satisfactory result was achieved for identifying their voting behaviours. The justification of results was validated through the mathematical process. Conclusion: A practical illustration is provided to highlight the importance of this hybrid model and to confirm its usefulness in identifying and forecasting voting behaviour. [ABSTRACT FROM AUTHOR]

The environmental, social, and governance (ESG) rating method is a powerful tool that can help investors to judge the investment value of companies based on the information disclosure. However, mainstream ESG rating methods ignore the distinction between companies with incomplete information disclosure and companies without information disclosure, which decreases the initiative and enthusiasm of companies to disclose information. In this study, a self-disclosure ESG (SDESG) rating method is proposed to evaluate companies’ ESG performance capabilities. First, based on the fuzzy set, fuzzy data is defined and applied to the SDESG rating method. Second, analogous to the academic reward system of a university, a reward mechanism of disclosure is used in the SDESG rating method. Finally, the effectiveness and reliability of the SDESG rating method are demonstrated through Refinitiv’s case. The results show that the SDESG rating method can distinguish companies with incomplete information disclosure from companies without information disclosure and allow companies that proactively disclose information to obtain better ESG scores under each industry. The implications of the study would increase companies’ enthusiasm to disclose information and maintain transparency within a company. [ABSTRACT FROM AUTHOR]

Chinese Language learning grows ever more essential to develop the students' personalities and values as the curriculum, thereby improving teaching strategies based on students' learning preferences are more crucial. Students' participation in learning the Chinese Language is generally minimal and typically operates in a passive learning mode. The development of the Chinese Language instruction in these higher educational settings will be impacted by the absence of an organized strategy for teaching the Chinese Language. An algorithm is called the Fuzzy Pattern-driven Personalized Teaching (FPPT) has been proposed to identify the association between the students learning patterns and interests in the Chinese Language in the higher education for providing the personalized teaching to solve these challenges. Fuzzy sets are incorporated into FP-Growth for personalized the Chinese Language learning to improve the suggestions by considering the ambiguous preferences and the proficiency levels. The fuzzy pattern is unrevealed by implementing the Frequent Pattern (FP) growth algorithm to find patterns in the students learning activity and preferences so that personalized the teaching methods can be developed to meet the needs of each student and maximize their motivation for the language learning. Using the support and the confidence measures, these identified Fuzzy association relationships of student learning interest results in personalized the Chinese Language teaching in the higher education. The experimental results showed that the proposed FPPT system significantly improved each student's learning outcome, communication effectiveness, learning motivation, and the Language proficiency level. [ABSTRACT FROM AUTHOR]

In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the λ-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems. [ABSTRACT FROM AUTHOR]

There are many vague and uncertain issues in real-life. To address these problems, many models and theories have been developed. Therefore, the present study aims to describe the concept of trapezoidal fuzzy multi-number aggregation operators and also provide its application in architecture. Our main focus is on the trapezoidal fuzzy multi-number weighted arithmetic average (TFMNWAA) operator, the trapezoidal fuzzy multi-number weighted geometric average (TFMNWGA) operator and trapezoidal fuzzy multi-number hybrid aggregation (TFMNHA) operator. And then, we investigate the fundamental properties of the operators in detail such as idempotency, commutativity and boundedness. Then the notion of a new score function of ranking the trapezoidal fuzzy multi-numbers is defined. We apply the TFMNHA operator to multi-criteria decision-making trapezoidal fuzzy multi-number. Finally, a discussion is presented with a numerical example is provided to show its applicability and usefulness. [ABSTRACT FROM AUTHOR]

Environmental management is becoming a popular practice in many organisations. However, the transition from old to new practices does not come without any challenges. Numerous studies have argued that the process of adopting a new practice such as environmental management will depend on firms' absorptive capacity, i.e. the ability of firms to identify, acquire and transform external information and knowledge. However, absorptive capacity alone does not guarantee success. To deliver the intended outcomes, absorptive capacity works in conjunction with other internal and external factors. Based on a configuration perspective, this study used data from 107 manufacturing firms to identify an asymmetric role played by absorptive capacity with factors, such as firm size, decentralisation, customer engagement and global environmental awareness in supporting the practice of environmental management. This study contributes to the development of knowledge in environmental management literature and provides several practical recommendations. [ABSTRACT FROM AUTHOR]

The primary purpose of this paper is to introduce the concept of the fuzzy module of fractions and investigate a relationship between fuzzy modules of fractions and rough sets (RSs). In this respect, first, the concept of the soft module of fractions is introduced. Then, the idea of fuzzy approximations of the FS of a module of fractions is defined by using a soft module of fractions and obtaining a new hybrid model called multi-granulation soft rough FSs (MGSR-FSs) in a module of fractions. Moreover, the idea of a fuzzy upper rough module of fractions is introduced. However, it is important to note that the fuzzy lower approximation of a fuzzy module of fractions is not a fuzzy lower rough module of fractions. Several examples are provided to elaborate on the proposed notions. [ABSTRACT FROM AUTHOR]

The concept of q-rung orthopair neutrosophic set is introduced in this paper and fundamental properties of it are studied. Also the ordinary notion of topological space is extended to q-rung orthopair neutrosophic environment, as well as the fundamental concepts of convergence, continuity, compactness and Hausdorff topological space. All these generalizations are illustrated by suitable examples. [ABSTRACT FROM AUTHOR]

In this paper, we first propose the model of multi-leader–follower games with fuzzy goals involving fuzzy parameters and introduce its α -FNS equilibrium. Next, we shift our attention to the existence of α -FNS equilibrium and prove it by Kakutani's fixed point theorem. Finally, we illustrate an example to show that the equilibrium existence result is valid. [ABSTRACT FROM AUTHOR]

In this paper, we explore interval-valued fuzzy translation and multiplication in z-algebras, delving into their detailed properties through the application of the concepts of fuzzy zalgebras and fuzzy z-subalgebras in z-algebras. Our specific focus is on presenting the notions of int-val-fuz-translation and multiplication, along with elucidating their homomorphism properties within the scope of this work. Additionally, we investigate several results based on in-val-fuz magnified translation in z-subalgebras. [ABSTRACT FROM AUTHOR]

P.M. Pu and Y.M. Liu extended Moore-Smith's convergence of nets to fuzzy topology and Y.M. Liu provided analogous results to J. Kelley's classical characterization theorem of net convergence by introducing the notion of fuzzy convergence classes. In a previous paper, the authors of this study provided modified versions of this characterization by using an alternative notion of convergence of fuzzy nets, introduced by B.M.U. Afsan, named fuzzy net ideal convergence. Our main scope here is to generalize and simplify the preceding results. Specifically, we insert the concept of a fuzzy function ideal convergence class, L , on a non-empty set, X, consisting of triads (f , e , I) , where f is a function from a non-empty set, D, to the set FP (X) of fuzzy points in X, which we call fuzzy function, e ∈ FP (X) , and I is a proper ideal on D, and we provide necessary and sufficient conditions to establish the existence of a unique fuzzy topology, δ , on X, such that (f , e , I) ∈ L iff f I -converges to e, relative to the fuzzy topology δ. [ABSTRACT FROM AUTHOR]

In this study, we propose a new classification method by adopting some ideas originating from the fuzzy comprehensive evaluation (FCE). To make the FCE be a classifier, the class labels in classification problems are regarded as the evaluation remarks in the FCE, and the attributes in these two domains are regarded to be consistent. Then, to implement the FCE model B = W ∘ R and obtain an accurate classification result, on the one hand, a learning algorithm, which is based on the joint distribution of attribute values and is dynamic, is proposed to construct the fuzzy relational matrix R; on the other hand, equal weight is considered to constitute the weight vector W. Meanwhile, for a continuous dataset, the discretization method and the determination of the discretization class number corresponding to the proposed classifier are discussed. The proposed classifier not only innovatively extends the FCE to data mining but also has its own classification advantages, that is, it is easy to operate and has good interpretability. Finally, we perform some numerical experiments using publicly available datasets, and the experimental results demonstrate that the proposed classifier outperforms some existing classifiers. [ABSTRACT FROM AUTHOR]

This study provides the generalization of fuzzy real numbers by imposing the elevator's condition upon it's legs. Our aim is to construct three types of Lift Fuzzy Real Numbers, an extension of h-generalized fuzzy real numbers, to indicate medical signals, stock market values, and commercial establishment profits over time. It explores concepts like ɛ-cut, strong ɛ-cut, β-level set, and convexity, and presents a graphical representation based on profit earned by three industries. Appropriate numerical examples are provided to support the new ideas. It's interesting to note that Lift Fuzzy Real Numbers are also used to represent real numbers. Additionally, the connections between the Lift Fuzzy real numbers have been established. The new fuzzy real numbers offer an advantage in representing data sets not represented by existing fuzzy numbers. [ABSTRACT FROM AUTHOR]

Existing diffusion models can only do tasks for either restoration or binarization of degraded document images; in this paper, we pay close attention to the problem of simultaneous restoration and binarization. We first introduce a model of image formation for degraded document images, which decomposes a degraded document image into the product of background and foreground components. Then a weakly coupled nonlinear diffusion system is developed for simultaneous restoration and binarization of degraded document images. In this diffusion system, the first equation is used to estimate background component and the second equation is responsible for the foreground component. The restored and binarized images are finally obtained by the estimated background and foreground components, respectively. Two coupled diffusion equations are solved alternately by explicit finite differencing. The proposed model is tested on some degraded document images that represent five types of typical degradations including bleed-through, complex background, page stains, stamps and smeared ink, and is compared with eight closely related models for degraded document binarization, qualitatively and quantitatively. Experimental results illustrate that the proposed model has shown promising results in terms of restoration and binarization of degrade document images. • Model of image formation is introduced for describing degraded document images. • Nonlinear diffusion system is proposed for restoration and binarization of degraded text images. • Our model has shown promising results in terms of simultaneous restoration and binarization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The study of differential equation theory has come a long way, with applications in various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives to metric L r , which proved to be better in applications than approximate derivatives. However, most of the studies available are on Fuzzy Set Theory. In view of this, intuitionistic fuzzy L r -norm-based derivatives deserve study. In this study, the L r -norm-based derivative for intuitionistic fuzzy number valued functions is introduced. Some of its basic properties are also discussed, along with numerical examples. The results obtained show that the proposed derivative is not dependent on the existence of the Hukuhara difference. Lastly, the Cauchy problem for the intuitionistic fuzzy differential equation is discussed. [ABSTRACT FROM AUTHOR]

An intrusion detection method using rough-fuzzy set and parallel quantum genetic algorithm (RFS-QGAID) is proposed in this paper. The RFS-QGAID is applied to solve the serious problems of determining the optimal antibodies subsets used to detect an anomaly. To obtain a simplified antibodies collection for high dimensional Log data sets, RFS is applied to delete the redundant antibody features and obtain the optimal antibodies features combination. Then, the optimal attitudes are entered into the QGA classifier for learning and training in the following stage. At last, the detected Log antigens are fed into RFS-QGAID, and we can classify the intrusion types. With RFS-QGAID, we give the simulations, the results on real Log data sets show that: the higher detection accuracy of RFS-QGAID is higher detection accuracy, but the false negative rate is lower for small samples sets, the adaptive performance is higher than other detection algorithms. [ABSTRACT FROM AUTHOR]

The q-rung linear Diophantine fuzzy set is a recently developed tool to handle with uncertain and vague information in real-life issues and can be applied for reference parameter-based opinions. Similarity measures determine distance with dimensions that represent features of the objects. Despite the importance of exponential function-based similarity measures, there is no satisfactory formulation for q-rung linear Diophantine fuzzy sets in the literature. This paper proposes similarity measures based on exponential function for q-rung linear Diophantine fuzzy sets and thus presents the first formulas for calculating the similarity coefficient between two q-rung linear Diophantine fuzzy sets. The salient features of the new similarity measures are axiomatically addressed to ensure their good performance. Also, they are applied to the clustering problem and the results are analyzed. A comparative study is established and thus several advantages of the proposed similarity measures are discussed. [ABSTRACT FROM AUTHOR]

We explore switching techniques between q-fractional fuzzy sets (qFr sets) and various other classes of fuzzy sets to establish connections and provide a comprehensive framework. In particular, we examine the relationships between qFr sets and interval-valued fuzzy sets (IVFS), type 2 fuzzy sets(T2FS), intuitionistic fuzzy sets(IFS), Pythagorean fuzzy sets(PFS), q-rung orthopair fuzzy sets (q-ROFS), and linear diophantine fuzzy sets(LDFS). By examining these interconnections, we aim to understand better qFr sets and their applications in a wide range of fuzzy systems. It is possible to convert qFr sets into other fuzzy set models using the derived switching techniques, facilitating the utilization of existing methods and algorithms. The versatility of qFr sets, combined with the bridging techniques presented, holds promise for addressing complex problems in decision-making, pattern recognition, and other applications where uncertainty and imprecision play significant roles. Through case studies and practical applications, we illustrate the effectiveness and usefulness of the proposed switching techniques, showcasing their potential impact on real-world scenarios. [ABSTRACT FROM AUTHOR]

In literature, several models which can handle uncertainty in datasets have been introduced. Fuzzy set introduced by Zadeh in 1965, is one of the earliest such models and Atanassov generalised it by introducing the notion of Intuitionistic fuzzy sets(IFS) in 1986. However, these models are handicaped due to their inadequacy as parameterization tools. The notion of Soft sets (SS) was introduced by Molodtsov in 1999 to solve this problem. Almost at the same time, Neutrosophic set (NS) model was introduced by Smarandache, which is a huge generalisation of IFS. As has been the practice, the hybrid model of SS and NS was proposed to frame the notion of Neutrosophic Soft Set (NSS) by Ali and Smaranche in 2015 and studied their properties. Since its inception, one of the major areas of application of Soft Sets has been that of Multi-criterian Decision Making (MCDM). Many problems in MCDM were solved by using hybrid models of SS. Following this trend, in this paper, we develop an algorithm basing upon NSS to handle the problem of MCDM in the selection of faculty through an interview prcess. For this, we had to introduce an improved score function which is used to rank the candidates basing upon several of their characteristics including interview perfromances. This application is better handled by the NSS model as is evident from the results. We illustrated the superiority of our proposed algorithm by providing a comparative analysis with many exieting algorithms in the literature. [ABSTRACT FROM AUTHOR]

Many problems of practical interest can be modeled and solved by using interval-valued fuzzy graph (IVFG) algorithms. An IVFG is a very useful and effective tool for studying various calculations, fields of intelligence, and computer science, such as networking, imaging, and other fields, such as biological sciences. In different applications, they present an appropriate construction means. There were limitations in the definition of fuzzy graphs (FGs), which prompted us to propose a new definition for IVFGs. Some interesting properties related to the new IVFGs are investigated, and enough conditions under which the level graph on IVFGs is equivalent are obtained. Therefore, in this study, we present the properties of a level graph (LG) of an IVFG, and four operations, the Cartesian product (CP), composition (CO), union, and join, are investigated on it. Today, in a treatment system, one of the issues that can be very valuable and important to the quality of service to patients is finding qualified and efficient people in each department, which is not an easy task. But the interval-valued fuzzy graph, as an important fuzzy graph, can help us by considering the ability of each person in the form of intervals of numbers and the effectiveness of each one on the other (according to the relationships between them) in order to find the most worthy people. So, an application of IVFG to find the most effective person in a hospital information system has been introduced. [ABSTRACT FROM AUTHOR]

The rapid expansion of extensive brackish water aquaculture (BA) in Indonesia has created an urgent need to develop effective and reliable methods to evaluate and select sites suitable for aquaculture development. The lack of supporting spatial data at appropriate scales has limited the application of GIS-based multi-criteria evaluation methods (MCEs) in Indonesia. This study presents alternative fuzzy-based Geographic Information System (GIS) methods to evaluate and select sites suitable for extensive brackish water aquaculture. This study successfully produced fuzzy set maps from a water availability sub-model, a land conversion sub-model and a green belt buffer zone sub-model. With grades of membership, the fuzzy set maps provide smooth class boundary representation, which creates more options for decision-making than a map classified with crisp logic. Combining these sub-models produced an overall site suitability map at the scale of 1:50,000 for the study region. This final suitability map effectively excluded more than 95% of the unsuitable area for BA. This broad-scale site suitability assessment approach is a helpful planning tool to promote Indonesia's sustainable development of extensive brackish water aquaculture. It identifies possible conflicts in land uses and considers conservation issues early in the planning process. The output can be used to scope research areas for more detailed investigations in countries where BA is a vital livelihood. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of fuzzy Sβ - compactness. Some of the basic properties and characterization theorems would be investigated of this newly defined compactness in fuzzy setting. We would also introduce and study fuzzy Sβ - closed spaces. [ABSTRACT FROM AUTHOR]

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

In this study, we investigate a possible relationship between fuzzy differential subordination and the theory of geometric functions. First, using the Al-Oboudi differential operator and the Babalola convolution operator, we establish the new operator BS α , λ m , t : A n → A n in the open unit disc U. The second step is to develop fuzzy differential subordination for the operator BS α , λ m , t . By considering linear transformations of the operator BS α , λ m , t , we define a new fuzzy class of analytic functions in U which we denote by T ϝ λ , t (m , α , δ) . Several innovative results are found using the concept of fuzzy differential subordination and the operator BS α , λ m , t for the function f in the class T ϝ λ , t (m , α , δ) . In addition, we explore a number of examples and corollaries to illustrate the implications of our key findings. Finally, we highlight several established results to demonstrate the connections between our work and existing studies. [ABSTRACT FROM AUTHOR]

Given a uniform space (X, U), we introduce, from the uniformity U, some uniformities on the set F(X) of all normal, upper semicontinuous with compact support fuzzy sets on X: the Skorokhod uniformity, the level-wise uniformity, the endograph uniformity and the sendograph uniformity. For metric spaces we prove that these uniformities coincide with the uniformities induced by the Skorokhod metric (the level-wise metric, the endograph metric and the sendograph metric, respectively). We study completeness of this class of uniform spaces. [ABSTRACT FROM AUTHOR]

In this research work, we have introduced a new notion of weighted hesitant bipolar-valued fuzzy soft set (WHBFSS) as a generalization of hesitant bipolar-valued fuzzy soft set (HBFSS), and we examine some of its fundamental properties in detail. We've also defined some novel notions of the root mean square difference operator (RMSDO), root mean square difference score matrix (RMSDSM), and weighted score, and using these novel notations, we have proposed an advanced and adjustable decision-making method (DMM) for solving real-life decision-making problems (DMPs) based on both HBFSS and WHBFSS. A real-life example is provided to demonstrate the validity of our suggested method. Finally, a comparative analysis of our approach with an existing method is provided. [ABSTRACT FROM AUTHOR]

The author proposes an approach to finding numerical estimates of the credibility of fuzzy knowledge in fuzzy inference systems. An "input–output" system is modeled by means of fuzzy logic. According to Mamdani's rule, the system's output is found in the form of fuzzy knowledge with subsequent calculation of its credibility. Elements of the probability theory of fuzzy events are used to calculate the credibility of fuzzy knowledge. An example of calculating the credibility of fuzzy knowledge is given. [ABSTRACT FROM AUTHOR]

(1) Background--At present, the distribution of forestry resources in China is uneven, and the forestry development in some regions has problems such as large resource input, backward production technology and low production efficiency. How to find a way to promote the improvement of green total factor productivity of regional forestry has become an urgent issue for the forestry authorities of local governments. (2) Methods--Based on the technology-organization-environment (TOE) theoretical framework, six antecedents affecting green total factor productivity of regional forestry were selected. Based on the data of 29 provinces (autonomous regions and municipalities) in China from 2016 to 2020 (excluding Tianjin, Xizang, Hong Kong, Macao and Taiwan), this paper used fuzzy set qualitative comparative analysis to study the configuration paths of green total factor productivity improvement of regional forestry. (3) Results--The consistency index values of all the conditional variables are less than 0. 9, which indicates that a single factor cannot constitute the necessary condition for achieving high regional forestry green total factor productivity. Six antecedents constitute three configuration types to improve regional forestry green total factor productivity. The overall consistency of these three configuration types is 0. 872 and the total coverage is 0.729. Among them, the technology-driven path mostly exists in the eastern region, the configuration-driven path of "average forestland size + forestry carbon sinks" mostly exists in the central region, and the configuration-driven path of "financial support + forestry carbon sinks" mostly exists in the western region. If the average forestland size of operators and the forestry carbon sinks development as the core conditions exist, then the government financial support and the forestry utilization of foreign capital can replace each other in the process of achieving a high level of regional forestry green total factor productivity. The condition of "low average forestland size" exists in both of the two configuration types leading to low forestry green total factor productivity, and the two configurations can cover 73. 2% of the samples, indicating that the low average forestland size of operators is an important factor restricting the improvement of forestry green total factor productivity in most regions. (4) Conclusions and Discussions--Based on the above analysis, the following suggestions are put forward: First, select different configuration paths of forestry green total factor productivity improvement according to the forest resource endowments in different regions. For example, the regions belonging to the technology-driven configuration path can promote the application of digital technology in forestry production scenarios and integrated innovation by increasing digital infrastructure construction and forestry green technology innovation incentives, so as to promote the improvement of regional forestry green total factor productivity through digital development. Because the development of forestry carbon sinks is the core condition for improving forestry green total factor productivity in most central and western regions. Therefore, the local forestry authorities should simplify the forestry carbon sinks trading procedures, reduce the transaction costs of forestry operators, and stimulate their active participation in carbon sinks trading. Second, optimize the structure of foreign investment in forestry, change the previous single mode of driving regional forestry development mainly relying on financial capital investment, and give full play to the substitute role of forestry foreign investment in the improvement of regional green total factor productivity. Third, speed up the reform of regional forest property rights transfer mechanism, and improve the scale and efficiency of average forestland of forestry operators. [ABSTRACT FROM AUTHOR]

In the present scenario, the main aim of each and every organization is to be competitive, eco-friendly, and sustainable in order to run effectively and efficiently. Therefore, to meet and fulfill the above objectives, each organization must identify and choose the appropriate and best green and sustainable supplier, as a green supplier considers green technology, green products, green packaging, etc., while a sustainable supplier considers all three characteristics of sustainability, namely social, economic, and environmental. The problem of the evaluation and selection of green and sustainable suppliers is an example of a multi-criteria decision-making (MCDM) problem. In this research paper, to handle the uncertainty hidden in the green supply chain, the extended version of a MCDM technique named fuzzy additive ratio assessment (F-ARAS) is implemented for the evaluation of the relative weights of the green and sustainable supplier selection criteria, namely social, economic, and environmental, and also to determine the best green and sustainable supplier through fuzzy theory by using linguistic terms, which includes the application of interval-valued triangular fuzzy numbers (IVTFNs) in an organization. Finally, the technique, F-ARAS, has performed well and enables the organization's managers to attain their required solution and final decision. [ABSTRACT FROM AUTHOR]