Nowadays, Z-numbers are known as the most powerful tool for describing the uncertainty process concerning the degree of confidence. In this matter, regression based on Z-numbers is called an essential issue because it establishes a functional relationship among Z-number variables. More importantly, quantile regression is an efficient statistical method for estimating and inferring conditional quantile functions. Thus, this paper aims to develop quantile regression under three models. The first model encompasses explanatory variables, response variable, and Z-number parameters. The second one includes explanatory variables, a Z-number response variable, and crisp parameters. Finally, the third one includes crisp explanatory variables, response variable, and Z-number parameters. The idea of the method for the first model is to employ the mean squared error (MSE) method. On the other hand, the idea of the second model is to utilize a new ranking function. The concept of the third model is to propose a loss function between numbers based on Z-numbers, which can render some quantiles based on Z-numbers. Then, a quantile regression model is fitted based on the proposed loss function. Furthermore, two indices are defined to assess the goodness of fit of the optimal quantile regression models based on Z-numbers. Meanwhile, several examples are solved to assess the efficiency of the proposed models. Eventually, the applicability of the proposed approach is surveyed in heart disease prediction modeling based on a realistically simulated dataset, and future validation on real patient data is recommended. The obtained results reveal that the proposed method outperforms in every condition where regression based on Z-numbers fails and also provides in-depth results.
Wireless body area networks (WBANs) play a vital role in saving lives by accurately measuring physiological information in a cost-effective manner. However, reliability and energy consumption remain major constraints in WBANs. Many researchers have claimed that transmission through relay nodes can mitigate these constraints. Therefore, this work proposes a fuzzy-based relay MAC protocol based on the IEEE 802.15.6 model. Fuzzy rules have been used to select the relay node, considering three attributes: residual energy, received signal strength indicator (RSSI) and data rate. The combination of predefined and fuzzy-based opportunistic relay nodes has significantly reduced data relaying failure rates, leading to an increased packet delivery ratio. Through simulation, the performance of IEEE 802.15.6, DMTM-MAC, ADT-MAC and the proposed adaptive fuzzy-based MAC (AFBM) has been compared and analysed. The results indicate that AFBM effectively reduces packet delivery delay and energy consumption while improving data relaying and packet delivery ratios.
A neutrosophic distance measure using average functions is defined, and the metric axioms are verified by discussing its properties on a neutrosophic structure. Further, the similarity measure’s axioms are also derived for the complement of the proposed distance measure. This research paper presents a novel methodology for identifying suitable attributes of corresponding alternatives in decision-making problems using neutrosophic distance measure values. As an application, a numerical model is offered for the neutrosophic evaluation of smartphone selection by customers. Moreover, it is perceived that the decision of the proposed distance measure is consistent with the results derived from other existing distance measures.
Organizational decisions, often originating from diverse groups of managers with varying criteria, encounter challenges due to the inherent ambiguity in human judgments, particularly those involving preferences. This paper proposes a nuanced solution using a heterogeneous fuzzy group decision-making method, accommodating diverse criteria based on real numbers, interval numbers, triangular fuzzy numbers, trapezoidal fuzzy numbers, and intuitive fuzzy numbers. Two numerical examples validate the method’s effectiveness, demonstrating noteworthy consistency. Utilizing Spearman’s rank correlation coefficient as a metric underscores its robust agreement with established methods. The subsequent analysis underscores the method’s adeptness in handling decision-making complexities within diverse groups, thereby contributing significantly to the understanding and management of organizational relationships in today’s context.
This paper presents a novel hybrid control strategy for a specific class of nonlinear systems based on interval Type 3 fuzzy logic systems (IT3-FLSs), and its effectiveness in the management of Type 1 diabetes is demonstrated. The main achievements of this work can be summarized as the following main points. First, an online system identification framework whose inputs are only from the measurable signals of the system, including glucose concentration and administered insulin, is introduced using a newly developed IT3-FLS. Second, the system identification method is independent of the type of specific model or a predefined model and aims to estimate the measurable output of the system to predict the system behavior. Third, a novel hybrid controller consisting of a final control signal steady-state controller, a proportional controller, a step-forward predictive controller, and an adaptive compensator is developed. Fourth, through Lyapunov-based stability analysis, adaptive learning rules are derived for both IT3-FLS identifier and adaptive compensator, and finally the asymptotic stability of the closed-loop system will be guaranteed. The proposed method is validated on a large range of virtual Type 1 diabetes patients modeled by the modified Bergman model (MBM) under significant uncertainties, noisy glucose measurements, and perturbations such as food intake. Comparative simulation results confirm the superior performance and robustness of the proposed hybrid strategy over existing insulin-glucose control approaches.
Cross-entropy is a useful tool for quantifying the divergence between systems. In this paper, we develop an interval-valued q-rung orthopair fuzzy cross-entropy measure. Subsequently, the satisfaction-based cross-entropy (SCE) is derived from the compromise rule, integrating decision-makers’ risk preferences to enhance rationality. In addition, we introduce a novel boundary cross-entropy (BCE) metric specifically designed for interval-valued q-rung orthopair fuzzy numbers (IVq-ROFNs). Building on these measures, we propose a cross-entropy-based modified multiattributive border approximation area comparison (MABAC) method. One of the prominent components of the developed method is to determine the weights of attributes depending on the coefficient of variation method and the cross-entropy, and the other is to develop a new SCE-based model to determine the weights of experts. Moreover, for the modified MABAC method, the values of the boundary approximation area (BAA) matrix are obtained by the q-RIVOFWG operator, and the BCE values between alternatives are derived from the BAA matrix. The final decision outcomes are determined based on the total BCE values. The proposed MABAC group decision-making (GDM) method is verified through a course learning evaluation case study. Its practicability and effectiveness are demonstrated via comparative analysis, sensitivity analysis, and time complexity analysis.
Pythagorean hesitant fuzzy sets (PHFSs) effectively represent uncertain information in decision-making by accommodating situations where the sum of membership and nonmembership degrees exceeds 1, provided their squared sum remains at most 1. This study proposes a novel distance measure for PHFSs and rigorously demonstrates its rationality and validity. By integrating this distance measure with conflict analysis, we define the conflict degree in Pythagorean hesitant fuzzy environments. Then a new multicriteria decision-making (MCDM) method is developed to address problems with completely unknown criterion weights, avoiding artificial data manipulation based on decision-makers’ risk preferences. The proposed distance measure serves as a key tool for quantifying dissimilarity between PHFSs while maintaining decision consistency and reliability. Finally, an illustrative example of habitat selection evaluation for endangered species, accompanied by comparative analysis, validates the effectiveness and feasibility of the proposed method.
This paper presents a generalized framework termed the multidimensional topological measure space (MDTMS), developed through multidimensional fuzzy sets, multidimensional topology, and an associated distance measure. The suggested framework enhances traditional fuzzy models by facilitating a more nuanced representation and examination of intricate, multiparameter data. Essential core components, including multidimensional fuzzy topology, basis, and subspace, are rigorously described within this framework. We create many mathematical instruments to facilitate study inside the MDTMS framework, encompassing concepts of multidimensional carrier, closure, core, and interior. Additionally, we analyze sequences of multidimensional fuzzy sets and introduce two forms of convergence, together with their fundamental characteristics. To illustrate the practical significance of the proposed framework, we introduce a decision-making methodology grounded in Euclidean multidimensional distance functions incorporated within the MDTMS structure. Examples are shown to demonstrate the relevance and efficacy of the proposed notions.
This paper addresses critical limitations in the application of intuitionistic fuzzy sets (IFSs) for complex decision-making problems under uncertainty. While IFSs offer a robust framework for modeling imprecision through membership, nonmembership, and hesitancy degrees, existing methodologies often simplify the multiplication of intuitionistic fuzzy numbers (IFNs) to linear approximations, overlooking potential nonlinear interactions. Furthermore, a comprehensive signed distance measure for triangular IFNs (TIFNs) and a method for intuitionistic fuzzy nonlinear signed distance are largely absent from the literature. To bridge these gaps, this study develops novel equations for the multiplication of two IFNs, treating the result as a nonlinear IFN, thereby enhancing the precision of fuzzy arithmetic. The practical utility of the proposed methodology is demonstrated through an application involving sustainable business model innovations (SBMI) evaluation under ESG principles. The numerical example is provided, showcasing how the developed techniques can provide an accurate and nuanced assessment for complex multicriteria decision-making problems.
Transportation Problem (TP) is considered a combinatorial optimization problem, and its aim is to minimize the total transportation cost from several sources to different destinations. In this paper, an intensive literature review of the TP is presented in detail with an enhancement of the novel heuristic entitled Dhouib-Matrix-TP1 (DM-TP1) to solve the TP under a hexagonal fuzzy environment. Indeed, all parameters of the TP-such as transportation cost, demand, and supply-are represented using hexagonal fuzzy numbers (HFNs), which offer a richer structure for modeling uncertainty with less information loss compared to triangular or trapezoidal fuzzy numbers. To convert these HFNs to crisp ones, the centroid ranking function is used. After that, the DM-TP1 method is applied to rapidly find an initial basic feasible solution using the original metric (Average-Min). Experiment results of DM-TP1 on different literature Hexagonal Fuzzy Transportation Problems (HFTPs) prove its performance. Moreover, DM-TP1 illustrates graphically the generated solution and allows the decision maker to ergonomically handle the TPs under HFNs.
In this research paper, a dynamically self-adaptive Type 1 fuzzy logic system (T1FLS) is presented to simulate the 3D printing fused deposition modelling (FDM) process. The need for such a dynamically self-adaptive system stems from (i) the dynamic nature of manufacturing processes, in particular, 3D printing processes; (ii) the fact that data may not be sufficient or may not cover the whole space at the early stage of model development; and (iii) the need to know how a model behaves in the space examined. Therefore, the impacts of four FDM parameters (i.e., the number of shells, infill density, print speed and raster width) on different mechanical properties are first studied for five different materials, namely, electrostatic dissipative acrylonitrile butadiene styrene (ESD-ABS), polyether imide (PEI) Ultem 1010, amorphous polyether ketone ketone (PEKK-A), PEI Ultem 9085 and polycarbonate (PC). T1FLSs are then developed to map such parameters to the mechanical properties in a way that allows the prediction of these properties. The system performance is then assessed in the space investigated, as a step used to develop dynamically self-adaptive T1FLSs using a new data set that expands the space used to develop the T1FLSs. The development of such dynamically self-adaptive T1FLSs has improved the predictive performance by an overall average improvement value of 2.7% in the coefficient of determination.
Users expect software to be error-free; however, preventing faults in software while being developed is difficult. Although predicting faults in software is arduous, it radically helps to improve the software quality. Due to the complexity of software, time, and budget limitations, such prediction helps to deliver more robust and error-free software with lower expenses. This paper introduces an iterative method based on fuzzy systems and machine learning to predict software faults. High interpretability, transparency, balancing data, and finding the best interval for converting numerical features to fuzzy features are basic challenges for predicting software faults. The proposed framework is split into four phases. In the first phase, the crisp inputs are converted to fuzzy sets. In the second phase, a membership function is constructed using triangular fuzzy sets. In the third phase, training data are balanced, and fuzzy rules are generated. In the last phase, the similarity of inputs with the rules’ antecedents is calculated, and the fired rules are aggregated to label the test data. Eclipse, Promise, and Travis repositories are evaluated with the proposed method. The calculated AUC of the proposed method on Promise, Travis, and Eclipse datasets are, respectively, equal to 89%, 62% and 87%, which are comparable to the results obtained by deep learning methods but with higher interpretability and transparency.
Multiobjective transportation problem (MOTP) seeks to optimize multiple, often conflicting objectives within transportation and logistics systems. However, in real-world scenarios, parameters such as transportation costs, time, availability, and demand are inherently uncertain. To address these uncertainties, various extensions of fuzzy logic such as intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), Fermatean fuzzy sets (FFSs), and hesitant fuzzy sets (HFSs) and more have already been applied to MOTPs. Despite these advancements, the dual HFS (DHFS) has not yet been incorporated into MOTP. This research article introduces the novel concept of dual hesitant fuzzy MOTP (DHFMOTP), utilizing DHFS for the first time in this MOTP. A new score function for DHFS and an accompanying algorithm are developed effectively to solve the DHFMOTP. To validate the proposed methodology, two numerical problems are solved. Computed results demonstrate the significant improvements. The proposed score function and algorithm for DHFMOTP consistently yielded more optimal results than the existing methods. Future studies could explore the integration of other advanced fuzzy extensions and hybrid algorithms for further improvement of decision-making efficiency in transportation problems under uncertainty.
Industrial waste involves any hazardous substance, chemical, or byproduct and waste discharged during the operation of an industry. Due to its nature and probable detriment to the environment, industrial waste is a great matter of concern for governments all over the world. Selection of industry-linked industrial waste management strategies (IWMSs) is the main objective of this research endeavor. Applying greater generality in the dimensions of the abovementioned applications could potentially enhance a lot of their efficiency. Einstein norms/application of Einstein operations have not been effectively applied within the complex spherical fuzzy sets (CSFSs) framework as such; this study now advances the application of Einstein operators in CSFS which would provide an adiaphorous approach to solving issues related to decision-making problems (DMPs). The actual situations in which decisions are made invariably present numerous conflicting factors, which complicate the process even further. The methodology of multiattribute group decision-making (MAGDM) is an essential means of handling such situations. This paper deals with the challenge pertaining to MAGDM and utilizes the established Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). In order to aid successful problem-solving, new aggregation operators are proposed, namely, complex spherical fuzzy Einstein weighted averaging (CSFEWA) operator, complex spherical fuzzy Einstein ordered weighted averaging (CSFEOWA) operator, and complex spherical fuzzy Einstein hybrid weighted averaging (CSFEHWA) operator.
This study introduces several operations on n-dimensional fuzzy sets, including union, intersection, and complement, and examines the validity of De Morgan's law within this framework. To further elucidate the conceptual underpinnings, the study also presents illustrative examples of t-norm, t-conorm, and negation operations on n-dimensional fuzzy sets. Furthermore, the paper proposes a novel structure termed the n-dimensional fuzzy soft sets, which extends the concepts of both soft sets and n-dimensional fuzzy sets. The foundational properties of n-dimensional fuzzy soft sets are explored in detail, and various operations such as union, intersection, negation, t-norms, and t-conorms are defined and analyzed within this context. Additionally, the study discusses relevant laws, including De Morgan's law as they pertain to the proposed structure. To demonstrate the practical utility of this new model, the study presents its application in decision-making scenarios, such as the selection of the most suitable vendor for a critical project. A comparative analysis with existing decision-making strategies based on intuitionistic fuzzy soft sets and interval-valued fuzzy soft sets highlights the enhanced effectiveness and robustness of the proposed methodology.
Fuzzy set theory is a versatile concept that finds applications in various fields such as mathematics, engineering, control engineering, computer science, and artificial intelligence. When there is uncertainty in the data and/or information available to make a decision, fuzzy numbers play a significant role. They have a major influence on the decision-making process. Hence, the ranking of fuzzy numbers become more significant in solving such problems. As the uncertainty becomes more, the role of fuzzy soft sets plays an important role. There are many ranking techniques for fuzzy numbers but it is necessary to rank the trapezoidal fuzzy soft sets (TrFSSs) to deal with uncertainty. The present paper focuses on introducing a novel ranking method specifically designed for TrFSSs. Furthermore, some examples are presented illustrating the application of this ranking method. Furthermore, the paper explores the use of the proposed ranking method in solving the multicriteria decision-making problems. So far, this is the first ranking method for TrFSSs.
Type-3 fuzzy logic has been recently used in many control methods. The type-3 fuzzy controller enhances the handling of uncertainty and improves robustness by integrating fuzzy sets with fuzzy membership functions. The latest approaches using type-3 fuzzy logic in the field of control are studied and evaluated. An overview of developments in control methods based on type-3 fuzzy logic is also provided. It is shown that type-3 fuzzy system has many advantages compared to type-1 and type-2 fuzzy. The advantages and challenges of using type-3 fuzzy logic are identified and discussed. The studies are classified according to the type of control approach, as well as by the type of control applications. Finally, the main achievements, open challenges, and future directions and impacts are identified, to provide important guidance for interested researchers.
For sustainable growth, investments in renewable energy must be maximized. Maximizing investments in renewable energy opens the door to a more successful and environmentally friendly future. Analyzing technological viability, cost-effectiveness, regulatory compliance, and environmental impact are all part of this optimization process. This paper delves into a sophisticated methodology designed to tackle uncertainties in decision-making by leveraging the innovative concept of Pythagorean hesitant fuzzy sets (PHFSs). We defined aggregation operations and distance measures for PHFS. After that, we introduced Measurement of Alternatives and Ranking According to the Compromise Solution (MARCOS), a novel methodology under PHFS, it is a robust tool acknowledged for navigating complex decision scenarios with multiple criteria. Following that, we showcased a case study on enhancing renewable energy investments through an AI-based strategy for sustainable development, utilizing the newly developed MARCOS algorithm. The study highlights the significance of its adaptability and efficiency in practical applications. Furthermore, we compared this methodology with the Technique for Establishing Order Performance by Similarity to the Ideal Solution (TOPSIS), offering insights into their respective strengths. This offers a concrete demonstration of its real-world utility and potential impact in decision-making scenarios. Finally, in the last, we conclude the whole study.
The domain of decision-making theory has made significant progress, especially within the industrial and management fields. Diverse decision-making challenges such as multicriteria decision-making (MCDM), multiattribute decision-making (MADM), and multiattribute group decision-making (MAGDM) have been thoroughly examined, equipping decision-makers with effective strategies for tackling these issues. In the context of the automotive industry, a specific hurdle emerges when identifying the most suitable site for establishing a warehouse to store goods destined for multiple destinations. This article addresses a scenario amid uncertainty, leveraging substantial data. Neutrosophic sets (NSs) emerge as a comprehensive tool for effectively managing the imprecision inherent in such data. Among these sets, single-valued neutrosophic sets (SVNSs) stand out due to their adeptness in handling inconsistent or incomplete data. The octagonal single-valued neutrosophic numbers (OSVNNs) has a new tool for representing the uncertainty information in a simplified manner. Octagonal structure allows for representing different distinctions of truth, neutrality, and falsity of any complex situation and it is an efficient tool to compare different options based on their level of ambiguity. They have a wide range of applications in various fields, becoming increasingly important in addressing many difficult and uncertain issues. The article aims to propose a new ranking function for OSVNNs to convert the OSVNN data into precise values, drawing from the existing mean interval method (MIM). The conventional decision-making approaches such as weighted sum model (WSM), weighted product model (WPM), technique for order of preference by similarity to ideal solution (TOPSIS), and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) are employed to obtain the optimal warehouse location using OSVN application. Furthermore, it demonstrates the application along with the proposed ranking function using the software MATLAB to determine the most favorable alternatives. Finally, sensitivity analyses are performed to assess how different scenarios could impact the optimal location selection for automotive logistics.
This paper introduced a novel concept of q-rung orthopair fuzzy (q-ROF) metric spaces, in connection with the idea of q-ROF sets, which generalizes well-known concepts of fuzzy metric spaces and intuitionistic fuzzy metric spaces. An elaborated example has been provided representing the increase in selection space due to the q-ROF metric and limitations for the case of intuitionistic fuzzy metric space. We have presented the definitions of introduced concepts along with examples, so they are way more understandable for readers. Some basic topological results have been defined and proved for q-ROF metric space. The concept of q-ROF Menger boundedness is introduced, and its application in game theory is presented. Also we have presented the significance of introduced metric compared to existing versions of fuzzy metric in the consequent sections. Baire’s theorem and uniform limit theorem are also established in the perspective of q-ROF metric spaces. An application of the obtained results in the field of game theory is also presented to draw the attention of investigators searching new fields of research.
