Fuzzy Operators Research Articles

Convex (L,M)-fuzzy remote neighborhood operators

Convex (L,M)-fuzzy remote neighborhood operators

Multi-attribute decision making method based on the generalised spherical fuzzy Heronian operators

Traditional fuzzy decision-making methods still have certain limitations in practical applications, such as the problem of the sum of attribute memberships and non-memberships possibly exceeding 1. Additionally, due to the attributes in real decision-making processes often not being mutually independent but rather exhibiting a certain degree of correlation, traditional fuzzy decision-making methods may not fully capture and express this complexity. To overcome these limitations, this paper proposes a new multi-attribute decision-making method addressing the problem of integrating information with correlated attributes in the generalized spherical fuzzy environment. Initially, by combining the generalized spherical fuzzy set with the Heronian averaging operator, the paper introduces the generalized spherical fuzzy weighted Heronian averaging operator and thoroughly discusses some valuable properties of both operators, providing corresponding proofs. Furthermore, the paper proposes the multi-attribute decision-making method using the generalized spherical fuzzy weighted Heronian averaging operator, enriching not only the theoretical framework of multi-attribute decision-making methods but also offering more possibilities for practical applications. Finally, the application of this method in the field of commercial bank lending decision-making will be further explored to enhance the accuracy and efficiency of credit decisions, reduce risks, and promote the healthy development of the banking industry.

An [formula omitted]-cut intervals based Fuzzy Best–Worst Method for Multi-Criteria Decision-Making

To address ambiguity arising from linguistic decision judgments, Guo and Zhao introduced a model of the well-known Multi-Criteria Decision-Making (MCDM) method, Best-Worst Method (BWM), using fuzzy sets, known as Fuzzy Best–Worst Method (FBWM). Despite its versatility, FBWM has limitations, such as criteria-weights being independent of fuzzy comparison values’ shape and reliance on approximate fuzzy arithmetic operations. In response to these limitations, we introduce a novel model of Fuzzy Best–Worst Method based on α-cut intervals. In this model, the calculation of optimal weights involves formulating an optimization problem that utilizes exact fuzzy arithmetic operations defined in terms of α-cut intervals. This approach aims to optimize the entire shape of fuzzy comparison values simultaneously. However, it turns out that, although we have proven the existence of optimal solution for this problem, solving it proves to be challenging. To resolve this issue, we approximate optimal weight set(s) using triangular fuzzy weight sets and assess the Error of Approximation (EA). The approximate weight set with the desired EA is then defuzzified to obtain a crisp weight set. In situations where there are multiple approximate weight sets with the same EA, interval-weights are calculated. Following that, we establish the necessary conditions for a Fuzzy Pairwise Comparison System (FPCS) to be consistent. Using these conditions, we calculate a lower bound of the Consistency Index (CI), providing a measure of the accuracy of weights. Finally, we discuss numerical examples and a real-world scenario, ranking of risk factors in supply chain 4.0, to validate the effectiveness of the proposed model.

A 2-order additive fuzzy measure identification method based on hesitant fuzzy linguistic interaction degree and its application in credit assessment

To reflect both fuzziness and hesitation in the evaluation of interactivity between attributes in the identification process of 2-order additive fuzzy measure, this work uses the hesitant fuzzy linguistic term set (HFLTS) to describe and depict the interactivity between attributes. Firstly, the interactivity between attributes is defined by the supermodular game theory. According to this definition, a linguistic term set is established to characterize the interactivity between attributes. Under the linguistic term set, the experts employ linguistic expressions generated by context-free grammar to qualitatively describe the interactivity between attributes. Secondly, through the conversion function, the linguistic expressions are transformed into the hesitant fuzzy linguistic term sets (HFLTSs). The individual evaluation results of all experts were further aggregated with the defined hesitant fuzzy linguistic weighted power average operator (HFLWPA). Thirdly, based on the standard Euclidean distance formula of the hesitant fuzzy linguistic elements (HFLEs), the hesitant fuzzy linguistic interaction degree (HFLID) between attributes is defined and calculated by constructing a piecewise function. As a result, a 2-order additive fuzzy measure identification method based on HFLID is proposed. Based on the proposed method, using the Choquet fuzzy integral as nonlinear integration operator, a multi-attribute decision making (MADM) process is then presented. Taking the credit assessment of the big data listed companies in China as an application example, the analysis results of application example prove the feasibility and effectiveness of the proposed method. This work successfully reflects both the fuzziness and hesitation in evaluating the interactivity between attributes in the identification process of 2-order additive fuzzy measure, enriches the theoretical framework of 2-order additive fuzzy measure, and expands the applicability and methodology of 2-order additive fuzzy measure in multi-attribute decision making.

Fire Risk Assessment Method of Energy Storage Power Station Based on Cloud Model

In response to the randomness and uncertainty of the fire hazards in energy storage power stations, this study introduces the cloud model theory. Six factors, including battery type, service life, external stimuli, power station scale, monitoring methods, and firefighting equipment, are selected as the risk assessment set. The risks are divided into five levels. Membership function is constructed using cloud model. The forward generator is responsible for calculating the complete coefficient matrix and the comprehensive evaluation matrix, while the reverse generator handles the same calculations separately. By utilizing fuzzy synthesis operators and cloud computing, the numerical attributes of the evaluation cloud model are derived, resulting in the creation of a visual representation that illustrates the fire hazard level for energy storage power stations. The results show that the cloud model can be used for fire risk assessment in energy storage power stations. Fuzzy variables can be accurately and clearly represented and corresponded to different safety levels. The effectiveness and feasibility of this assessment method have been verified through case analysis.

Basic concepts of complete residuated lattice-valued fuzzy mathematical morphology

The aim of this paper is to present basic concepts of lattice-valued fuzzy mathematical morphology. We use a complete residuated lattice as the codomain of fuzzy sets, a pair of fuzzy powerset operators, called the fuzzy erosion operator and the fuzzy dilation operator, is defined and their properties and relationships are studied. The pair of two operators forms a Galois adjunction and so that the induced fuzzy opening operator and fuzzy closing are an interior operator and a closure operator respectively. It is shown that the dilation stable sets and the erosion stable sets are equivalent, which form a fuzzy Alexandrov topology.

Implementation of Learning Management Systems (LMS) in higher education systems through bipolar complex hesitant fuzzy Aczel-Alsina power aggregation operators: A case review for China.

A learning management system (LMS) is a web-based application or software platform computed to facilitate the development, tracking, management, reporting, and delivery of education and training programs. Many valuable and dominant factors are working behind the Learning Management System (LMS), but no one can find which factor is most important and valuable for LMS during COVID-19 among the following five alternatives, called Improved Accessibility, Blended Learning, Collaboration and Communications, Assessment and Evaluation, and Administrative Efficiency. For this, first, we derive the techniques of bipolar complex hesitant fuzzy (BCHF) sets, and then we evaluate some flexible operational laws, called Algebraic operational laws and Aczel-Alsina operational laws. Secondly, using the above techniques, we elaborate the technique of BCHF Aczel-Alsina power averaging (BCHFAAPA), BCHF Aczel-Alsina power weighted averaging (BCHFAAPWA), BCHF Aczel-Alsina power geometric (BCHFAAPG), and BCHF Aczel-Alsina power weighted geometric (BCHFAAPWG) operators. Some basic properties are also investigated for each proposed operator. Further, to evaluate the problem concerning LMS, we compute the multi-attribute decision-making (MADM) techniques for invented operators. Finally, we select some prevailing operators and try to compare their ranking results with our proposed results to enhance the worth and capability of the invented theory.

Linear diophantine fuzzy Aczel-Alsina aggregation operators by using fuzzy-C means clustering algorithm

This paper investigates the detailed analysis of linear diophantine fuzzy Aczel-Alsina aggregation operators, enhancing their efficacy and computational efficiency while aggregating fuzzy data by using the fuzzy C-means (FCM) method. The primary goal is to look at the practical uses and theoretical foundations of these operators in the context of fuzzy systems. The aggregation process is optimised using the FCM algorithm, which divides data into clusters iteratively. This reduces computer complexity and enables more dependable aggregation. The mathematical underpinnings of Linear Diophantine Fuzzy Aczel-Alsina aggregation operators are thoroughly examined in this study, along with an explanation of their purpose in handling imprecise and uncertain data. It also investigates the integration of the FCM method, assessing its impact on simplifying the aggregation procedure, reducing algorithmic complexity, and improving the accuracy of aggregating fuzzy data sets. This work illuminates these operators performance and future directions through extensive computational experiments and empirical analysis. It provides an extensive framework that shows the recommended strategy’s effectiveness and use in a variety of real-world scenarios. We obtain our ultimate outcomes through experimental investigation, which we use to inform future work and research. The purpose of the study is to offer academics and practitioners insights on how to improve information fusion techniques and decision-making processes.

МАТЕМАТИЧНІ СИСТЕМИ ДЛЯ РЕАЛІЗАЦІЇ ШТУЧНИХ НЕЙРОННИХ МЕРЕЖ, ОРІЄНТОВАНИХ НА ХМАРОВІ ОБЧИСЛЕННЯ

The article provides a detailed overview of research focusing on artificial neural networks (ANNs) and their applications in cloud computing. Research methods of organizational development and changes based on artificial intelligence technologies and intellectual support systems are presented in the plane of: intellectual expert systems; inductive systems; semantic networks, neural networks, genetic algorithms. The aim of the study. The research is aimed at the study and analysis of modern mathematical systems used to implement artificial neural networks (ANNs). The main focus of the work is on how each artificial neuron in the network is characterized by its current state, which is similar to nerve cells in the brain that can be excited or inhibited. A detailed description of the functioning of neurons is provided, including the processes of summation of input signals and activation using activation functions. Special attention is paid to multilayer neural networks and their ability to form complex multidimensional functions. The methods of building decision-making models based on the analysis of unclear situations and reference states determined by experts are defined. The process of comparing the real states of organizations with reference ones for making optimal decisions is considered. The importance of fuzzy logical operations for determining the degree of closeness of various situations is described. Fuzzy reference situations for cloud computing and their impact on decision-making in various scenarios are proposed. Examples of real and hypothetical fuzzy situations are given, and methods of determining the fuzzy correspondence between different reference situations are also considered. The final part of the abstract emphasizes the possibilities and advantages of using such models in cloud computing, emphasizing their importance for the development of organizations and systems.

Determination of the most influential robot in the medical field by utilizing the bipolar complex fuzzy soft aggregation operators

From science fiction to the hospital, robots are transforming the medical field. These robots mostly look like R2D2 from Star Wars more than humanoids, yet they are having a substantial impact on the medical field. Robots in the medical field support by releasing medical staff from repetitive chores that distract their consideration to more vital responsibilities and by dropping the danger and expenditure of medical treatment for patients. The robots can also move hazardous materials and execute accurate surgery in small spaces. Considering this influence of robots on the medical field, in this manuscript, we investigate the influence of robots on the medical field and discover which robot is more influential in the medical field. For this, the bipolar complex fuzzy soft set (BCFSS) is a substantial mathematical model that covers genuine decision-making (DM) dilemmas where the obscurity and imprecision contain a negative pole, 2nd dimension, and parameterization at one time. Moreover, in this study, we establish arithmetic and geometric aggregation operators (AOs) in the setting of BCFSS, like bipolar complex fuzzy soft-weighted arithmetic averaging (BCFSWAA) and bipolar complex fuzzy soft-weighted geometric averaging (BCFSWGA) operators. Moreover, for discovering the most influential robot, we invent a technique of DM relying on the diagnosed AOs in the environment of BCFSS, and then, we describe a numerical example (determination of the most influential robot in the medical field). To demonstrate the superiority and condescension of our work we compare it with prevailing work.

Multi-criteria constrained interval type-2 fuzzy decision-making: A space analysis perspective

Practical decision-making problems invariably involve inherent uncertainty in information, making it challenging to obtain precise evaluations. In this research, the utilization of constrained interval type-2 fuzzy sets (CIT2 FSs) enables the representation of complex uncertainty in decision information, and a space analysis approach, called CIT2 fuzzy multi-criteria acceptability analysis (CIT2FMAA), is proposed for conducting reliable decision-making. The CIT2FMAA introduces a novel paradigm for type-2 fuzzy decision-making, wherein CIT2 fuzzy evaluations are acknowledged as spaces of type-1 fuzzy evaluations and processed using type-1 fuzzy operations and methodologies. First, from a space analysis perspective, the type-2 fuzzy measures of logical rank expressions are formalized as CIT2 fuzzy rank acceptability indexes, and the CIT2 fuzzy rank acceptability analysis is developed to rank CIT2 fuzzy numbers. Second, the weighted average of the CIT2 fuzzy numbers is defined, and the CIT2FMAA is proposed to support uncertain multi-criteria decision-making. Subsequently, a sampling algorithm is designed for implementing CIT2 fuzzy rank acceptability analysis and CIT2FMAA. Finally, a linguistic disease diagnosis is performed to demonstrate the efficiency of CIT2FMAA. Compared to traditional type-2 fuzzy decision-making methods, CIT2FMAA is more efficient because it not only derives ranks of alternatives but also provides confidence degrees for those ranks.

Combinative distance-based assessment method using linguistic T-spherical fuzzy aggregation operators and its application to multi-attribute group decision-making

Clean energy has become a hot topic worldwide because of the continuous rise in the climate's temperature. Reduced air pollution is only one of the many economic and environmental advantages of clean energy. An effective contractor with experience and knowledge in clean energy projects is always required to handle the complicated process of planning, implementing, and maintaining the new clean energy infrastructure. Contractor selection for renewable energy projects (REPs) is a multi-attribute group decision-making (MAGDM) problem. Linguistic T-spherical fuzzy set (LT-SFS) can be compatible with fuzzier information, and the contractor selection problem also has a lot of fuzzy information, which makes LT-SFS very suitable for contractor selection for REPs. Hence, the present work proposes a MAGDM methodology utilizing a combinative distance-based assessment (CODAS) method within the LT-SF context. For that, the Einstein and Frank t-norm and t-conorm has been used to define new and generalized operational laws for linguistic T-spherical fuzzy numbers. Then, the linguistic T-spherical fuzzy Einstein and linguistic T-spherical fuzzy Frank aggregation operators are proposed to integrate the information data provided by experts. Moreover, the proposed aggregation operators based-CODAS approach is designed to evaluate and rank the available alternatives. A real-life decision problem of selecting the best suitable contractor for a renewable energy project is solved to verify our suggested technique. Moreover, the sensitivity analysis is also carried out by changing the parameter's value to check the consistency of the rank order. Finally, the new model is compared with existing approaches to demonstrate its strength. The comparative analysis shows that the results of the suggested technique are more feasible and beneficial than those of existing approaches.

Bayesian Inference with Complex Knowledge Graph Evidence

Knowledge Graphs (KGs) provide a widely used format for representing entities and their relationships and have found use in diverse applications including question answering and recommendation. A majority of current research on KG inference has focused on reasoning with atomic facts (triples) and has disregarded the possibility of making complex evidential observations involving logical operators (negation, conjunction, disjunction) and quantifiers (existential, universal). Further, while the application of complex evidence has been explored in KG-based query answering (KGQA) research, in many practical online settings, observations are made sequentially. For example, in KGQA, additional context may be incrementally suggested to narrow down the answer. Or in interactive recommendation, user critiques may be expressed sequentially in order to narrow down a set of preferred items. Both settings are indicative of information filtering or tracking tasks that are reminiscent of belief tracking in Bayesian inference. In fact, in this paper, we precisely cast the problem of belief tracking over unknown KG entities given incremental complex KG evidence as a Bayesian filtering problem. Specifically, we leverage Knowledge-based Model Construction (KBMC) over the logical KG evidence to instantiate a Markov Random Field (MRF) likelihood representation to perform closed-form Bayesian inference with complex KG evidence (BIKG). We experimentally evaluate BIKG in incremental KGQA and interactive recommendation tasks demonstrating that it outperforms non-incremental methodologies and leads to better incorporation of conjunctive evidence vs. existing complex KGQA methods like CQD that leverage fuzzy T-norm operators. Overall, this work demonstrates a novel, efficient, and unified perspective of logic, KGs, and online inference through the lens of closed-form BIKG.

Novel fuzzy topologies formed by fuzzy primal frameworks

This paper introduces a new fuzzy structure named “fuzzy primal.” Then, it studies the essential properties and discusses their basic operations. By applying the q-neighborhood system in a primal fuzzy topological space and the Łukasiewicz disjunction, we establish a fuzzy operator (·) ⋄ on the family of all fuzzy sets, followed by its core characterizations. Next, we use (·) ⋄ to investigate a further fuzzy operator denoted by Cl⋄. To determine a new fuzzy topology from the existing one, the earlier fuzzy operators are explored. Such a new fuzzy topology is called primal fuzzy topology. Various properties of primal fuzzy topologies are found. Among others, the structure of a fuzzy base that generates a primal fuzzy topology. Furthermore, the concept of compatibility between fuzzy primals and fuzzy topologies is introduced, and some equivalent conditions to that concept are examined. It is shown that if a fuzzy primal is compatible with a fuzzy topology, then the fuzzy base that produces the primal fuzzy topology is itself a fuzzy topology.

Covering variable precision fuzzy rough sets based on overlap functions and the application to multi-label classification

Fuzzy rough sets (FRSs) play a significant role in the field of data analysis, and one of the common methods for constructing FRSs is the use of the fuzzy logic operators. To further extend FRSs theory to more diverse information backgrounds, this article proposes a covering variable precision fuzzy rough set model based on overlap functions and fuzzy β-neighbourhood operators (OCVPFRS). Some necessary properties of OCVPFRS have also been studied in this work. Furthermore, multi-label classification is a prevalent task in the realm of machine learning. Each object (sample or instance) in multi-label data is associated with various labels (classes), and there are numerous features or attributes that need to be taken into account within the attribute space. To enhance various performance metrics in the multi-label classification task, attribute reduction is an essential pre-processing step. Therefore, according to overlap functions and fuzzy rough sets’ excellent work on applications: such as image processing and multi-criteria decision-making, we establish an attribute reduction method suitable for multi-label data based on OCVPFRS. Through a series of experiments and comparative analysis with existing multi-label attribute reduction methods, the effectiveness and superiority of the proposed method have been verified.

An extended COPRAS method based on complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean aggregation operators

An extended COPRAS method based on complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean aggregation operators

Application of aggregation operators for forecasting [formula omitted] fluctuations: From available Caribbean data sites to unequipped ones

Air pollution is a substantial issue for public health. Predicting the levels of airborne particles, especially those originating from natural phenomena like sand mists from the African dust belt, enables more effective warnings for affected populations. Currently, there are only three islands that continuously measure PM10 concentrations in the Caribbean area. Thus, there is a main issue for the forecast of these particulate pollutants for unequipped sites. In this article, a new approach based on the use of aggregation operators in a non-fuzzy framework allows to predict the quantity of PM10 for certain sites in this geographical area. It is the characteristics of non-linearity and downward reinforcement of the fuzzy operators used (triple Pi and t-norms) which make it possible to model the evolution of a phenomenon as complex as the sand mists from African dust belt. The time series having been normalized, the tests were carried out on two of the three sites (Martinique and Guadeloupe) to predict the values of the third site (Puerto Rico) and assess the quality of the prediction. The mean absolute error (MAE), the mean bias error (MBE), the root mean square error (RMSE) and the index of agreement (IOA) values show that this approach provides significant results. The African dust seasonality strongly impacts these performances metrics. These initial promising findings emphasize that the utilization of aggregation operators is a robust method for forecasting PM10 fluctuations, eliminating the need for complex parameterization or learning phase that would otherwise entail significant computational costs.

Artificial intelligence‐enabled smart city management using multi‐objective optimization strategies

AbstractThis article outlines an integrated strategy that combines fuzzy multi‐objective programming and a multi‐criteria decision‐making framework to achieve a number of transportation system management‐related objectives. To rank fleet cars using various criteria enhancement, the Fuzzy technique for order of preference by resemblance to optimum solution are initially integrated. We then offer a novel Multi‐Objective Possibilistic Linear Programming (MOPLP) model, based on the rankings of the vehicles, to determine the number of vehicles chosen for the work while taking into consideration the constraints placed on them. The search for optimal solutions to MOPs has benefited from the decades‐long development of classical optimisation techniques. As a result of its potential for use in the real world, multi‐objective optimisation (MOO) under uncertainty has gained traction in recent years. Recently, fuzzy set theory has been used to solve challenges in multi‐objective linear programming. In this paper, we present a method for solving MOPs that makes use of both linear and non‐linear membership functions to maximize user happiness. A hypothetical case study of transportation issue is taken here. This innovative approach improves management for the betterment of transportation networks in smart cities. The method is a more robust and versatile approach to the complex difficulties of contemporary urban transportation because it incorporates the TOPSIS method for vehicle ranking and then using Distance Operator and variable Membership Functions in fuzzy goal programming operation on the selected vehicles. The results provide valuable insights into the strengths and limitations of each technique, facilitating informed decision‐making in real‐world optimization scenarios.

Fuzzy Logic-Based Landslide Susceptibility Mapping in Earthquake-Prone Areas: A Case Study of the Mila Basin, Algeria

Abstract —This research focuses on analyzing landslides triggered by a moderate earthquake (Mw = 4.9) in the northeastern region of the Mila province, which resulted in significant damage and economic losses in the El Kherba district and Grarem Gouga city. Through an extensive field-based investigation, a comprehensive inventory of landslides has been compiled. To assess the susceptibility to landslides triggered by seismic activity, a GIS-based fuzzy logic model was employed. The model incorporates various input factors, such as lithology, slope angle, normalized difference vegetation index (NDVI), distance from rivers and roads, precipitation, and seismic hazard, which is shown on a map. The study compares the performance of different fuzzy operators and gamma values and determines that using fuzzy gamma operators with a gamma value of 0.8 yields a satisfactory consistency with the distribution of landslides. Moreover, incorporating the map of seismic hazard as a causative factor enhances the accuracy of landslide susceptibility mapping. This study underscores the utility of the fuzzy logic model in disaster management and the planning of development activities.

Overlap function-based fuzzy β-covering relations and fuzzy β-covering rough set models

As an extension of the fuzzy covering, fuzzy β-covering has garnered significant scholarly concern. However, certain limitations impede its practical application. To address the issue of inaccurate characterization of object relationships caused by the current fuzzy β-neighborhood operator, four new operators were developed, which exhibit both symmetry and reflexivity through the utilization of established fuzzy β-neighborhood operators, overlap functions and grouping functions. Furthermore, we demonstrate that these operators satisfy the fuzzy β-covering relation, and utilize the fuzzy β-covering relations on the basis of overlap functions to propose new fuzzy β-covering rough set model. Additionally, incorporating the attribute significance, an attribute reduction algorithm is designed. Ultimately, we substantiate the rationality and superiority of our proposed algorithm by conducting a sequence of experiments. Meanwhile, we analyze the impacts of varying overlap functions and β values on the algorithm's performance.