Application Of Fuzzy Set Theory Research Articles

Translation of a Bipolar Fuzzy Set in Hilbert Algebras

This study explores the application of bipolar fuzzy set theory within Hilbert algebras, introducing and examining the concept of bipolar fuzzy (β, α)-translations of a bipolar fuzzy set φ =(φ+, φ−) in two distinct forms: Type I and Type II. Fundamental properties of these bipolar fuzzy translations are investigated in depth, alongside the introduction of bipolar fuzzy extensions andintensities, broadening the utility and flexibility of bipolar fuzzy sets in capturing nuanced bipolar information. Moreover, this work addresses the intricate relationships between the complement of a bipolar fuzzy subalgebra, bipolar fuzzy ideal, and bipolar fuzzy deductive system with respect to their level cuts. The findings significantly contribute to the broader theoretical foundation and potential applications of bipolar fuzzy logic in Hilbert algebras, offering valuable insights for managing complex bipolar information in uncertain environments.

Application of picture fuzzy set theory to reliability and risk analysis of complex industrial systems

Application of picture fuzzy set theory to reliability and risk analysis of complex industrial systems

Human Reliability Analysis for Fishing Vessels in Korea Using Cognitive Reliability and Error Analysis Method (CREAM)

In this paper, we introduce a model designed to predict human error probability (HEP) in the context of fishing boat operations utilizing the cognitive reliability and error analysis method (CREAM). We conducted an analysis of potential accidents on fishing boats and calculated the cognitive failure probability (CFP) for each identified accident. The common performance conditions (CPCs) from the original CREAM were adapted to better reflect the conditions on fishing boats, with the adapted CPCs’ validity confirmed through expert consultations. To apply CREAM, data were gathered via a survey of fishermen, with the uncertainty in the collected data addressed through the application of fuzzy set theory (FST). We then established a Bayesian network (BN) model to elucidate the relationship between the fuzzy data and HEP, utilizing a weighted sum algorithm to determine conditional probabilities within the BN. Both basic and extended versions of CREAM were applied to analyze the most common accidents among fishermen, calculating the CFP for each type of accident. According to our analysis, the poorer the dynamic CPC, the higher the probability that a fall accident will occur inside the boat due to human error, necessitating a countermeasure. The paper proposes safety enhancements for small fishing boats and illustrates the increased precision of human reliability analysis (HRA) models in forecasting human error by incorporating quantitative methods. It calls for further data collection and refinement of the model for more accurate operational risk assessments.

БАЗОВЫЕ ТЕХНОЛОГИИ, РЕКОМЕНДУЕМЫЕ ДЛЯ ИСПОЛЬЗОВАНИЯ В ХОДЕ СТРАТЕГИЧЕСКОГО ПЛАНИРОВАНИЯ ПРОМЫШЛЕННЫХ ПРЕДПРИЯТИЙ

Strategic planning of industrial enterprises is carried out in conditions of significant infor-mation uncertainty regarding the external conditions of the enterprise's functioning and its positioning in its industry environment, in order to ensure effective competition. Therefore, it is necessary to develop new approaches to strategic planning of enterprises in conditions of uncertainty. The aim of the study is to present a number of new basic technologies that are advisable to use in the course of strategic planning of industrial enterprises based on the application of fuzzy set theory and soft computing. The following basic technologies are analyzed in the article: analysis of industry anisotropy; application of matrix aggregate calculator (MAС) technology to assess economic resilience; fuzzy numerical interpretation of the «scarlet» and «blue» market oceans; strategic positioning of the enterprise in the «resili-ence – efficiency» space; predictive modeling of activity levels based on probability processes; assessment of the risk of non-fulfillment of the plan according to strategic indicators. All the basic technologies described in the work are recommended for implementation in standard processes of strategic planning and forecasting of industrial enterprises. Such an application will ensure that the planning procedure is consistent with the expressed strategic goals of the business owner. The study is original, it uses methods of fuzzy set theory and soft computing. A new technology for analyzing industry anisotropy based on R-lens clustering is proposed, as well as a method for predicting performance levels based on probability processes.

A hybrid incomplete decision system using fuzzy sets and rough set theory with varying object sets and values

Researchers in science and engineering face various obstacles due to a lack of specific and full data. Many different approaches have been devised to deal with these restrictive requirements, but two notable schools of thought are the fuzzy set (FS) theory and the rough set (RS) theory, both of which have spawned many extensions and hybridizations. Although RS theory originated from an indiscernibility relation (also known as an equivalence relation in mathematics), emphasis rapidly shifted to similarity or coverings (and their fuzzy analogues). Many other hybrid schemes were suggested with this goal in mind. The gap between those concepts shrank because to this thorough analysis. Fuzzy set theory is a legitimate way to convey the ambiguity of assessment data, yet it is still inadequate for dealing with certain intricate problems in the actual world. In reality, decision makers will undoubtedly provide different kinds of ambiguous and nuanced assessments. Atanassov’s intuitionistic fuzzy set theory broadened the application of fuzzy set theory by imbuing it with an element of uncertainty. Sometimes in real life, you have to deal with a neutral element on top of the indeterminate one. Picture fuzzy sets were developed specifically for this purpose. Membership roles may be positive, neutral, or negative/refusal. In contrast, hesitant fuzzy sets and its hybrid models are useful when decision makers are on the fence about which option to choose. As a binary relation on a set, a graph is symmetric. It is a staple in mathematical modelling and is used in almost every scientific and technological discipline. Graph theory has been essential in the mathematical modelling and subsequent resolution of several real-world situations. Information about connections between things is often best represented using graph theory, which uses vertices to stand in for the items and edges for the relationships between them. The suggested dynamic algorithm is better to the static approach in dealing with the multidimensional dynamic changes of the hybrid incomplete decision system, according to a series of experiments carried out on nine UCI datasets.

Fuzzy Intuitionistic Alpha Cut of B-Spline Curve Interpolation Modeling for Shoreline Island Data

Traditional approaches are unable to handle the uncertainty data issue, which leads to inaccurate data analysis and prediction. Data with uncertainty are frequently collected during the data collection phase but cannot be directly used to create geometric models. Therefore, using intuitionistic alpha cuts for the uncertainty data, this paper discusses B-Spline curve interpolation modeling. To resolve the uncertain data and produce the mathematical model, fuzzy set theory, intuitionistic fuzzy sets, and geometry modeling are combined. Three main procedures are used in detail, the first of which is the application of fuzzy set theory to defined uncertainty data, followed by the use of an intuitionistic fuzzy set to take into account the membership, non-membership, and indeterminacy values of the alpha, and finally the fuzzification and defuzzification procedures. The B-spline curve interpolation function is used in geometric modeling to create mathematical geometry in the form of curves. As a result, several numerical examples are provided, along with their algorithms for producing the desired curve.

A Hybrid Fuzzy Multi-Criteria Decision-Making Model for Evaluating the Influence of Industry 4.0 Technologies on Manufacturing Strategies

Manufacturing is transitioning from traditional and mass manufacturing to mass personalization, fast, and intelligent production. Through full automation in various fields and data sharing, Industry 4.0 (I4.0) contributes to the digitalization of manufacturing by enhancing industrial flexibility and product customization. I4.0 is being utilized as a strategy for advanced manufacturing to counter global competitiveness. A company’s manufacturing strategy outputs (MSOs) are critical to its ability to move forward and remain competitive. Despite their importance, I4.0 technologies have received less attention in the literature, and it is unclear how they influence MSOs. Thus, this study aims to build a powerful hybrid MCDM method for ranking the influence of I4.0 technologies on MSOs by adopting a combination of AHP and fuzzy TOPSIS. The application of fuzzy set theory has addressed the ambiguity in comparing various I4.0 technologies. The AHP was used to calculate the weights of criteria and sub-criteria, and the fuzzy-TOPSIS method was utilized to rank the I4.0 technologies. The results revealed that the cost criterion is the most critical factor when implementing I4.0 technologies. In contrast, additive manufacturing (AM) is the most suitable I4.0 technology for countering global competition.

Generalized Frame for Orthopair Fuzzy Sets: (m,n)-Fuzzy Sets and Their Applications to Multi-Criteria Decision-Making Methods

Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and borderline cases. One of the generalized versions of orthopairs is intuitionistic fuzzy sets which is a well-known theory for researchers interested in fuzzy set theory. To extend the area of application of fuzzy set theory and address more empirical situations, the limitation that the grades of membership and non-membership must be calibrated with the same power should be canceled. To this end, we dedicate this manuscript to introducing a generalized frame for orthopair fuzzy sets called “(m,n)-Fuzzy sets”, which will be an efficient tool to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature. We first establish its fundamental set of operations and investigate its abstract properties that can then be transmitted to the various models they are in connection with. Then, to rank (m,n)-Fuzzy sets, we define the functions of score and accuracy, and formulate aggregation operators to be used with (m,n)-Fuzzy sets. Ultimately, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making problems in the environment of (m,n)-Fuzzy sets. The proposed technique has been illustrated and analyzed via a numerical example.

New generalization of fuzzy soft sets: $ (a, b) $-Fuzzy soft sets

<abstract><p>Many models of uncertain knowledge have been designed that combine expanded views of fuzziness (expressions of partial memberships) with parameterization (multiple subsethood indexed by a parameter set). The standard orthopair fuzzy soft set is a very general example of this successful blend initiated by fuzzy soft sets. It is a mapping from a set of parameters to the family of all orthopair fuzzy sets (which allow for a very general view of acceptable membership and non-membership evaluations). To expand the scope of application of fuzzy soft set theory, the restriction of orthopair fuzzy sets that membership and non-membership must be calibrated with the same power should be removed. To this purpose we introduce the concept of $ (a, b) $-fuzzy soft set, shortened as $ (a, b) $-FSS. They enable us to address situations that impose evaluations with different importances for membership and non-membership degrees, a problem that cannot be modeled by the existing generalizations of intuitionistic fuzzy soft sets. We establish the fundamental set of arithmetic operations for $ (a, b) $-FSSs and explore their main characteristics. Then we define aggregation operators for $ (a, b) $-FSSs and discuss their main properties and the relationships between them. Finally, with the help of suitably defined scores and accuracies we design a multi-criteria decision-making strategy that operates in this novel framework. We also analyze a decision-making problem to endorse the validity of $ (a, b) $-FSSs for decision-making purposes.</p></abstract>

Optimal Selection of Cities of Energy Outlets in Developing Countries: An Application of Fuzzy Set Theory to Sri Lankan Solar Industry

The concept of benefit gains is inherently fuzzy in nature. Hence, this study seeks to propose a logic-based innovative formalism that helps in effective decision-making in dynamic, imprecise, inconclusive, and volatile business environments underpinned by technology. Such an attempt, deriving from Fuzzy Set Theory, is needed as we apply this model to the financial gain-based optimal selection of cities to establish business outlets with reference to the solar power generation industry. Modelling the perceptions of domain experts is an integral part of the fuzzy approach. However, these linguistic inputs of experts become intelligible only when quantified through similarity methods and fuzzy tolerance relations comparing the yielded values against proximity ratios. The acquisition of expert knowledge was made by interviewing five economic and finance-proficient individuals in Sri Lanka with tacit know-how. The fuzzy inference was used to transform qualitative words and quantitative data into objective crisp values. The study was operationalized through computing with words, cosine amplitude transformation, and Bellman Zadeh approach. Both the Fuzzy Inference System and Bellman Zadeh’s approach were amalgamated for data analysis. In deriving the membership values, two business goals of monetary nature were formulated. The findings reveal that the country’s politics, business owners’ financial solvency, operational maintenance, and business foresight are the constraints that impact financial gains and accomplishing defined goals at variance. Among these, politics and business foresight are external factors, while solvency and operational maintenance are internalised.

A Novel Method for Network Intrusion Detection

Intrusion detection is one of the key research directions of network information security. In order to make up for the deficiencies of traditional security technologies such as firewall, encryption, and authentication, by analyzing the characteristics of network attacks and existing intrusion detection models, the advantages of triadic concept analysis and the application of fuzzy set theory in network intrusion detection are analyzed. The intrusion detection model FCTA based on triadic concept analysis is proposed, which promotes the further development of network intrusion detection. First, we analyze the characteristics of the data and use TF-IDF and Z-Score to normalize and standardize the data to construct a fuzzy triadic background containing quadratic characteristics. It is used to describe the triadic relationship between network connections, network connection characteristics, and intrusion types of network packets. Then, the (i)-induced operator is used to construct the fuzzy triadic concept set based on the fuzzy triadic background and transformed into a fuzzy attribute triadic concept set. Then, the new samples are classified by calculating the similarity between the new samples and the elements in the fuzzy attribute triadic concept set by using the Euclidean distance formula. In order to reduce the model space complexity, compression storage technology is adopted in the model building process.. Finally, by using the IDS-2018 dataset, the rationality and effectiveness of the FCTA model are demonstrated. The average accuracy and average intrusion detection rate of FCTA classification are much higher than BP neural network, SVM algorithm, and KNN algorithm, and the FCTA misjudgment rate is much lower than the BP neural network algorithm, the KNN algorithm, and the SVM algorithm; with the increase of data volume, the accuracy rate and intrusion detection rate increase significantly.

A New Divergence Measure based on Fuzzy TOPSIS for Solving Staff Performance Appraisal

Various divergence measure methods have been used in many applications of fuzzy set theory for calculating the discrimination between two objects. This paper aims to develop a novel divergence measure incorporated with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, along with the discussions of its properties. Since ambiguity or uncertainty is an inevitable characteristic of multi-criteria decision-making (MCDM) problems, the fuzzy concept is utilised to convert linguistic expressions into triangular fuzzy numbers. A numerical example of a staff performance appraisal is given to demonstrate suggested method's effectiveness and practicality. Outcomes from this study were compared with various MCDM techniques in terms of correlation coefficients and central processing unit (CPU) time. From the results, there is a slight difference in the ranking order between the proposed method and the other MCDM methods as all the correlation coefficient values are more than 0.9. It is also discovered that CPU time of the proposed method is the lowest compared to the other divergence measure techniques. Hence, the proposed method provides a more sensible and feasible solutions than its counterparts.

Fuzzy-rough hybrid dimensionality reduction

Dimensionality reduction including feature selection and feature extraction is a significant preprocessing method for data analysis, which is an important application of fuzzy rough set theory. Linear discriminant analysis (LDA) is a commonly used supervised feature extraction method, which can generate transformations while retaining as much class discrimination information as possible. However, it is worth noting that linear discriminant analysis is not interpretable. To improve the interpretability of the model and avoid losing part of the original feature information when only using feature selection for dimensionality reduction, this paper proposes a hybrid dimensionality reduction method based on fuzzy rough set and linear discriminant analysis. It can obtain a reduction set that contains complementary transformation features and original features. First, the semi-feature set is generated by criterion based on the normalized fuzzy joint mutual information, and the hybrid feature set is further induced by applying LDA to the feature set. Then, the redundancy between features is evaluated by the normalized fuzzy mutual information. The significance of a feature is defined by the proposed normalized effective classification information amount and the symmetric effective classification information amount. Next, the priority value between features according to the significance of them is defined to delete the redundant feature from the hybrid feature set. Furthermore, a hybrid dimensionality reduction algorithm based on fuzzy rough set is designed further. Finally, the performance of the proposed method is compared with some methods. The experimental results show that the proposed algorithm can obtain effective feature subset, which improve the performance of a classifier.

The Application of Variable Fuzzy Sets Theory on the Quality Assessment of Surrounding Rocks

The quality assessment of surrounding rocks has tremendous influences on engineering construction, so its investigation is significant. The uniaxial compressive strength of rocks σ c , the integrity coefficients of rock mass K V , the conditions of the structural plane S S , the seepage amount of groundwater W , and the intersection angle θ between the axis line and structural plane are selected as the quality assessment index of surrounding rocks at first. Then, the entropy weight-variable fuzzy sets model is introduced. Second, the relative membership degree matrix about the variable fuzzy sets is established, and the weight coefficients are determined based on the entropy weight method. Finally, the fracture behavior level of surrounding rocks is determined using the mean ranking feature value. The conclusions demonstrate that the results obtained based on the variable fuzzy sets method are consistent with the current specification; its accuracy arrives at 80%. Compared with the traditional way, its assessment process has higher reliability and efficiency. So, it could provide a new alternate way to assess the risk level in civil engineering accurately.

Quantitative supply chain segmentation model for dynamic alignment

Companies deal with different customer groups, requirements differ among them, which makes it important to define the service level precisely and improve customer service through different supply chain strategies for each group. An alternative to deal with imprecision related to the segmentation processes suggested by either the Leagile or the Dynamic Alignment Schools is the application of fuzzy set theory. The objective of this work is to develop a quantitative model that uses the fuzzy set theory and, based on sales data, assess the company’s supply chain(s). The model's aim is to facilitate managers' decision-making processes to achieve the dynamic alignment. It was possible to identify the supply chains that serve the client groups evaluated, providing answers faster than the analysis proposed by the models found in the literature. The application in two real situations validated the model since the results obtained were consistent with the reality pointed out by the experts of the companies assessed. The model indicates possible actions for the realignment of the supply chain by their managers. Results obtained should improve practice, preparing managers to cope with the organizations` multiple supply chains. This study is the first one that aims to segment quantitatively supply chains on a company applying fuzzy set theory, providing a novel approach to align operations and supply chain strategy dynamically.

Review on fuzzy multi-criteria decision-making methods in medical diagnosis

In a real-world computing environment, the information is not complete, precise, and certain, making it very difficult to derive an actual decision. Uncertainty is a factor that makes the decision-making process more difficult in medical diagnosis. Everyone is different from the other at the physical level as well as mental level, symptoms of a disease expressed by patients are linguistic in nature and vary from person to person. That is why Decision making in medical diagnosis is becoming a vast research field in medical science. In medical diagnosis, generally, uncertainty (vagueness or imprecision) arises due to patients’ vague linguistic expression of their problems to medical experts. The field of medicine and decision-making are the most fruitful and interesting areas of applications of fuzzy set theory. In the present paper, we study the importance of different fuzzy sets and fuzzy multi-criteria decision-making methods in the field of medical diagnosis.

Text Classification Using Intuitionistic Fuzzy Set Measures—An Evaluation Study

A very important task of Natural Language Processing is text categorization (or text classification), which aims to automatically classify a document into categories. This kind of task includes numerous applications, such as sentiment analysis, language or intent detection, heavily used by social-/brand-monitoring tools, customer service, and the voice of customer, among others. Since the introduction of Fuzzy Set theory, its application has been tested in many fields, from bioinformatics to industrial and commercial use, as well as in cases with vague, incomplete, or imprecise data, highlighting its importance and usefulness in the fields. The most important aspect of the application of Fuzzy Set theory is the measures employed to calculate how similar or dissimilar two samples in a dataset are. In this study, we evaluate the performance of 43 similarity and 19 distance measures in the task of text document classification, using the widely used BBC News and BBC Sports benchmark datasets. Their performance is optimized through hyperparameter optimization techniques and evaluated via a leave-one-out cross-validation technique, presenting their performance using the accuracy, precision, recall, and F1-score metrics.

Problems of Teaching Future Teachers of Humanities the Basics of Fuzzy Logic and Ways to Overcome Them

The rapid development of computer technology has led to the use of fuzzy set theory in the medical, financial, economic, commercial and other fields as one of the basic components of artificial intelligence. This is due to its universal mechanism designed to analyze research in the field of humanities research. The mathematical apparatus of fuzzy set theory allows them to be performed with unformalized data, and the development and improvement of information and communication technologies make it possible to automate this process. Unformalized, abstract, "blurred" statistics, which are difficult to analyze, are also common in pedagogy. But in pedagogical practice, fuzzy logic has not been widely used. The article proves the importance and expediency of teaching students, future teachers of computer science, skills in the application of fuzzy set theory. The ability to use the mechanisms of fuzzy logic in applied programs will allow future teachers in their further pedagogical activities to conduct multi-criteria analysis of various characteristics of their students, analysis of pedagogical methods, comprehensive assessment of competencies and more. The article presents the experience of teaching fuzzy set theory, the logic of teaching and its sequence, as well as the results of such training at a pedagogical university. The necessity of the step-by-step study of fuzzy set theory is proved - from acquaintance with its basic concepts, giving examples of its application in expert systems, neural networks and artificial intelligence systems to independent construction of fuzzy knowledge representation model, development of linguistic variables and use of spreadsheet or specialized programs. The results of the experimental introduction of the topic "Fuzzy model of knowledge representation" in a training course of computer disciplines are shown. Examination of learning outcomes reveals a positive attitude of the students toward mastering the skills of using fuzzy set theory and willingness to apply it in their further pedagogical activities.

Evaluating the Effectiveness of an Intrusion Detection System Based on Matrix Games and Fuzzy Sets

We consider a problem formulated as a matrix game in which the gain of officials using a specific intrusion detection system (criminal actions) of intruders (player 1) is the probability of timely detection of these criminal actions (player 2). As a rule, it is not possible to unambiguously set the probability of timely detection of criminal actions, so it is proposed to use the apparatus of fuzzy set theory to evaluate it. Reviewed and discussed the basic concepts of fuzzy set theory, and an example of practical application of this theory to assess the efficiency of the detection system of criminal damage. Application of fuzzy set theory in assessing the possible actions of an attacker can detect existing vulnerabilities in information security of automated systems continue to spend improving the detection of criminal acts (hackers) to prevent the possibility of applying economic and other damage to the company.

Application of Rough and Fuzzy Set Theory for Prediction of Stochastic Wind Speed Data Using Long Short-Term Memory

Despite the great significance of precisely forecasting the wind speed for development of the new and clean energy technology and stable grid operators, the stochasticity of wind speed makes the prediction a complex and challenging task. For improving the security and economic performance of power grids, accurate short-term wind power forecasting is crucial. In this paper, a deep learning model (Long Short-term Memory (LSTM)) has been proposed for wind speed prediction. Knowing that wind speed time series is nonlinear stochastic, the mutual information (MI) approach was used to find the best subset from the data by maximizing the joint MI between subset and target output. To enhance the accuracy and reduce input characteristics and data uncertainties, rough set and interval type-2 fuzzy set theory are combined in the proposed deep learning model. Wind speed data from an international airport station in the southern coast of Iran Bandar-Abbas City was used as the original input dataset for the optimized deep learning model. Based on the statistical results, the rough set LSTM (RST-LSTM) model showed better prediction accuracy than fuzzy and original LSTM, as well as traditional neural networks, with the lowest error for training and testing datasets in different time horizons. The suggested model can support the optimization of the control approach and the smooth procedure of power system. The results confirm the superior capabilities of deep learning techniques for wind speed forecasting, which could also inspire new applications in meteorology assessment.