Fuzzy Logic Operations Research Articles

An Approximate Inference Scheme Based on Distance-Induced Relations: Weld Forming Prediction

The construction of fuzzy conditional relations has been considered in Raha’s similarity-based inference schema, but inappropriate conclusions will be drawn in some cases due to the use of a single modification function. This paper presents an approximate reasoning method to generate induced conditional relations from distance measures. Two types of modification functions are given, and the type can be chosen according to the inclusion relation between a given fact and the antecedent of a rule. The fuzzy logic operators for constructing conditional relations are discussed, and the monotonicity and approximation properties of the reasoning scheme are inspected. By comparing and analyzing some basic properties of the three reasoning methods, some advantages can be found in the proposed scheme. An example of weld forming prediction is provided to illustrate the application of the algorithm.

Noncommutative Logic Systems with Applications in Management and Engineering

Zadeh's (min-max, standard) fuzzy logic and various other logics are commutative, but natural language has nuances suggesting the premises are not equal, with premises contributing to the conclusion according to their prominency. Therefore, we suggest variants of salience-based, noncommutative and non-associative fuzzy logic (prominence logic) that may better model natural language and reasoning when using linguistic variables. Noncommutative fuzzy logics have several theoretical and applicative motivations to be used as models for human inference and decision making processes. Among others, asymmetric relations in economy and management, such as buyer-seller, provider-user, and employer-employee are noncommutative relations and induce noncommutative logic operations between premises or conclusions. A class of noncommutative fuzzy logic operators is introduced and fuzzy logic systems based on the corresponding noncommutative logics are described and analyzed. The prominence of the operators in the noncommutative operations is conventionally assumed to be determined by their precedence. Specific versions of noncommutative logics in the class of the salience-based, noncommutative logics are discussed. We show how fuzzy logic systems may be built based on these types of logics. Compared with classic fuzzy systems, the noncommutative fuzzy logic systems have improved performances in modeling problems, including the modeling of economic and social processes, and offer more flexibility in approximation and control. Applications discussed include management and engineering problems and issues in the field of firms’ ethics or ethics of AI algorithms.

The Implementation of Career and Educational Guidance System (CEGS) as a Cloud Service

The present tools of career and educational guidance provided by educational organizations do not seem to address the problems faced by students, and graduates for applying to their promised job. The growing benefits of cloud software as services increase the requirements of implementing novel applications for career and educational guidance as a cloud service provided by the universities' portal. In this research, the authors present the benefits of using career guidance apps and introduce the implementation of career and educational guidance system (CEGS) in Higher Education. The system is designed specifically for school-level, university students, and graduates. Fuzzy logic operations were used to represent the system inputs, outputs, and rules. The paper aims to present a career and educational guidance application as a digital transformation application in the area of career counseling. The proposed system provides a student with interactive tools to select suitable colleges that match their educational skills and help graduates to select suitable careers for their practical experiences as well as provide them with essential training programs that are needed for particular jobs. The authors used the 2*3 factorial design method for the initial evaluation of the proposed system and to evaluate both students' and graduates' feedbacks. The researcher also uses the one-way ANOVA to find out if there is a remarkable difference between the users' perceptions scores.

A Novel Fuzzy Linguistic Fusion Approach to Naive Bayes Classifier for Decision Making Applications

Naive Bayes is one of the most widely used classifier algorithms in various data mining problems. The performance of the Naí¯ve Bayes Classifier is comparable to other classifiers as it yields impressive results in multiple applications. An increase in the performance of the Naive Bayes Classifier is possible by identifying and forming segments of the data handled by the classifier. In this paper, a novel fuzzy-based fusion approach to selected quantitative features is proposed. The approach is used to improve the prediction accuracy of the Naive Bayes Classifier (NBC). The linguistic computing model with fusion operators, using ranked indexes of the linguistic terms in the dataset is made use in this proposed approach. Fuzzy values are generated only for the numerical attributes in the initial phase using 2-tuple linguistic computations. The equivalent real value computations are performed in order to express the results in the initial domain of the expression. These computations ensure improved comprehensiveness of the results of the classifier. The model incorporates the concepts of linguistic terms, fuzzy logic, fusion methods, and aggregation operations to the classical Naí¯ve Bayes Classifier. Such incorporation is used to improve the performance of the classifier in various decision-making applications. The proposed model is validated using a standard benchmark dataset-Stat log Heart disease dataset. It is obtained from the UCI Machine Learning Repository. The proposed Linguistic Fuzzy Naive Bayes Classifier showed better accuracy compared to the Simple Naive Bayes Classifier performance.

How to implement MCDM tools and continuous logic into neural computation?: Towards better interpretability of neural networks

The theories of multi-criteria decision-making (MCDM) and fuzzy logic both aim to model human thinking. In MCDM, aggregation processes and preference modeling play the central role. This paper suggests a consistent framework for modeling human thinking by using the tools of both fields: fuzzy logical operators as well as aggregation and preference operators. In this framework, aggregation, preference, and the logical operators are described by the same unary generator function. Similarly to the implication being defined as a composition of the disjunction and the negation operator, preference operators were introduced as a composition of the aggregative operator and the negation operator. After a profound examination of the main properties of the preference operator, our main goal is the implementation into neural networks. We show how preference can be modeled by a perceptron, and illustrate the results in practical neural applications.

An improved flux limiter using fuzzy modifiers for Hyperbolic Conservation Laws

The objective of the work in this paper is to computationally tackle a range of problems in hyperbolic conservation laws, which is an interesting branch of computational fluid dynamics. For the simulation of issues in hyperbolic conservation laws, this work explores the concept of fuzzy logic-based operators. This research presents a unique mixture of fuzzy sets and logic with a new branch of conservation laws from fluid dynamics. The approach considers a computational procedure based on the reconstruction of several high-order numerical methods termed as flux-limited methods using some fuzzy logic operators. With the aid of fuzzy modifiers, these flux limiters are further modified. This approach results in improved convergence of approximations and maintains the problem’s basic properties to be solved. Additionally, to ensure improved results, modified flux-limited methods are imposed on some famous test problems. The application results are provided wherever required. The work has demonstrated that it is possible to use such technique and apply it to complex areas of computational fluid dynamics to produce a more straightforward approach to studying other topics like flux-limited methods and hence opens up an exciting gateway for future work.

PROMETHEE II method based on variable precision fuzzy rough sets with fuzzy neighborhoods

The model of covering-based fuzzy rough sets (CFRSs) can be regarded as a hybrid one by combining covering-based rough sets with fuzzy sets. In this paper, based on fuzzy neighborhoods, we propose two types of covering-based variable precision fuzzy rough sets (CVPFRSs) via fuzzy logical operators, i.e., type-I CVPFRSs and type-II CVPFRSs. Then, several basic properties of the two types of CVPFRSs are discussed. In addition, by virtue of the idea of PROMETHEE II methods, we construct a novel method to multi-attribute decision-making (MADM) in the context of medical diagnosis based on the proposed rough approximation operators. Finally, a test example for illustrating the proposed method is given. Meanwhile, a comparative analysis and an experimental evaluation are further discussed to interpret and evaluate the effectiveness and superiority of the proposed method. The proposed rough set model not only extends the theory of CFRSs, but also provides a new perspective for MADM with fuzzy evaluation information.

A novel fuzzy rough set model with fuzzy neighborhood operators

It is not widely acknowledged that none of existing fuzzy β-neighborhood operators satisfies the reflexivity when β≠1. To overcome this shortcoming, four types of fuzzy β-neighborhood operators are redefined, which shows that two redefined operators are reflexive. By means of fuzzy logical operators, the (I,T)-fuzzy rough set (ITFRS) model based on the reflexive fuzzy β-neighborhood operators is constructed in this paper. By combining ITFRS models with the classical TOPSIS method, a new decision-making method is proposed to handle multi-criteria decision-making (MCDM) problems under uncertain and fuzzy environments, where the distance between two intuitionistic fuzzy sets (IFSs) is expressed by an intuitionistic fuzzy number (IFN). Meanwhile, both numerical examples with different types of data are given to explain the feasibility of the proposed method and its effectiveness is also illustrated by a comparative analysis. Finally, the stability of the proposed method is further verified based on an experimental analysis in a real-life MCDM problem.

Fuzzy implications in lattice effect algebras

Implications are one of the key operations in fuzzy logic and approximate reasoning. We prove that the Dishkant arrow in a lattice effect algebra is a partial triangular implication if and only if the lattice effect algebra is an MV-effect algebra. Then we show that a certain implication based on the Sasaki arrow is a partial triangular implication. Furthermore, we propose a new partial triangular implication, which is also a fuzzy implication in lattice effect algebras.

Incrementally updating approximations based on the graded tolerance relation in incomplete information tables

The incremental learning methods based on rough set theory are effective in acquiring knowledge in dynamically changing information tables. In this paper, we focus on the effective acquisition of decision rules by incrementally updating approximations when an incomplete information table changes. First of all, we present a four-step model to obtain three-way decision rules in an incomplete information table based on the graded tolerance relation. The first step presents the graded tolerance relation between objects. The second step calculates the degrees of objects belonging to approximations by using fuzzy logic operators. Besides, we propose a relation matrix to calculate the degrees efficiently. The third step gets three-way approximations by applying a pair of thresholds to the degrees. The fourth step obtains three-way decision rules based on the descriptions of objects. According to the four-step model, we find the notion of approximations plays an essential role in rule acquisition. Incrementally updating approximations are an effective method to obtain decision rules when an incomplete information changes. Accordingly, we study the incrementally updating approximations by incrementally updating the relation matrix when changing attributes, objects, and the attribute value of an object. Finally, experimental results illustrate that the incremental methods are more effective than non-incremental methods.

A wildfire warning system applied to the state of Acre in the Brazilian Amazon

In this paper, we present a dynamic wildfire warning map that combines both spatial and weather information. In particular, our wildfire early warning model is obtained by aggregating two indexes called wildfire risk and wildfire danger. The wildfire risk index, which is based on georeferenced features such as altitude and forest type, measures the fuel necessary for a wildfire to start at a certain location on a map. The wildfire danger uses weather conditions to yield temporal information concerning the possibility of a wildfire to spread. Machine learning techniques and fuzzy logic operations are used to determine the wildfire risk and danger indexes from available data. Although both wildfire risk and wildfire danger indexes can be used separately, using concepts from fuzzy logic, they can be combined to yield a wildfire warning system that takes into account both weather and static information. We illustrate the wildfire early warning model by considering weather and geographical data for the state of Acre.

A Hybrid Fuzzy Convolutional Neural Network Based Mechanism for Photovoltaic Cell Defect Detection with Electroluminescence Images

In the intelligent manufacturing process of solar photovoltaic (PV) cells, the automatic defect detection system using the Industrial Internet of Things (IIoT) smart cameras and sensors cooperated in IIoT has become a promising solution. Many works have been devoted to defect detection of PV cells in a data-driven way. However, because of the subjectivity and fuzziness of human annotation, the data contains a high quantity of noise and unpredictable uncertainties, which creates great difficulties in automatic defect detection. To address this problem, we propose a novel architecture named fuzzy convolution, which integrates fuzzy logic and convolution operations at microscopic level. Combining the proposed fuzzy convolution with the regular convolution, we build a network called Hybrid Fuzzy Convolutional Neural Network (HFCNN). Compared with convolutional neural networks (CNNs), HFCNN can address the uncertainties of PV cell data to improve the accuracy with fewer parameters, making it possible to apply our method in smart cameras. Experimental results on a public dataset show the superiority of our proposed method compared with CNNs.

Mediative Multi-Criteria Decision Support System for Various Alternatives Based on Fuzzy Logic

Present research paper, deals with a new method for solving multi-criteria decision-making problems, in an environment where conflict of interest exits. In this present paper we have defined the Mediative fuzzy point operators. By using Mediative fuzzy logic and Mediative fuzzy point operators we have established some new generalized mathematical results of Intuitionistic fuzzy logic theory in the form of Mediative fuzzy logic theory. Second, we have applied these results to multi-criteria for making it into Mediative multi-criteria for decision support system where multiple alternatives and various criteria’s exits. Numerical examples have also been carried out to prove the effectiveness and advantages of this paper.

Pythagorean Picture Fuzzy Sets, Part 1- basic notions

Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟intuitionistic fuzzy set. The new concept could be useful for many computational intelligentproblems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].Newconcept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with theYager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notionson PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy softset. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picturenegation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.As aresult we will have a new branch of the picture fuzzy set theory.

Fuzzy logic interpretation of quadratic networks

Over past several years, deep learning has achieved huge successes in various applications. However, such a data-driven approach is often criticized for lack of interpretability. Recently, we proposed artificial quadratic neural networks consisting of quadratic neurons in potentially many layers. In cellular level, a quadratic function is used to replace the inner product in a traditional neuron, and then undergoes a nonlinear activation. With a single quadratic neuron, any fuzzy logic operation, such as XOR, can be implemented. In this sense, any deep network constructed with quadratic neurons can be interpreted as a deep fuzzy logic system. Since traditional neural networks and quadratic counterparts can represent each other and fuzzy logic operations are naturally implemented in quadratic neural networks, it is plausible to explain how a deep neural network works with a quadratic network as the system model. In this paper, we generalize and categorize fuzzy logic operations implementable with individual quadratic neurons, and then perform statistical/information-theoretic analyses of exemplary quadratic neural networks.

Ground Subsidence Susceptibility (GSS) Mapping in Grosseto Plain (Tuscany, Italy) Based on Satellite InSAR Data Using Frequency Ratio and Fuzzy Logic

This study aimed at evaluating and mapping Ground Subsidence Susceptibility (GSS) in the Grosseto plain (Tuscany Region, Italy) by exploiting multi-temporal satellite InSAR data and by applying two parallel approaches; a bivariate statistical analysis (Frequency Ratio) and a mathematical probabilistic model (Fuzzy Logic operator). The Grosseto plain experienced subsidence and sinkholes due to natural causes in the past and it is still suffering slow-moving ground lowering. Five conditioning subsidence-related factors were selected and managed in a GIS environment through an overlay pixel-by-pixel analysis. Firstly, multi-temporal ground subsidence inventory maps were prepared in the study area by starting from two inventories referred to distinct temporal intervals (2003–2009 and 2014–2019) derived from Persistent Scatterers Interferometry (PSI) data of ENVISAT and SENTINEL-1 satellites. Then, the susceptibility modelling was performed through the Frequency Ratio (FR) and Fuzzy Logic (FL) approaches. These analyses led to slightly different scenarios which were compared and discussed. Results show that flat areas on alluvial and colluvial deposits with thick sedimentary cover (higher than 20 m) on the bedrock in the central and eastern sectors of the plain are the most susceptible to land subsidence. The obtained FR- and FL-based GSS maps were finally validated with a ROC (Receiver Operating Characteristic) analysis, in order to estimate the overall performance of the models. The AUC (Area Under Curve) values of ROC analysis of the FR model were higher than the ones of FL model, suggesting that the former is a better and more appropriate predictor for subsidence susceptibility analysis in the study area. In conclusion, GSS maps provided a qualitative overview of the subsidence scenarios and may be helpful to predict and preliminarily identify high-risk areas for environmental local authorities and decision makers in charge of land use planning in the study area. Finally, the presented methodologies to derive GSS maps are easily reproducible and could also be applied and tested in other test sites worldwide, in order to check the modeling performance in different environmental settings.

Fuzzy Controller for Solar Cell Optimization

This study describes the Fuzzy Logic Control for the movement of Solar Cells that use fuzzy logic algorithms to achieve intelligent and flexible knowledge-based systems in the design of hardware to achieve efficiency in controlling the movement of solar cells that are better and maximize the function of the solar cell motor works based on time input. Fuzzy Logic allows mapping from the input given based on time to an output. involves components of variables, membership functions, Fuzzy Logic operators and if-then rules. And with an analysis it can produce optimum output of Solar cell rotation.

Logic-driven autoencoders

Autoencoders are computing architectures encountered in various schemes of deep learning and realizing an efficient way of representing data in a compact way by forming a set of features. In this study, a concept, architecture, and algorithmic developments of logic-driven autoencoders are presented. In such structures, encoding and the decoding processes realized at the consecutive layers of the autoencoder are completed with the aid of some fuzzy logic operators (namely, OR, AND, NOT operations) and the ensuing encoding and decoding processing is carried out with the aid of fuzzy logic processing. The optimization of the autoencoder is completed through a gradient-based learning. The transparent knowledge representation delivered by autoencoders is facilitated by the involvement of logic processing, which implies that the encoding mechanism comes with the generalization abilities delivered by OR neurons while the specialization mechanism is achieved by the AND-like neurons forming the decoding layer. A series of illustrative examples is also presented.

The lambda -additive measure in a new light: the Q_{nu } measure and its connections with belief, probability, plausibility, rough sets, multi-attribute utility functions and fuzzy operators

The aim of this paper is twofold. On the one hand, the lambda -additive measure (Sugeno lambda -measure) is revisited, and a state-of-the-art summary of its most important properties is provided. On the other hand, the so-called nu -additive measure as an alternatively parameterized lambda -additive measure is introduced. Here, the advantages of the nu -additive measure are discussed, and it is demonstrated that these two measures are closely related to various areas of science. The motivation for introducing the nu -additive measure lies in the fact that its parameter nu in (0,1) has an important semantic meaning as it is the fix point of the complement operation. Here, by utilizing the nu -additive measure, some well-known results concerning the lambda -additive measure are put into a new light and rephrased in more advantageous forms. It is discussed here how the nu -additive measure is connected with the belief-, probability- and plausibility measures. Next, it is also shown that two nu -additive measures, with the parameters nu _1 and nu _2, are a dual pair of belief- and plausibility measures if and only if nu _1+nu _2 = 1. Furthermore, it is demonstrated how a nu -additive measure (or a lambda -additive measure) can be transformed to a probability measure and vice versa. Lastly, it is discussed here how the nu -additive measures are connected with rough sets, multi-attribute utility functions and certain operators of fuzzy logic.

Multi‐objective robust fuzzy fractional order proportional–integral–derivative controller design for nonlinear hydraulic turbine governing system using evolutionary computation techniques

AbstractThe present paper proposes a novel multi‐objective robust fuzzy fractional order proportional–integral–derivative (PID) controller design for nonlinear hydraulic turbine governing system (HTGS) by using evolutionary computation techniques. The fuzzy fractional order PID (FOPID) controller takes closed loop error and its fractional derivative as inputs and performs fuzzy logic operations. Then, it produces the output through the fractional order integrator. The predominant advantages of the proposed controller are its capability to handle complex nonlinear processes like HTGS in heuristic manner, due to fuzzy incorporation and extending an additional flexibility in tuning the order of fractional derivative/integral terms to enhance the closed loop performance. The present work formulates the optimal tuning problem of fuzzy FOPID controller for HTGS as a multi‐objective one instead of a traditional single‐objective one towards satisfying the conflicting criteria such as less settling time and minimum damped oscillations simultaneously to ensure the improved dynamic performance of HTGS. The multi‐objective evolutionary computation techniques such as non‐dominated sorting genetic algorithm‐II (NSGA‐II) and modified NSGA‐II have been utilized to find the optimal input/output scaling factors of the proposed controller along with the order of fractional derivative/integral terms for HTGS system under no load and load turbulence conditions. The performance of the proposed fuzzy FOPID controller is compared with PID and FOPID controllers. The simulations have been conducted to test the tracking capability and robust performance of HTGS during dynamic set point changes for a wide range of operating conditions and model parameter variations, respectively. The proposed robust fuzzy FOPID controller has ensured better fitness value and better time domain specifications than the PID and FOPID controllers, during optimization towards satisfying the conflicting objectives such as less settling time and minimum damped oscillations simultaneously, due to its special inheritance of fuzzy and FOPID properties.