B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

The concept of b-vex and logarithmic b-vex for fuzzy mappings are introduced by relaxing the definition of convexity of a fuzzy mapping. Most of the basic properties of b-vex fuzzy mapping are discussed and established for the nondifferentiable case. Necessary and sufficient conditions for b-vex fuzzy mapping are presented. Sevaral important results are given for nonlinear fuzzy optimization problems assuming that the objective and constraint functions are b-vex fuzzy mappings.

Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings

A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements.

The Pointwise Characterizations of Fuzzy Mappings and Fuzzy Cardinal Numbers

In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.

Semistrictly Convex Fuzzy Mappings

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.

Variational Inclusions for Fuzzy Mappings

In this paper,a perturbed iterative algorithm for finding approximate solutions of variational inclusions for fuzzy mapping,is presented and a convergence result which includes,as a special case,some known results in this field,is given.

Chinese Fuzzy Ontology Mapping Based on Support Vector Machine

Taking into account that fuzzy ontology mapping has wide application and cannot be dealt with in many fields at present,a Chinese fuzzy ontology model and a method for Chinese fuzzy ontology mapping are proposed.The mapping discovery between two ontologies is achieved by computing the similarity between the concepts of two ontologies.Every concept consists of four features of concept name,property,instance and structure.First,the algorithms of calculating four individual similarities corresponding to the four features are given.Secondly,the similarity vectors consisting of four weighted individual similarities are built,and the weights are the linear function of harmony and reliability.The similarity vector is used to represent the similarity relation between two concepts which belong to different fuzzy ontolgoies.Lastly,Support Vector Machine(SVM) is used to get the mapping concept pairs by the similarity vectors.Experiment results are satisfactory.

An Equivalent Condition for （K） Integrability of Fuzzy-valued Mappings

In this paper, we first discuss the relationship between the McShane integral and Pettis integral for vector-valued functions. Then by using the embedding theorems for the fuzzy number space E^1, we give a new equivalent condition for （K） integrabihty of a fuzzy set-valued mapping F ： [a, b] → E^1.

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

FUZZY APPROACHING SET AND FUZZYAPPROACHING FUNCTIONAL MAPPING

By establishing the concepts of fuzzy approaching set and fuzzy approaching functional mapping and making research on them, a new method for time series prediction is introduced.

An Intelligent Medical Expert System Using Temporal Fuzzy Rules and Neural Classifier

As per World Health Organization report which was released in the year of 2019,Diabetes claimed the lives of approximately 1.5 million individuals globally in 2019 and around 450 million people are affected by diabetes all over the world.Hence it is inferred that diabetes is rampant across the world with the majority of the world population being affected by it.Among the diabetics,it can be observed that a large number of people had failed to identify their disease in the initial stage itself and hence the disease level moved from Type-1 to Type-2.To avoid this situation,we propose a new fuzzy logic based neural classifier for early detection of diabetes.A set of new neuro-fuzzy rules is introduced with time constraints that are applied for thefirst level classification.These levels are further refined by using the Fuzzy Cognitive Maps(FCM)with time intervals for making thefinal decision over the classification process.The main objective of this proposed model is to detect the diabetes level based on the time.Also,the set of neuro-fuzzy rules are used for selecting the most contributing values over the decision-making process in diabetes prediction.The proposed model proved its efficiency in performance after experiments conducted not only from the repository but also by using the standard diabetic detection models that are available in the market.

Cat Swarm with Fuzzy Cognitive Maps for Automated Soil Classification

Accurate soil prediction is a vital parameter involved to decide appro-priate crop,which is commonly carried out by the farmers.Designing an auto-mated soil prediction tool helps to considerably improve the efficacy of the farmers.At the same time,fuzzy logic(FL)approaches can be used for the design of predictive models,particularly,Fuzzy Cognitive Maps(FCMs)have involved the concept of uncertainty representation and cognitive mapping.In other words,the FCM is an integration of the recurrent neural network(RNN)and FL involved in the knowledge engineering phase.In this aspect,this paper introduces effective fuzzy cognitive maps with cat swarm optimization for automated soil classifica-tion(FCMCSO-ASC)technique.The goal of the FCMCSO-ASC technique is to identify and categorize seven different types of soil.To accomplish this,the FCMCSO-ASC technique incorporates local diagonal extrema pattern(LDEP)as a feature extractor for producing a collection of feature vectors.In addition,the FCMCSO model is applied for soil classification and the weight values of the FCM model are optimally adjusted by the use of CSO algorithm.For exam-ining the enhanced soil classification outcomes of the FCMCSO-ASC technique,a series of simulations were carried out on benchmark dataset and the experimen-tal outcomes reported the enhanced performance of the FCMCSO-ASC technique over the recent techniques with maximum accuracy of 96.84%.

Cardinal Numbers of Fuzzy Sets

Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.

APPROXIMATION CAPABILITIES OF MULTILAYER FEEDFORWARD REGULAR FUZZY NEURAL NETWORKS

Four layer feedforward regular fuzzy neural networks are constructed. Universal approximations to some continuous fuzzy functions defined on F 0 (R) n by the four layer fuzzy neural networks are shown. At first,multivariate Bernstein polynomials associated with fuzzy valued functions are empolyed to approximate continuous fuzzy valued functions defined on each compact set of R n . Secondly,by introducing cut preserving fuzzy mapping,the equivalent conditions for continuous fuzzy functions that can be arbitrarily closely approximated by regular fuzzy neural networks are shown. Finally a few of sufficient and necessary conditions for characterizing approximation capabilities of regular fuzzy neural networks are obtained. And some concrete fuzzy functions demonstrate our conclusions.

Analysis of Economic Order Quantity Under Fuzzy Environments

In the economic order quantity （EOQ） model, the decision maker has vague information about holding cost, ordering cost and market demand. With these uncertainties characterized as fuzzy variables, a new formula is developed by analyzing the fuzzy total cost. By comparing with other four EOQ formulas, i.e., using the crisp numbers with the highest membership values in classic EOQ formula, using the expected values of fuzzy parameters in classic EOQ formula, using the fuzzy variables in classic EOQ formula and then calculating the expected value, and calculat- ing EOQ by hybrid intelligent algorithm simulation, the effectiveness of this formula Js illustrated.

A Data and Knowledge Collaboration Strategy for Decision-Making on the Amount of Aluminum Fluoride Addition Based on Augmented Fuzzy Cognitive Maps

In the aluminum reduction process, aluminum uoride (AlF3) is added to lower the liquidus temperature of the electrolyte and increase the electrolytic ef ciency. Making the decision on the amount of AlF3 addi- tion (referred to in this work as MDAAA) is a complex and knowledge-based task that must take into con- sideration a variety of interrelated functions;in practice, this decision-making step is performed manually. Due to technician subjectivity and the complexity of the aluminum reduction cell, it is dif cult to guarantee the accuracy of MDAAA based on knowledge-driven or data-driven methods alone. Existing strategies for MDAAA have dif culty covering these complex causalities. In this work, a data and knowl- edge collaboration strategy for MDAAA based on augmented fuzzy cognitive maps (FCMs) is proposed. In the proposed strategy, the fuzzy rules are extracted by extended fuzzy k-means (EFKM) and fuzzy deci- sion trees, which are used to amend the initial structure provided by experts. The state transition algo- rithm (STA) is introduced to detect weight matrices that lead the FCMs to desired steady states. This study then experimentally compares the proposed strategy with some existing research. The results of the comparison show that the speed of FCMs convergence into a stable region based on the STA using the proposed strategy is faster than when using the differential Hebbian learning (DHL), particle swarm optimization (PSO), or genetic algorithm (GA) strategies. In addition, the accuracy of MDAAA based on the proposed method is better than those based on other methods. Accordingly, this paper provides a feasible and effective strategy for MDAAA.

A situation awareness assessment method based on fuzzy cognitive maps

The status of an operator’s situation awareness is one of the critical factors that influence the quality of the missions.Thus the measurement method of the situation awareness status is an important topic to research.So far,there are lots of methods designed for the measurement of situation awareness status,but there is no model that can measure it accurately in real-time,so this work is conducted to deal with such a gap.Firstly,collect the relevant physiological data of operators while they are performing a specific mission,simultaneously,measure their status of situation awareness by using the situation awareness global assessment technique(SAGAT),which is known for accuracy but cannot be used in real-time.And then,after the preprocessing of the raw data,use the physiological data as features,the SAGAT’s results as a label to train a fuzzy cognitive map(FCM),which is an explainable and powerful intelligent model.Also,a hybrid learning algorithm of particle swarm optimization(PSO)and gradient descent is proposed for the FCM training.The final results show that the learned FCM can assess the status of situation awareness accurately in real-time,and the proposed hybrid learning algorithm has better efficiency and accuracy.

THE FUZZY NUMERICAL VALUE SIMULATION OF NANOMETER ELECTRO-THERMAL IN HOT-WORKING

The fuzzy numerical value analysis method is adopted for the first time, which solves the problem of nanometer electro-thermal in filming process, The key technique is embodied by controlling the time distribution, temperature and press in the filming process. The concrete technique of filming is showed by establishing the fuzzy mumbership function of above three indexes, which improves the precision of the materials of nanometer electro-thermal in hot-working. At the same time, the principles of the fuzzy relationship mapping inversion （FRMI） is put forward, Therefore, the standardization and continuity can be met.

Using fuzzy cognitive maps to model performance measurement system of Internet-based supply chain

Fuzzy cognitive maps （FCM） is a well-established artificial intelligence technique, which can be effectively applied in the domains of performance measurement, decision making and other management science. FCM can be a useful tool in a group decision-making environment by using scientifically integrated expert knowledge. The theories of FCM and balance scorecard （BSC） both emphasize cause-and-effect relationships among indicators in a complex system, but few reports have been published addressing the combined application of these two techniques. In this paper we propose a FCM simulation model for the sample performance measurement system of Intemet-based supply chain, which is constructed by BSC theory. We gave examples to explain how FCM can be adapted to execute the causal mechanism of BSC, and also how FCM can support group decision-making and forecasting in performance measurement.

Application of fuzzy cognitive map in information intelligent push

Since computer system functions are becoming increasingly complex, the user has to spend much more time on the process of seeking information, instead of utilizing the required infor- mation. Information intelligent push technology could replace the traditional method to speed up the information retrieval process. The fuzzy cognitive map has strong knowledge representation ability and reasoning capability. Information intelligent push with the basis on fuzzy cognitive map could ab- stract the computer user＇ s operations to a fuzzy cognitive map, and infer the user＇ s operating inten- tions. The reasoning results will be translated into operational events, and drive the computer system to push appropriate information to the user.

A New Control Strategy for Modeling Wind Energy Systems Using Fuzzy Cognitive Maps

Wind energy is currently a fast-growing interdisciplinary field that encompasses many different branches of engineering and science. Modeling and controlling wind energy systems are difficult and challenging problems. The basic structure of wind turbines and some wind control system methods are briefly reviewed. The need for using advanced theories from fuzzy and intelligent systems in studying wind energy systems is identified and justified. FCMs （fuzzy cognitive maps） are used to model wind energy systems. Simulation studies are performed and obtained results are discussed. A new mathematical approach has been proposed to model dynamical complex systems, the DYFUKN （dynamic fuzzy knowledge networks）. Many open problems in the areas of modeling and controlling wind energy systems are outlined.