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Providesa unique and methodologically consistent treatment of various areas of fuzzy modeling and includes the results of mathematical fuzzy logic and linguistics This book is the result of almost thirty years of research on fuzzy modeling. It provides a unique view of both the theory and various types of applications. The book is divided into two parts. The first part contains an extensive presentation of the theory of fuzzy modeling. The second part presents selected applications in three important areas: control and decision-making, image processing, and time series analysis and forecasting. The authors address the consistent and appropriate treatment of the notions of fuzzy sets and fuzzy logic and their applications. They provide two complementary views of the methodology, which is based on fuzzy IF-THEN rules. The first, more traditional method involves fuzzy approximation and the theory of fuzzy relations. The second method is based on a combination of formal fuzzy logic and linguistics. A very important topic covered for the first time in book form is the fuzzy transform (F-transform). Applications of this theory are described in separate chapters and include image processing and time series analysis and forecasting. All of the mentioned components make this book of interest to students and researchers of fuzzy modeling as well as to practitioners in industry. Features: * Provides a foundation of fuzzy modeling and proposes a thorough description of fuzzy modeling methodology * Emphasizes fuzzy modeling based on results in linguistics and formal logic * Includes chapters on natural language and approximate reasoning, fuzzy control and fuzzy decision-making, and image processing using the F-transform * Discusses fuzzy IF-THEN rules for approximating functions, fuzzy cluster analysis, and time series forecasting Insight into Fuzzy Modeling is a reference for researchers in the fields of soft computing and fuzzy logic as well as undergraduate, master and Ph.D. students. Vilém Novák, D.Sc. is Full Professor and Director of the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Irina Perfilieva, Ph.D. is Full Professor, Senior Scientist, and Head of the Department of Theoretical Research at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic. Antonín Dvorák, Ph.D. is Associate Professor, and Senior Scientist at the Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic.

Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.

In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the most recently developed methods. Each one of the 22 chapters include practical applications along with new results.

In the structure of ANFIS, there are two different parameter groups: premise and consequence. Training ANFIS means determination of these parameters using an optimization algorithm. In the first ANFIS model developed by Jang, a hybrid learning approach was proposed for training. In this approach, while premise parameters are determined by using gradient descent (GD), consequence parameters are found out with least squares estimation (LSE) method. Since ANFIS has been developed, it is used in modelling and identification of numerous systems and successful results have been achieved. The selection of optimization method utilized in training is very important to get effective results with ANFIS. It is seen that derivate based (GD, LSE etc.) and non-derivative based (heuristic algorithms such us GA, PSO, ABC etc.) algorithms are used in ANFIS training. Nevertheless, it has been observed that there is a trend toward heuristic based ANFIS training algorithms for better performance recently. At the same time, it seems to be proposed in derivative and heuristic based hybrid algorithms. Within the scope of this study, the heuristic and hybrid approaches utilized in ANFIS training are examined in order to guide researchers in their study. In addition, the final status in ANFIS training is evaluated and it is aimed to shed light on further studies related to ANFIS training.

Flood prediction has gained prominence world over due to the calamitous socio-economic impacts this hazard has and the anticipated increase of its incidence in the near future. Artificial intelligence (AI) models have contributed significantly over the last few decades by providing improved accuracy and economical solutions to simulate physical flood processes. This study explores the potential of the AI computing paradigm to model the stream flow. Artificial neural network (ANN), fuzzy logic, and adaptive neuro-fuzzy inference system (ANFIS) algorithms are used to develop nine different flood prediction models using all the available training algorithms. The performance of the developed models is evaluated using multiple statistical performance evaluators. The predictability and robustness of the models are tested through the simulation of a major flood event in the study area. A total of 12 inputs were used in the development of the models. Five training algorithms were used to develop the ANN models (Bayesian regularization, Levenberg Marquardt, conjugate gradient, scaled conjugate gradient, and resilient backpropagation), two fuzzy inference systems to develop fuzzy models (Mamdani and Sugeno), and two training algorithms to develop the ANFIS models (hybrid and backpropagation). The ANFIS model developed using hybrid training algorithm gave the best performance metrics with Nash-Sutcliffe Model Efficiency (NSE) of 0.968, coefficient of correlation ( R 2 ) of 97.066%, mean square error (MSE) of 0.00034, root mean square error (RMSE) of 0.018, mean absolute error (MAE) of 0.0073, and combined accuracy (CA) of 0.018, implying the potential of using the developed models for flood forecasting. The significance of this research lies in the fact that a combination of multiple inputs and AI algorithms has been used to develop the flood models. In summary, this research revealed the potential of AI algorithm-based models in predicting floods and also developed some useful techniques that can be used by the Flood Control Departments of various states/regions/countries for flood prognosis.

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

An intuitionistic fuzzy economic order quantity (EOQ) inventory model with backlogging is investigated using the score functions for the member and non-membership functions. The demand rate is varying with selling price and promotional effort (PE). A crisp model is formulated first. Then, intuitionistic fuzzy set and score function (or net membership function) are applied in the proposed model, considering selling price and PE as fuzzy numbers. To obtain the best inventory policy, ranking index method has been adopted, showing that the score function can maintain the ranking rule also. Moreover, optimization is made under the general fuzzy optimal (GFO) and intuitionistic fuzzy optimal (IFO) policy. Finally, a graphical illustration, numerical examples with sensitivity analysis and conclusion is made to justify the model.

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and 0,1 2 -sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m -polar fuzzy set (actually, 0,1 m -set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m -polar fuzzy sets. We also give examples to show how to apply m -polar fuzzy sets in real world problems.

In this paper, we have developed an interval type-2 fuzzy logic controller  (T2FLC) approach for assessment of the risks that workers expose to at construction sites. Using this novel approach, past accident data, subjective judgments of experts, and the current safety level of a construction site are to be combined. The method is then implemented on a tunneling construction site and risk level for all type of accidents is formulated. In T2FLC assists to trace inputs and outputs in a well-organized manner for building the inferences train so that various types of risk assessment can be predicted in industry. Finally, a comparative study has been successfully performed with type-1 and type-2 fuzzy dataset for improving risk assessment that can be easily determined in the type-2 fuzzy prediction model for improving accuracy. Validity of the proposed model is done with the help of statistical analysis and multiple linear regressions.