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The purpose of this paper is to answer the question that what the best shape of fuzzy sets is in fuzzy systems for function approximation which is essential in many applications of fuzzy systems.

The uniform approximation rates indicate the approximating capabilities of fuzzy systems for function approximation. By Fourier analysis, the uniform approximation rates are estimated for the fuzzy systems with various shapes of if‐part fuzzy sets in the case of single‐input and single‐output. Based on the approximation rates, the relationships between the approximating capabilities and the shapes of fuzzy sets are developed and compared.

The since functions as the input membership functions in fuzzy systems are proved to have the almost best approximation property in a particular class of membership functions.

From the viewpoint of function approximation, the input membership functions are not necessarily positive in fuzzy systems.

For engineers, the sinc‐shaped membership function is a good choice to improve their fuzzy systems in real applications.

The uniform approximation rates of fuzzy systems for function approximation are estimated. Mathematically, the relationships between the approximating capabilities and the shapes of fuzzy sets are analyzed for fuzzy systems.

With the object of translating some concepts and results from classical Reliability Theory into particular types of multistate systems, this article starts by presenting some basic definitions of fuzzy systems. The concepts of fuzzy coherent and fuzzy crisp‐based systems are examined and some results on fuzzy coherent structures are presented. Both static and non‐static models are considered.

On the basis of the f*‐Divergence for fuzzy information systems, this article presents a sequential selection method for a fixed number of fuzzy systems. f*‐Divergence is a measure of the quantity of information concerning the state space provided by the fuzzy system when the a priori probability distribution is defined on the space. The method described by the author determines a procedure which maximises the “Terminal” f*‐Divergence.

The concept of L‐fuzzy systems is introduced as a generalisation of that of general systems. A universal structure of a special kind of L‐fuzzy system is given, some mapping properties of L‐fuzzy systems are studied and a number of open questions posed.

The purpose of this paper is to evaluate various reliability parameters of a multi‐robot system, arranged in a complex configuration. The effects of failures and course of action on the system performance have also been investigated.

The present work is based on a multi‐robotic system, in which two robots are working independently with a conveyer unit. Petri net (PN) tool is applied to represent the asynchronous and concurrent processing of the system. To enhance the relevance of the reliability study, fuzzy numbers are developed from available data of the components, using fuzzy possibility theory to define membership functions. The use of fuzzy arithmetic in the PN model increases the flexibility for application to various systems and conditions. Various reliability parameters (such as mean time between failures, ENOF, reliability, availability, etc.) are computed using fuzzy lambda‐tau methodology. As the available data are imprecise, incomplete, vague and conflicting, the fuzzy methodology can deal easily with approximations.

The adopted methodology in the present work improves the shortcomings/drawbacks of the existing probabilistic approaches and gives a better understanding of the system behavior through its graphical representation.

In an earlier study failure behavior of a single robot was analyzed. This paper is an extension of the previous work, in which failure behavior of multi‐robotic system is analyzed. Also, the interactions among the working units of multi‐robotic system are deeply studied. The paper contains a new idea about the reliability analysis of robotic system. Fuzzy lambda‐tau methodology, a fuzzy PROBIST technique, is used for the proposed robotic system and the results obtained are compared with crisp results. Reliability analysis of a multi‐robotic system is presented in this paper, which may help the system analysts to analyze and predict the system behavior and to reallocate the required resources.

Several different simulation techniques, such as discrete event simulation (DES), system dynamics (SD) and agent-based modelling (ABM), have been used to model complex construction systems such as construction processes and project management practices; however, these techniques do not take into account the subjective uncertainties that exist in many construction systems. Integrating fuzzy logic with simulation techniques enhances the capabilities of those simulation techniques, and the resultant fuzzy simulation models are then capable of handling subjective uncertainties in complex construction systems. The objectives of this chapter are to show how to integrate fuzzy logic and simulation techniques in construction modelling and to provide methodologies for the development of fuzzy simulation models in construction. In this chapter, an overview of simulation techniques that are used in construction is presented. Next, the advancements that have been made by integrating fuzzy logic and simulation techniques are introduced. Methodologies for developing fuzzy simulation models are then proposed. Finally, the process of selecting a suitable simulation technique for each particular aspect of construction modelling is discussed.

The main goal of this paper is to develop novel Tω(weakest t-norm)-based fuzzy arithmetic operations to analyze the intuitionistic fuzzy reliability of Printed Circuit Board Assembly (PCBA) using fault tree.

The paper proposes a fuzzy fault tree analysis (FFTA) method for evaluating the intuitionistic fuzzy reliability of any nonrepairable system with uncertain information about failures of system components. This method uses a fault tree for modeling the failure phenomenon of the system, triangular intuitionistic fuzzy numbers (TIFNs) to determine data uncertainty, while novel arithmetic operations are adopted to determine the intuitionistic fuzzy reliability of a system under consideration. The proposed arithmetic operations employ Tω(weakest t-norm) to minimize the accumulating phenomenon of fuzziness, whereas the weighted arithmetic mean is employed to determine the membership as well as nonmembership degrees of the intuitionistic fuzzy failure possibility of the nonrepairable system. The usefulness of the proposed method has been illustrated by inspecting the intuitionistic fuzzy failure possibility of the PCBA and comparing the results with five other existing FFTA methods.

The results show that the proposed FFTA method effectively reduces the accumulating phenomenon of fuzziness and provides optimized degrees of membership and nonmembership for computed intuitionistic fuzzy reliability of a nonrepairable system.

The paper introduces Tω(weakest t-norm) and weighted arithmetic mean based operations for evaluating the intuitionistic fuzzy failure possibility of any nonrepairable system in an uncertain environment using a fault tree.

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

The purpose of this study is to develop a fuzzy expert system to design robust forecast of return quantity in order to handle uncertainties from the return process in reverse logistic network.

The most important factors which have impact on return of products are defined. Then the factors which have collinearity with others are eliminated by using dimension redundancy analysis. By training data of selected factors with fuzzy expert system, the return amounts of alternative cities are forecasted.

The performance metrics of the proposed model are found as satisfactory. That means the result of this study indicates that fuzzy expert systems can be used as a supportive tool for forecasting return quantity of alternative areas.

In the future, the proposed model can be used for forecasting other uncertain parameters such as return quality and return time. Other fuzzy systems such as type-2 fuzzy sets can be used, or other expert systems such as artificial neural networks can be integrated into fuzzy systems.

An application at an e-recycling facility is conducted for clarifying how the method is used in a real decision process.

It is the first study which aims to model an alternative forecasting by utilizing fuzzy expert system. Furthermore, a comprehensive factor list which includes predictors of the system is defined. Then, a dimension redundancy analysis is developed to reveal factors having significant impact on the return process and eliminate the rest.

The purpose of this paper is to analyze the reliability of the washing system in a paper plant in a more promising way under vague environment by reducing the accumulating phenomenon of fuzziness and accelerating the computation process using the T_ω (weakest t-norm) based fuzzy lambda-tau (TBFLT) technique.

This paper presents a unified approach for analyzing the fuzzy reliability of the washing system under vague environment. This approach applies the TBFLT technique which uses triangular fuzzy numbers for incorporating data uncertainty, fault tree and lambda-tau method for finding system failure rate and repair time mathematical expressions while simplified T_ω-based arithmetic operations are applied for computing various reliability parameters of the system. The effectiveness of the TBFLT technique has been demonstrated by analyzing fuzzy reliability of the system using five different techniques including TBFLT. Moreover, this paper applies extended Tanaka’s (1983) approach to rank the critical components of the system.

The TBFLT technique has the advantage of low computation complexity in comparison to other techniques and effectively reduces the accumulating phenomenon of fuzziness. This main finding verifies the conclusion made by Chen (1994).

The author has suggested a simple and more applicable technique for analyzing the fuzzy reliability of any complex process industrial system under vague environment. The effectiveness of the technique has been demonstrated by computing various reliability parameters of the washing system of a paper plant.