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The aim of this paper is to review the literature that has addressed direct and inverse problems in option pricing in a fuzzy setting. In a direct problem, the stochastic process for the underlying asset is assumed and the option prices are derived by no-arbitrage or equilibrium conditions. In an inverse problem, the option prices are taken as given and used to infer the underlying asset process. Models are divided into discrete-time and continuous-time ones. Special attention is paid to real options, a particular class of nonfinancial options that are used to evaluate real investments. Directions for future research are outlined. In particular in inverse problems, there is still room for promising research, both in discrete time and in continuous time. Moreover, given that many proposed methods remain difficult to use in practice, there is mainly the need to apply the fuzzy models obtained on real market data and to compare the results with nonfuzzy techniques in order to assess the usefulness and the improvements in the modeling of imprecise data with fuzzy sets and fuzzy random variables. [ABSTRACT FROM AUTHOR]

This short paper discusses the modeling of random fuzzy renewal reward processes in which the interarrival times and rewards are represented by nonnegative random fuzzy variables. Based on random fuzzy theory, a random fuzzy variable denotes a measurable function from a credibility space to a collection of random variables. Under this setting, the long-run expected reward per unit time is addressed and the theorem on random fuzzy renewal rewards is established. The utility of this research is demonstrated with a realistic application case. [ABSTRACT FROM AUTHOR]

Uncertainty in manufacturing processes is caused both by randomness, as in material properties, and by fuzziness, as in the inexact knowledge. Previous research has seldom considered these two types of uncertainty when modeling manufacturing processes. In this paper, a hybrid fuzzy least-squares regression (HFLSR) approach to modeling manufacturing processes, which does take into consideration these two types of uncertainty, is proposed and described, and a new form of weighted fuzzy arithmetic is introduced to develop the hybrid fuzzy least-squares regression method. The proposed HFLSR approach not only features the capability of dealing with the two types of uncertainty, but also addresses the consideration of replication of responses in experiments. To investigate the effectiveness of the proposed approach to process modeling, it was applied to the modeling solder paste dispensing process. Modeling results were compared with those based on statistical regression and fuzzy linear regression. It was found that the accuracy of prediction based on the HFLSR is slightly better than that based on statistical regression and much better than that based on the Peters fuzzy regression. [ABSTRACT FROM AUTHOR]

In this paper, a new class of fuzzy random optimization problem called two-stage fuzzy random programming or fuzzy random programming with recourse (FRPR) problem is first presented; then its deterministic equivalent programming problem is characterized. Because the FRPR problems include fuzzy random variable parameters with an infinite support, they are inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, an approximation approach to the fuzzy random variables with infinite supports by finitely supported ones is proposed, which results in finite-dimensional FRPR problems. After that, this paper is devoted to establishing the conditions under which the objective value (optimal objective value, and minimizers) of such finite-dimensional FRPR problem can be shown to converge to the objective value (respectively, optimal objective value and minimizers) of the original infinite-dimensional FRPR problem. [ABSTRACT FROM AUTHOR]

In practice, the lifetimes of unrepairable systems contain both randomness and fuzziness. So it is appropriate to assume the lifetimes of systems to be fuzzy random variables. In this paper, the definitions of reliability and mean time to failure (MTTF) of unrepairable systems with fuzzy random lifetimes are given, respectively. Then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established. Furthermore, the reliability and MTTF of series systems, parallel systems, series-parallel systems, parallel-series systems, and cold standby systems are discussed, respectively. Finally, some numerical examples are presented to illustrate how to calculate the reliability and MTTF of unrepairable systems with fuzzy random lifetimes. [ABSTRACT FROM AUTHOR]

As a fuzzification of the Choquet integral, the defuzzified choquet integral with fuzzy-valued integrand (DCIFI) takes a fuzzy-valued integrand and gives a crisp-valued integration result. In this paper, the DCIFI acts as a projection to project high-dimensional heterogeneous fuzzy data to one-dimensional crisp data to handle the classification problems involving different data forms, such as crisp data, interval values, fuzzy numbers, and linguistic variables, simultaneously. The nonadditivity of the signed fuzzy measure applied in the DCIFI can represent the interaction among the measurements of features towards the discrimination of classes. Values of the signed fuzzy measure in the DCIFI are considered to be unknown parameters which should be learned before the classifier is used to classify new data. We have implemented a genetic algorithm (GA)-based adaptive classifier-learning algorithm to optimally learn the signed fuzzy measure values and the classified boundaries simultaneously. The performance of our algorithm has been tested both on synthetic and real data. The experimental results are satisfactory and outperform those of existing methods, such as the fuzzy decision trees and the fuzzy-neuro networks. [ABSTRACT FROM AUTHOR]

This paper deals with a novel buffer management scheme based on evolutionary computing for shared-memory asynchronous transfer mode (ATM) switches. The philosophy behind it is adaptation of the threshold for each logical output queue to the real traffic conditions by means of a system of fuzzy inferences. The optimal fuzzy system is achieved using a systematic methodology, based on genetic algorithms (GAs), which allows the fuzzy system parameters to be derived for each switch size, offering a high degree of scalability to the fuzzy control system. Its performance is comparable to that of the push-out (PO) mechanism, which can be considered ideal from a performance viewpoint, and at any rate much better than that of threshold schemes based on conventional logic. In addition, the fuzzy threshold (FT) scheme is simple and cost-effective when implemented using VLSI technology. [ABSTRACT FROM AUTHOR]

In the fuzzy clustering literature, two main types of membership are usually considered: A relative type, termed probabilistic, and an absolute or possibilistic type, indicating the strength of the attribution to any cluster independent from the rest. There are works addressing the unification of the two schemes. Here, we focus on providing a model for the transition from one schema to the other, to exploit the dual information given by the two schemes, and to add flexibility for the interpretation of results. We apply an uncertainty model based on interval values to memberships in the clustering framework, obtaining a framework that we term graded possibility. We outline a basic example of graded possibilistic clustering algorithm and add some practical remarks about its implementation. The experimental demonstrations presented highlight the different properties attainable through appropriate implementation of a suitable graded possibilistic model. An interesting application is found in automated segmentation of diagnostic medical images, where the model provides an interactive visualization tool for this task. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators called quasi-triangular norms. They are denoted by H and parameterized by a parameter ν : H(a1, a2, . . . , an; ν). From the construction of function H, it follows that it becomes a t-norm for ν = 0 and a dual t-conorm for ν = 1. For ν close to 0, function H resembles a t-norm and for ν close to 1, it resembles a t-conorm. In the paper, we also propose adjustable quasi-implications and a new class of neuro-fuzzy systems. Most neuro-fuzzy systems pro- posed in the past decade employ ‘engineering implications’ defined by a t-norm as the minimum or product. In our proposition, a quasi-implication I(a, b; ν) varies from an ‘engineering implication’ T(a, b) to corresponding S-implication as ν goes from 0 to 1. Consequently, the structure of neuro-fuzzy systems presented in this paper is determined in the process of learning. Learning procedures are derived and simulation examples are presented. [ABSTRACT FROM AUTHOR]