Nonlinear boundary value problems and multicomponent distillation

AbstractMulticomponent distillation is essentially a nonlinear boundary value problem in difference equations. Different computational approaches can be developed based on the choice of different parameters as the unknown variables, different stages as the initial stage, and different methods to solve the difference equations. In this work, these different aspects are explored. One particular interesting approach is to choose the (m − 1) liquid phase concentrations and total liquid molal rate as the unknowns, where m is the number of components in the system. This approach results in a system of nonlinear simultaneous mixed difference and algebraic equations and presents some interesting computational problems

Multi-criteria de Novo programming with fuzzy parameters

AbstractA multiple criteria de Novo program with fuzzy parameters is developed based on the possibility concept of fuzzy set. This approach is much more flexible than the standard de Novo programming and allows the decision maker to choose his appropriate membership grades based on the risk factor he is willing to take. A numerical example is given to illustrate the approach

Ranking of fuzzy sets based on the concept of existence

AbstractVarious approaches have been proposed for the comparison or ranking of fuzzy sets. However, due to the complexity of the problem, a general method which can be used for any situation still does not exist. This paper formalizes the concept of existence for the ranking of fuzzy sets. Many of the existing fuzzy ranking methods are shown to be some application of this concept. An improved fuzzy ranking method is then introduced, based on this concept. This newly introduced method is expanded for treating both normal and nonnormal, convex and nonconvex fuzzy sets. Emphasis is placed on the use of the subjectivity of the decision maker, such as the optimistic or the pessimistic view points. An improved procedure for obtaining linguistic conclusions is also developed. Finally, some numerical examples are given to illustrate the approach

The estimation of normalized fuzzy weights

AbstractThe estimation of a normalized set of positive fuzzy weights constitutes the most important aspects in the fuzzy multiple attribute decision making process. A systematic treatment of this problem is carried out in this paper. The concept of fuzzy normalization is first defined and the meaning of consistency in a fuzzy environment is discussed. Based on these definitions and discussions, the various approaches in the literature are examined and several improvements or new approaches are proposed. Numerical examples are used to evaluate and to compare the various existing and the newly proposed approaches

Analysis of fuzzy queues

AbstractA general approach for queuing systems in a fuzzy environment is proposed based on Zadeh's extension principle, the possibility concept and fuzzy Markov chains. To illustrate the approach, analytical results for M/F/1 and FM/FM/1 systems are presented. Fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations. A simple numerical example is also presented

Application of an adaptive neural fuzzy inference system to thermal comfort and group technology problems

AbstractThe Adaptive Neural Fuzzy Inference System (ANFIS) is used to design two vague systems, namely thermal comfort and group technologies in production and operations management. Results show that both systems can be modeled successfully by the combined use of a fuzzy approach and neural network learning

Asymptotic equilibrium and stability of fuzzy differential equations

AbstractThe local existence and uniqueness theorems and the global existence of solutions were investigated in [1–3], respectively, for the Cauchy problem of fuzzy-valued functions of a real variable whose values are in the fuzzy number space (En, D). In this paper, we first study the asymptotic equilibrium for fuzzy evolution equations. Then, the stability properties of the trivial fuzzy solution of the perturbed semilinear fuzzy evolution equations are investigated by extending the Lyapunov's direct method

Invariant imbedding, method of characteristics, and parameter estimation

AbstractParameter estimation in a physical system from observed data is carried out by a method which combines invariant imbedding formalism and the method of characteristics. This avoids the necessity of making use of an initial guess for the parameter necessary if one adopts quasilinearization techniques. Numerical results for a simple one parameter system is presented

Application of invariant imbedding to the estimation of process duration

AbstractThis work deals with the application of invariant imbedding to solve a particularly important design problem, namely, the duration of the process. A numerical example is used to illustrate the approach. The advantage of this approach is its straightforward nature and uses only the usual design data. It avoids any iterations and thus no convergence problems need to be considered

Fuzzy clustering in cell formation with multiple attributes

AbstractAn approach based on fuzzy clustering and aggregation operators is proposed to design cell formation involving multiple criteria or multiple attributes. The three most basic attributes in cell formation, namely, number of machines required, processing time, and common tools required on machines, are considered. The results are compared with the single attribute results of Chu and Hayya (1991) [27]