Production planning in fuzzy environment

This paper describes a fuzzy system designed to support production planning in an industrial unit producing cardboard boxes. In this industrial unit, orders forn boxes of widthw, lengthl, heighth, made ofq layers of typek paper for delivery int units of time are produced. In the production of such orders apart from meeting the orders specifications, it is usually tried to minimize the margin trim loss, the number of machine setups and the holding cost of the finished orders. Considering the dynamism of production systems that are influenced by such factors as market demand fluctuations, changes in commercial priorities, raw material availability and production capabilities, we solve this multi-objective problem by fuzzy set theory.     

Handling fuzzy temporal constraints in a planning environment

An interleaved integration of the planning and scheduling process is presented with the idea of including soft temporal constraints in a partial order planner that is being used as the core module of an intelligent decision support system for the design forest fire fighting plans. These soft temporal constraints have been defined through fuzzy sets. This representation allows us a flexible representation and handling of temporal information. The scheduler model consists of a fuzzy temporal constraints network whose main goal is the consistency checking of the network associated to each partial order plan. Moreover, we present a model of estimating this consistency, and show the monitoring and rescheduling capabilities of the system. The resulting approach is able to tackle problems with ill defined knowledge, to obtain plans that are approximately consistent and to adapt the execution of plans to unexpected delays. This work has been partially supported under the project MCyT TIC2002-04146-C05-2 and the contract NET033957 with the Andalusian Regional Government.     

Decision-making in a fuzzy environment with fuzzy termination time

The multistage control of a deterministic and stochastic system in a fuzzy environment is considered. The fuzzy environment is meant as fuzzy constraints imposed on subsequent controls and a fuzzy goal to be attained. The fuzzy decision is assumed to be the intersection of fuzzy constraints and a fuzzy goal. The problem is to find a maximizing decision. The termination time is given as a specified fuzzy set in the space of control stages. For solving the problem, the dynamic programming is applied.     

Optimal stopping in a fuzzy environment

The problem under consideration is that of optimally controlling and stopping either a deterministic or a stochastic system in a fuzzy environment. The optimal decision is the sequence of controls that maximizes the membership function of the intersection of the fuzzy constraints and a fuzzy goal. The fuzzy goal is a fuzzy set in the cartesian product of the state space with the set of possible stopping times. Dynamic programming is applied to yield a numerical solution. This approach yields an algorithm that corrects a result of Kacprzyk.     

Distribution planning in a turbulent environment

This paper looks at planning within the present distribution environment, paying particular attention to recent trends and developments. The idea of a depot as the traditional building block of a distribution network is questioned and the various functions of a regional depot are explored.The concept of a transit point as a simple alternative to a depot is developed and examples are given of its use in practice. Several refinements are available, particularly in the area of trailer technology, and these are discussed. The necessary support system for transit point operation is identified and finally the implications for distribution planning are considered.     

Conditioning in fuzzy environment

The concepts of ‘conditional fuzzy algebra’ and ‘conditional evaluation of possibility’ are introduced when the conditioning event is either in the initial algebra or does not belong to it. In the latter case a ‘wider’ fuzzy environment in which ‘old’ and ‘new’ elements could be considered together is constructed, and a new evaluation of possibility which allows to evaluate the elements of such new environment is defined.     

A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to centralize multi-node decisions simultaneously to achieve the best use of the available resources along the time horizon so that customer demands are met at a minimum cost. This proposal is tested by using data from a real automobile SC. The fuzzy model provides the decision maker (DM) with alternative decision plans with different degrees of satisfaction.     

Scheduling arrivals to a production system in a fuzzy environment

A frequently encountered scheduling problem is to determine a material and job ready time while simultaneously finding a production sequence given customer-specified due dates. Often the production times and due dates are vague. This paper presents an investigation of scheduling ready times for a set of jobs with fuzzy service times and due dates. The ready time is constrained in that the possibility that a job is late must not exceed a predefined value. The objective in such an instance is to maximize the ready time without violating these constraints. The steps necessary to determine the maximum ready time and cases in which this effort may be significantly reduced are presented for single machine and flow shop production systems. Finally, a branch and bound technique is developed for cases in which the optimal job sequence cannot be determined a priori.     

Conflict resolution in fuzzy environment

Conflict resolution methodology is discussed with fuzzified Pareto frontier. Four solution concepts, namely, the Nash solution, the generalized Nash solution, the Kalai-Smorodinsky concept, and a solution method based on a special bargaining process are examined. The solutions are also fuzzy, the corresponding payoff values are fuzzy numbers, the membership functions of which are determined. Three particular cases are considered in the paper. Linear, quadratic, and general nonlinear Pareto frontiers with known shape are examined.     

Job evaluation in fuzzy environment

Job evaluation helps in developing and maintaining a pay structure based on values of the jobs. The job evaluation problem may be treated as managerial decision-making problem with multiple objectives. The present paper deals with the evaluation of a job in fuzzy environment. Fuzzy mathematical model has been developed for the job evaluation and solved with a suitable technique. A sample case study has been considered and the relative worth of various levels of job factors have been calculated numerically along with the scores of the benchmark jobs. An effort has been made to optimize the decision by maximizing the min operator.     

A stopping game in a stochastic and fuzzy environment

A zero-sum stopping game for a sequence of fuzzy-valued random variables is discussed. The fuzzy random variables are estimated by probabilistic expectation and fuzzy expectation. A saddle point is given for the stopping game.     

Behavior of finite-nonstationary deterministic automata in a fuzzy environment

The paper presents a method of finding optimal control of generalized deterministic abstract automaton, the structure of which is given by an arbitrary finite graph in a fuzzy environment. The control is found in order to achieve a fuzzy goal, which is given as a fuzzy set in any fixed finite vertex of the automaton structural graph. The problem solution is divided into two stages. The first stage provides the greatest possible degree of achieving the fuzzy goal depending on the path from the initial graph vertex to the fixed one, while the second stage makes it possible to construct a set of input words that ensure the achievement of this goal on the selected path. The conclusion presents an example of the application of the proposed method for constructing a regular expression of control sequences for the given abstract finite-nonstationary deterministic automaton.     

On the fuzzy team decision in a changing environment

This paper formulates a fuzzy team decision problem in a changing environment. The concept of a fuzzy set is introduced to formulate the team decision processes in a dynamic environment which contains fuzzy states, fuzzy information functions, fuzzy information signals, fuzzy decision functions and fuzzy actions.     

S-curve regression model in fuzzy environment

The purpose of this paper is to discuss the problem for least squares fitting of fuzzy-valued data, which are expressed as fuzzy numbers, and to develop an S-shaped curve regression model for fitting this type of data. It is shown that the solution of the S-curve regression model is equivalent to the solution of the corresponding linear equations, and, furthermore, the solution can be explicitly obtained by solving the linear equations.     

European option pricing model in a stochastic and fuzzy environment

The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.     

An optimistic decision-making in fuzzy environment

Bellman and Zadeh have originated three systems of multistage decision processes in a fuzzy environment: deterministic, stochastic and fuzzy systems. In this article, we consider an optimization problem with an optimistic criterion on a fuzzy system. By making use of minimization–maximization expectation in a fuzzy environment, we derive a recursive equation for the fuzzy decision process through invariant imbedding approach. By illustrating a three-state, two-decision and two-stage model, we give an optimal solution through dynamic programming. The optimal solution is also verified by the method of multistage fuzzy decision tree-table.     

Dynamic programming for fuzzy systems with fuzzy environment

A dynamic programming functional equation for a multi-stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation. This is an extension of the Bellman-Zadeh model.     

Using the Hamming distance to extend TOPSIS in a fuzzy environment

Considering the fact that, in some cases, determining precisely the exact value of attributes is difficult and that their values can be considered as fuzzy data, this paper extends the TOPSIS method for dealing with fuzzy data, and an algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. In this approach, to identify the fuzzy ideal solution and fuzzy negative ideal solution, one of the Yager indices which is used for ordering fuzzy quantities in [0, 1] is applied. Using Yager’s index leads to a procedure for choosing fuzzy ideal and negative ideal solutions directly from the data for observed alternatives. Then, the Hamming distance is proposed for calculating the distance between two triangular fuzzy numbers. Finally, an application is given, to clarify the main results developed in the paper.