Fuzzy Random Environment Research Articles

Random fuzzy location-scale family with linear fuzzy location function

Coexistence of fuzziness and the randomness has become an intrinsic character in modern manufacturing environments. Accordingly, it is necessary to introduce a new random fuzzy reliability concept and regression models to facilitate the random and fuzzy uncertainties. In this article, we propose the average chance reliability as a measure of quality index under random fuzzy uncertainty, which can be regarded as a counterpart of conventional reliability under probability theory. Furthermore, we extend the probabilistic location-scale family, which is actually a non-normal regression model, into a random fuzzy location-scale family, which is developed for the facilitation of the covariate modeling under random fuzzy environments. We will particularly focus our development on a random fuzzy location-scale family, in which the location function is a fuzzy regression model with each fuzzy exploratory variable being piecewise linear credibility distributed.

A CLASS OF INTEGRATED LOGISTICS NETWORK MODEL UNDER RANDOM FUZZY ENVIRONMENT AND ITS APPLICATION TO CHINESE BEER COMPANY

In this paper, we integrated the forward logistics and the reuse reverse logistics to set up a closed-loop integrated logistics system under a random fuzzy environment. A random fuzzy multi-objective programming model was established which can describe the integrated logistics as a cycle of production, distribution, consumption, collection, transportation, recycling, disposal, reuse and redistribution. We then used the expected value operator and the chance-constrained operator to handle the random fuzzy objective functions and the random fuzzy constraints. The solution scheme was pursued by a genetic algorithm based on random fuzzy simulation and compromise approach. And an application to a Chinese beer company was given as an illustration.

Modeling data envelopment analysis by chance method in hybrid uncertain environments

This article first presents several formulas of chance distributions for trapezoidal fuzzy random variables and their functions, then develops a new class of chance model (C-model for short) about data envelopment analysis (DEA) in fuzzy random environments, in which the inputs and outputs are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. Since the objective and constraint functions contain the chance of fuzzy random events, for general fuzzy random inputs and outputs, we suggest an approximation method to compute the chance. When the inputs and outputs are mutually independent trapezoidal fuzzy random variables, we can turn the chance constraints and the chance objective into their equivalent stochastic ones by applying the established formulas for the chance distributions. In the case when the inputs and the outputs are mutually independent trapezoidal fuzzy random vectors, the proposed C-model can be transformed to its equivalent stochastic programming one, in which the objective and the constraint functions include a number of standard normal distribution functions. To solve such an equivalent stochastic programming, we design a hybrid algorithm by integrating Monte Carlo (MC) simulation and genetic algorithm (GA), in which MC simulation is used to calculate standard normal distribution functions, and GA is used to solve the optimization problems. Finally, one numerical example is presented to demonstrate the proposed modeling idea and the efficiency in the proposed model.

Optimal run lengths in deteriorating production processes in random fuzzy environments

This paper presents a random fuzzy economic manufacturing quantity (EMQ) model in a deteriorating process. It is assumed that the setup cost and the average holding cost are characterized as fuzzy variables and the elapsed time until shift is a random fuzzy variable. As a function of these parameters, the average total cost is also a random fuzzy variable, and the unimodality of its expected value is studied. To obtain the optimal run length and the minimum average cost, simultaneous perturbation stochastic approximation (SPSA) algorithm based on random fuzzy simulation is provided. Random fuzzy EMQ models with fuzzy deterioration, fuzzy linear deterioration and fuzzy exponential deterioration are presented, respectively. These models can be solved by the proposed algorithm. Numerical examples are presented in the end.

A class of random fuzzy programming and its application to supply chain design

Supply chain design problems have recently raised a lot of interest since the opportunity of an integrated management of the supply chain can reduce the propagation of undesirable events through the network and can affect decisively the profitability of the members. Often uncertainties may be associated with demand, supply or various relevant costs. In most of the existing models uncertainties are treated as randomness and are handled by appealing to probability theory. However, in certain situations uncertainties are due to random fuzziness and in these case the random fuzzy programming is applicable, while no attempt has been made to define those uncertain parameters as random fuzzy variables. We propose a random fuzzy programming model and a methodology for solving a multi-stage supply chain design problem of a realistic scale in the random fuzzy environment. Based on the concept of random fuzzy variable, we use probability theory, fuzzy set theory and optimizing theory as our research tool. At a given possibility α , we provide an auxiliary programming model of the random fuzzy programming and convert it to a deterministic mixed 0–1 integer programming model, of which the optimal solutions are proved to exist. Then we present a novel technique called spanning-tree based on genetic algorithm (st-GA) to get the heuristic solutions. A computational example involving a relatively large supply chain is presented to highlight the significance of the random fuzzy model as well as the effectiveness of the proposed solution method. Random fuzzy variable is a very useful tool to describe the uncertain parameters and our methodology may be applied to any optimization problems with random fuzzy factors.

Multi-objective decision making model under fuzzy random environment and its application to inventory problems

In this paper, we concentrate on developing a fuzzy random multi-objective model about inventory problems. By giving some definitions and discussing some properties of fuzzy random variable, we design a method of solving solution sets of fuzzy random multi-objective programming problems. These are applied to numerical inventory problems in which all inventory costs, purchasing and selling prices in the objectives and constraints are assumed to be fuzzy random variables in nature, and then the impreciseness of fuzzy random variables in the above objectives and constraints are transformed into fuzzy variables which are similar trapezoidal fuzzy numbers. The exact parameters of fuzzy membership function and probability density function can be obtained through fuzzy random simulating the past dates. By comparing the results with those from the fuzzy multi-objective models, we believe that the proposed fuzzy random multi-objective model and hybrid intelligent algorithm provide significant solutions to construct other inventory models with fuzzy random variables in real life.

A class of multi-objective supply chain networks optimal model under random fuzzy environment and its application to the industry of Chinese liquor

An important issue, when shipping cost and customers demand are random fuzzy variables in supply chain network (SCN) design problem, is to find the network strategy that can simultaneously achieve the objectives of minimization total cost comprised of fixed costs of plants and distribution centers (DCs), inbound and outbound distribution costs, and maximization customer services that can be rendered to customers in terms of acceptable delivery time. In this paper, we propose a random fuzzy multi-objective mixed-integer non-linear programming model for the SCN design problem of Luzhou Co., Ltd. which is representative in the industry of Chinese liquor. By the expected value operator and chance constraint operator, the model has been transformed into a deterministic multi-objective mixed-integer non-linear programming model. Then, we use spanning tree-based genetic algorithms (st-GA) by the Prüfer number representation to find the SCN to satisfy the demand imposed by customers with minimum total cost and maximum customer services for multi-objective SCN design problem of this company under condition of random fuzzy customers demand and transportation cost between facilities. Furthermore, the efficacy and the efficiency of this method are demonstrated by the comparison between its numerical experiment results and those of tradition matrix-based genetic algorithm.

Facility location–allocation problem in random fuzzy environment: Using (α,β) -cost minimization model under the Hurewicz criterion

Facility location–allocation (FLA), which has been proved to be a valuable method in siting service facility, is widely used in real life, such as emergency service systems, telecommunication net works, public services, etc. Many researchers have studied the FLA problem in a deterministic, stochastic or fuzzy environment. However, those models cannot satisfy various customers’ demands in some cases. Thus, this paper considers the FLA problem under random fuzzy environment using ( α , β ) -cost minimization model under the Hurwicz criterion. It will be proved that this model can deal with various FLA problems in random, fuzzy and random fuzzy environments. By varying the value λ , it can balance the optimistic level of the decision makers. For solving the random fuzzy model efficiently, the simplex algorithm, random fuzzy simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, a numerical example is presented for illustration.

Three types of models for stochastic scheduling with fuzzy information

In this paper we consider the scheduling problems on a single machine in random fuzzy environments. Three types of random fuzzy programming models are provided for single machine scheduling with random fuzzy processing times. A hybrid intelligent algorithm is designed to solve the proposed models and its effectiveness is illustrated by numerical experiments.