Maximum entropy principle with imprecise side-conditions III: Crisp continuous solutions

In this paper we consider the maximum entropy principle with imprecise side-conditions, where the imprecise side-conditions are modeled as fuzzy sets. In two previous papers our solution produced: (1) fuzzy discrete probability distributions and fuzzy probability density functions; and (2) crisp discrete probability distributions. In this paper we consider only continuous probability density functions and we have the constraint that the solution must be crisp (non-fuzzy).     

Maximum entropy principle with imprecise side-conditions

In this paper we consider the maximum entropy principle with imprecise side-conditions, where the imprecise side-conditions are modeled as fuzzy sets. Our solution produces fuzzy discrete probability distributions and fuzzy probability density functions.     

New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle

Keeping in view the non-probabilistic nature of experiments, two new measures of weighted fuzzy entropy have been introduced and to check their authenticity, the essential properties of these measures have been studied. Under the fact that measures of entropy can be used for the study of optimization principles when certain partial information is available, we have applied the existing as well as the newly introduced weighted measures of fuzzy entropy to study the maximum entropy principle.     

Note on the article: Maximum entropy analysis of the M/M/1 queueing system with multiple vacations and server breakdowns

Wang et al. [Wang, K. H., Chan, M. C., & Ke, J. C. (2007). Maximum entropy analysis of the M^[x]/M/1 queueing system with multiple vacations and server breakdowns. Computers & Industrial Engineering, 52, 192–202] elaborate on an interesting approach to estimate the equilibrium distribution for the number of customers in the M^[x]/M/1 queueing model with multiple vacations and server breakdowns. Their approach consists of maximizing an entropy function subject to constraints, where the constraints are formed by some known exact results. By a comparison between the exact expression for the expected delay time and an approximate expected delay time based on the maximum entropy estimate, they argue that their maximum entropy estimate is sufficiently accurate for practical purposes. In this note, we show that their maximum entropy estimate is easily rejected by simulation. We propose a minor modification of their maximum entropy method that significantly improves the quality of the estimate.     

Global existence of periodic solutions in a six-neuron BAM neural network model with discrete delays

In this paper, a six-neuron BAM neural network model with discrete delays is considered. Using the global Hopf bifurcation theorem for FDE due to Wu [Symmetric functional differential equations and neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] and the Bendixson's criterion for high-dimensional ODE due to Li and Muldowney [On Bendixson' criterion, J. Differential Equations 106 (1994) 27-39], a set of sufficient conditions for the system to have multiple periodic solutions are derived when the sum of delays is sufficiently large.     

Control of discrete event systems with respect to strict duration: Supervision of an industrial manufacturing plant

In this paper, we propose a (max, +)-based method for the supervision of discrete event systems subject to tight time constraints. Systems under consideration are those modeled as timed event graphs and represented with linear (max, +) state equations. The supervision is addressed by looking for solutions of constrained state equations associated with timed event graph models. These constrained state equations are derived by reducing duration constraints to elementary constraints whose contributions are injected in the system’s state equations. An example for supervisor synthesis is given for an industrial manufacturing plant subject to a strict temporal constraint, the thermal treatment of rubber parts for the automotive industries. Supervisors are calculated and classified according to their performance, considering their impact on the production throughput.     

Correlation between learning (probability of success) and fuzzy entropy in control of intelligent robot's part macro-assembly tasks with sensor fusion techniques

A correlation between a learning and a fuzzy entropy, using the control of robotic part macro-assembly (part-bringing) task as an example, is introduced. Two intelligent part-bringing algorithms, to bring a part from an initial position to an assembly hole or a receptacle (target or destination) for a purpose of a part mating in a partially unknown environment containing obstacles, related to a robotic part assembly task are introduced. An entropy function, which is a useful measure of the variability and the information in terms of uncertainty, is introduced to measure its overall performance of a task execution related to the part-bringing task. The degree of uncertainty associated with the part-bringing task is used as an optimality criterion, e.g. minimum entropy, for a specific task execution. Fuzzy set theory, well-suited to the management of uncertainty, is used to address the uncertainty associated with the macro-assembly procedure. In the first algorithm, a macro-assembly, locating various shaped assembly holes (targets) in the workspace corresponding to the shapes of the parts and then bringing the part to the corresponding target, despite existing obstacles is introduced. This is accomplished by combining a neural network control strategy coordinating with a mobile rectilinear grid composed of optical sensors as well as fuzzy optimal controls. Depending on topological relationships among the part's present position, the position of obstacles, and the target position in the workspace, a specific rulebase from a family of distinct fuzzy rulebases for avoiding obstacles is activated. The higher the probability, the input pattern (or value) of the neural network to be identified as the desired output is, the lower the fuzzy entropy is. Through the fuzzy entropy, a degree of identification between the input pattern and the desired output of the neural network can be measured. In the second algorithm, a macro-assembly with a learning algorithm and a sensor fusion for bringing the part to the target is introduced. By employing a learning approach, the uncertainty associated with the part-bringing task is reduced. The higher the probability of success is, the lower the fuzzy entropy is. The results show clearly the correlation between a probability of success related to the task execution of the part-bringing and the fuzzy entropy, and also show the effectiveness of above methodologies. The proposed technique is not only a useful tool to measure the behaviour of the learning but applicable to a wide range of robotic tasks including motion planning, and pick and place operations with various shaped parts and targets.