Optimal models for single-period supply chain problems with fuzzy demand

The aim of this paper is to develop an optimal technique for dealing with the fuzziness aspect of demand uncertainties. Triangular fuzzy numbers are used to model external demand, and decision models in both non-coordination and coordination situations are constructed. It is shown that in the decision models there exists a unique solution that can be expressed analytically. Based on the closed form solutions for both models, the behaviors and relationships of both the manufacturer and the retailer are quantitatively analyzed, and a cooperative policy for the optimization of the whole supply chain is put forward.     

Using space windowing for a preliminary analysis of complex time data in human component system studies. Examples with eye-tracking in advertising and car/head movements in driving

Empirical studies of human systems often involve recording multidimensional signals because the system components may require physical measurements (e.g., temperature, pressure, body movements and/or movements in the environment) and physiological measurements (e.g., electromyography or electrocardiography). Analysis of such data becomes complex if both the multifactor aspect and the multivariate aspect are retained. Three examples are used to illustrate the role of fuzzy space windowing and the large number of data analysis paths. The first example is a classic simulated data set found in the literature, which we use to compare several data analysis paths generated with principal component analysis and multiple correspondence analysis with crisp and fuzzy windowing. The second example involves eye-tracking data based on advertising, with a focus on the case of one category variable, but with the possibility of several space windowing models and time entities. The third example concerns car and head movement data from a driving vigilance study, with a focus on the case involving several quantitative variables. The notions of analysis path multiplicity and information are discussed both from a general perspective and in terms of our two real examples.     

Using anatomical knowledge expressed as fuzzy constraints to segment the heart in CT images

Segmenting the heart in medical images is a challenging and important task for many applications. In particular, segmenting the heart in CT images is very useful for cardiology and oncological applications such as radiotherapy. Although the majority of methods in the literature are designed for ventricle segmentation, there is a real interest in segmenting the heart as a whole in this modality. In this paper, we address this problem and propose an automatic and robust method, based on anatomical knowledge about the heart, in particular its position with respect to the lungs. This knowledge is represented in a fuzzy formalism and it is used both to define a region of interest and to drive the evolution of a deformable model in order to segment the heart inside this region. The proposed method has been applied on non-contrast CT images and the obtained results have been compared to manual segmentations of the heart, showing the good accuracy and high robustness of our approach.     

Static Bayesian games with finite fuzzy types and the existence of equilibrium

This paper studies a special game with incomplete information, in which the payoffs of the players are both random and fuzzy. Such a game is considered in the context of a Bayesian game with the uncertain types characterized as fuzzy variables. A static fuzzy Bayesian game is then introduced and the decision rules for players are given based on credibility theory. We further prove the existence of the equilibrium of the game. Finally, a Cournot competition model with fuzzy efficiency under asymmetric information is investigated as an application and some results are presented.     

Segmented software cost estimation models based on fuzzy clustering

Parametric software cost estimation models are based on mathematical relations, obtained from the study of historical software projects databases, that intend to be useful to estimate the effort and time required to develop a software product. Those databases often integrate data coming from projects of a heterogeneous nature. This entails that it is difficult to obtain a reasonably reliable single parametric model for the range of diverging project sizes and characteristics. A solution proposed elsewhere for that problem was the use of segmented models in which several models combined into a single one contribute to the estimates depending on the concrete characteristic of the inputs. However, a second problem arises with the use of segmented models, since the belonging of concrete projects to segments or clusters is subject to a degree of fuzziness, i.e. a given project can be considered to belong to several segments with different degrees.This paper reports the first exploration of a possible solution for both problems together, using a segmented model based on fuzzy clusters of the project space. The use of fuzzy clustering allows obtaining different mathematical models for each cluster and also allows the items of a project database to contribute to more than one cluster, while preserving constant time execution of the estimation process. The results of an evaluation of a concrete model using the ISBSG 8 project database are reported, yielding better figures of adjustment than its crisp counterpart.     

The solution and duality of imprecise network problems

Duality properties have been investigated by many researchers in the recent literature. They are introduced in this paper for a fully fuzzified version of the minimal cost flow problem, which is a basic model in network flow theory. This model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes. First, we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper. By applying Hukuhara’s difference, approximated and exact multiplication and Wu’s scalar production, we exhibit the flow in network models. Then, we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified MCFP to acquire fuzzy optimal flows. To give duality theorems, we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms. Finally, we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision-making problems.     

Robust Fuzzy Output Sliding Control without the Requirement of State Measurement

A robust fuzzy output sliding control for nonlinear robotic arms is proposed in this paper. The proposed method not only retains the advantages of the conventional sliding mode control such as robustness against parameter variations and external disturbances, but also uses measurable output signals to define the sliding surface function. A fuzzy controller is developed to modify the control law to avoid state measurement. Control system stability is proved by using the Lyapunov stability theorem. The system robustness is guaranteed. Simulations results demonstrate the validity and effectiveness of the proposed method for uncertain nonlinear robotic arms.     

Prosthetic Hand Finger Control Using Fuzzy Sliding Modes

In order to improve the life quality of amputees, providing approximate manipulation ability of a human hand to that of a prosthetic hand is considered by many researchers. In this study, a biomechanical model of the index finger of the human hand is developed based on the human anatomy. Since the activation of finger bones are carried out by tendons, a tendon configuration of the index finger is introduced and used in the model to imitate the human hand characteristics and functionality. Then, fuzzy sliding mode control where the slope of the sliding surface is tuned by a fuzzy logic unit is proposed and applied to have the finger model to follow a certain trajectory. The trajectory of the finger model, which mimics the motion characteristics of the human hand, is pre-determined from the camera images of a real hand during closing and opening motion. Also, in order to check the robust behaviour of the controller, an unexpected joint friction is induced on the prosthetic finger on its way. Finally, the resultant prosthetic finger motion and the tendon forces produced are given and results are discussed.     

Full perimeter obstacle contact sensor based on flex sensors

This paper presents an obstacle contact sensor system that can detect both the contact state and the direction of contact parallel to the movement plane of a mobile system carrying the sensor. This sensor system is based on a regular- or irregular-shaped ring surrounding the mobile system’s perimeter, connected to the mobile system’s body by a set of soft springs and also coupled mechanically to a set of four flex sensors measuring the relative displacement and direction of the ring when contacting an obstacle. The set of flex sensors is connected to a low-cost electronic module that implements a data acquisition block and a fuzzy processing block, delivering a value representing the estimated contact zone of the ring. Some experiments show how this detection system effectively reduces the sensor count needed for full coverage of the mobile system’s perimeter. Despite the kind of output implemented in the experiments, the contact force can also be estimated.     

Classification of Fuzzy Mathematical Morphologies Based on Concepts of Inclusion Measure and Duality

Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory. This paper discusses and compares several well-known and new approaches towards gray-scale and fuzzy mathematical morphology. We show in particular that a certain approach to fuzzy mathematical morphology ultimately depends on the choice of a fuzzy inclusion measure and on a notion of duality. This fact gives rise to a clearly defined scheme for classifying fuzzy mathematical morphologies. The umbra and the level set approach, an extension of the threshold approach to gray-scale mathematical morphology, can also be embedded in this scheme since they can be identified with certain fuzzy approaches.