Kuhu Pal

A possibilistic fuzzy c-means clustering algorithm

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.

A mixed c-means clustering model

We justify the need for computing both membership and typicality values when clustering unlabeled data. Then we propose a new model called fuzzy-possibilistic c-means (FPCM). Unlike the fuzzy and possibilistic c-means (FCM/PCM) models, FPCM simultaneously produces both memberships and possibilities, along with the usual point prototypes or cluster centers for each cluster We show that FPCM solves the noise sensitivity defect of FCM, and also overcomes the coincident clusters problem of PCM. Then we derive first order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima. Three numerical examples are given that compare FCM to FPCM. Our calculations show that FPCM compares favorably to FCM.

Breast cancer detection using rank nearest neighbor classification rules

In this article, we propose a new generalization of the rank nearest neighbor (RNN) rule for multivariate data for diagnosis of breast cancer. We study the performance of this rule using two well known databases and compare the results with the conventional k-NN rule. We observe that this rule performed remarkably well, and the computational complexity of the proposed k-RNN is much less than the conventional k-NN rule.

A new scheme for fuzzy rule-based system identification and its application to self-tuning fuzzy controllers

There are many important issues that need to be resolved for identification of a fuzzy rule-based system using clustering. We address three such important issues: 1) deciding on the proper domain(s) of clustering; 2) deciding on the number of rules; and 3) getting an initial estimate of parameters of the fuzzy systems. We justify that one should start with separate clustering of X (input) and Y (output). We propose a scheme to establish correspondence between the clusters obtained in X and Y. The correspondence dictates whether further splitting/merging of clusters is needed or not. If X and Y do not exhibit strong cluster substructures, then again clustering of X* (input data augmented by the output data) exploiting the results of separate clustering of X and Y, and of the correspondence scheme is recommended. We justify that usual cluster validity indices are not suitable for finding the number of rules, and the proposed scheme does not use any cluster validity index. Three methods are suggested to get the initial estimate of membership functions (MFs). The proposed scheme is used to identify the rule base needed to realize a self-tuning fuzzy PI-type controller and its performance is found to be quite satisfactory.

A new hybrid c-means clustering model

Earlier we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM imposes a constraint on the sum of typicalities over a cluster that leads to unrealistic typicality values for large data sets. Here we propose a new model called possibilistic fuzzy c-means (PFCM). PFCM produces memberships and possibilities simultaneously, along with the cluster centers. PFCM addresses the noise sensitivity defect of FCM, overcomes the coincident clusters problem of possibilistic c-means (PCM) and eliminates the row sum constraints of FPCM. Our numerical examples show that PFCM compares favorably to all of the previous models.

Synthesis, characterization and dehydriding behavior of the intermetallic compound LaMg12

Abstract The intermetallic compound LaMg 12 has been synthesized successfully using a new pellet-formation procedure which incorporates the encapsulation of the subliming Mg component, by La, from all sides. The assynthesized materials were characterized through X-ray diffraction (XRD), X-ray energy dispersive analysis (EDAX) and scanning electron microscopic (SEM) techniques. The dehydriding behavior of the intermetallic compound LaMg 12 was studied using volumetric methods after preliminary out-gassing the reactor vessel. The maximum hydrogen storage capacity obtained for this material is 3.7 wt% at high temperature (400 °C). It was observed that the release rate of hydrogen from LaMg 12 is faster than magnesium. The dependence of dehydriding characteristics on the surface structure has been elucidated.

Some neural net realizations of fuzzy reasoning

In this paper we analyze the neural network implementation of fuzzy logic proposed by Keller et al. [Fuzzy Sets Syst., 45, 1–12 (1992)], derive a learning algorithm for obtaining an optimal α for the net, and, for a special case, we show how one can directly (avoiding training) compute the optimal α. We address how training data can be generated for such a system. Effectiveness of the optimal α is then established through numerical examples. In this regard, several indices for performance evaluation are discussed. Finally, we propose a new architecture and demonstrate its effectiveness with numerical examples.

A neuro-fuzzy system for inferencing

We justify the need for a connectionist implementation of compositional rule of inference (COI) and propose a network architecture for the same. We call it COIN—the compositional rule of inferencing. Given a relational representation of a set of rules, the proposed architecture can realize the COI. The outcome of COI depends on the choice of the implication function and also on choice of inferencing scheme. The problem of choosing an appropriate implication function is avoided through neural learning. The system automatically finds an “optimal” relation to represent a set of fuzzy rules. We suggest a suitable modeling of connection weights so as to ensure learned weights lie in [0, 1]. We demonstrate through numerical examples that the proposed neural realization can find a much better representation of the rules than that by usual implication and hence results in much better conclusions than the usual COI. Numerical examples exhibit that COIN outperforms not only usual COI but also some of the previous neural implementations of fuzzy logic. ©1999 John Wiley & Sons, Inc.

The composite material La2mg17-x wt% MmNi4.5Al0.5 : Synthesis, characterization and hydriding behavior

Abstract The composite material La2Mg17-x wt% MmNi4.5Al0.5 has been synthesized for various values of x (x = 10, 20, 30 and 40). These materials are activated by heating at about 360 ± 10 °C temperature for nearly six hours under a hydrogen pressure of 30 atm. Several hydrogenation runs are carried out under isothermal and isobaric conditions for the composite material La2Mg17-x wt% MmNi4.5Al0.5. We observe the maximum hydrogen storage capacity of 4.9 wt% at 400 ± 10 °C for the composite material La2Mg17-10 wt% MmNi4.5Al0.5 The hydriding rates of these materials are about three to four times faster than that of pure La2Mg17. In this paper, the influence of surface composition, hydriding pressure and temperature on the storage capacity and kinetics of the composite materials has been elucidated employing the XRD and SEM techniques.

A note on the hysteresis effect of La2Mg17-based composite materials

Abstract La2Mg17-based composite materials La2Mg17-xwt% LaNi5 and La2Mg17-xwt% MmNi4.5Al0.5 have been synthesized for various values of x. The pressure-composition hydrogenation and dehydrogenation isotherms of these materials were determined volumetrically at 350, 375 and 400 °C. In all cases, the equilibrium hydrogen pressure for hydride formation, Pf is greater than the pressure for hydride decomposition, Pd. We have represented the hysteresis effect by considering the hysteresis factor, which is equal to P f P d . The effect of hydriding-dehydriding temperature and composition of the composites on the magnitude of the hysteresis factor have also been observed.