Amit Srivastava

In the present work, we have proposed a classification algorithm that uses Dempster Shafer (D-S) evidence theory since it has emerged as an effective tool in handling data classification problems. As basic probability assignment (BPA) is a pre-requisite for applying D-S theory, how to generate it is a hot issue. This paper proposes a novel method for generating basic probability assignments (BPAs) from training data. Dempster Shafer’s (D-S) rule of Combination is utilized for the unification of these BPAs and finally, classify each data item using these unified BPAs. Testing is carried out using some popular benchmark data sets consisting of three classes. Evaluated results show that the classification accuracy is comparatively high.

Data when used for analysis purpose, shows high degree of similarity between points in space, leading to problem of overlapping data in clusters. Currently problem of overlapping of data points in clusters are addressed by kernel methods which maps data points in higher dimensional space or mapping of data from higher dimension to lower dimension. We addresses this problem with a novel concept of mapping the nearest neighbor points to the test point in space by referring projected data in tangential space. In our approach projection of points from the surface of the unit hyper sphere to the tangential space and then finding out the nearest neighbour using log-Euclidean or Geodesic distance measures.This is a dynamic projection based approach in which points of the surface of the hyper sphere are viewed from different tangential plane and nearest neighbor points are visible where the density of the similar data points is high. The proposed concept is also empirically proven using the belief measure which justify the existence of same nearest points of the projected plane and on the surface of the unit hyper sphere.

Software bug prediction is mainly used for testing and code inspection. So, software bug prediction is carried out by network measures over the decades. But, the classical fault prediction method failed to obtain the semantic difference among various programs. Thus, it degrades the working of the prediction model, which is designed using these aspects. It is necessary to obtain the semantic difference for designing the prediction model accurately and effectively. In a software defect prediction system, it faces many difficulties in identifying the defect modules like correlation, irrelevance aspects, data redundancy, and missing samples or values. Consequently, many researchers are designed to detect software bug prediction that categorises faulty as well as non-faulty modules with software matrices. But, there are only a few works focussed to mitigate the class imbalance problem in bug prediction. In order to overcome the problem, it is required to develop an efficient software bug prediction method with the enhanced classifier. For this experimentation, the input data are taken from the standard online data sources. Initially, the input data undergo pre-processing phase and then, the pre-processed data are provided as input to the feature extraction by utilising the Auto-Encoder. These obtained features are utilised in getting the optimal fused features with the help of a new Hybrid Honey Badger Cat Swarm Algorithm (HHBCSA). Finally, these features are fed as input to the Optimised Parallel Cascaded Deep Network (OPCDP), where the “Extreme Learning Machine (ELM) and Deep Belief Network (DBN)” are used for the prediction of software bugs, in which the parameters from both classifiers are optimised by proposed HHBCSA algorithm. From the investigations, the recommended software bug prediction method offers a quicker bug prediction result, which helps to detect and remove the software bug easily and accurately.

Negation is absolutely essential in all conversations that allows for denial, contradiction and other countering aspects of human linguistic systems. Intuitively, the negative sentences are less informative and less specific than the affirmative ones. In other words, it has more uncertainty embedded in it. If an event is uncertain, negating it will require some sort of probabilistic formulation. Yager (IEEE Trans Fuzzy Syst 25:1899–1902, 2015) gave a probabilistic definition of negation of a probability distribution based on unbiased distribution of probabilities. In the present work, a generalization of negation based on the concept of biased distribution is proposed. Some numerical examples have been discussed for determining the validity and efficacy of the proposed generalization. Finally an application in medical diagnosis has been considered.

Information fusion in uncertain and complex environments is highly challenging. Dempster–Shafer (D-S) evidence theory has been successfully applied by various researchers in multi-sensor data fusion. However, it yields counterintuitive results in case of highly conflicting evidence. In this paper, we have developed a new divergence measure for belief functions that is nonnegative, symmetric, and satisfies the triangle inequality. Using the developed divergence measure, an algorithm for combining distinct basic probability assignments (BPAs) has been discussed and applied in target recognition systems and classification problems.

Evaluating the negation of an uncertain event is an open issue. Yager[14] suggested a transformation for evaluating the negation of a probability distribution. He used the idea that any event whose outcome is not certain can be negated by supporting the occurence of other events with no bias or prejudice for any particular outcome. Various authors have tried to generalize the negation transformation proposed by Yager[14] . However we need to focus on developing the basic structure of negation so that the behaviour of the process modelled by negation transformation can be understood in detail. Yager's negation is based on distribution of maximum entropy. If a probability distribution is uncertain(a state other than maximum entropy), the more iterations of negation, the more uncertain this probability event becomes eventually converging to a homogeneous state\textit{ i.e.} maximum entropy. In other words, it is the realization of the process. What is noted that during each negation, Yager's method ensures that the negation is intuitive, the next negation weakens the probability of the event occuring in the previous step. Since negation involves reallocation of probabilities at each step in such a way that the reallocation at each step can be determined from the reallocation at the previous step, therefore it is clear that Yager's negation has various attributes similar to that of a markov chain. In the present work, we have shown that Yager's definition of negation can be modelled as a markov chain which is irreducible, aperiodic with no absorbing states. Two examples has been discussed to strengthen and support the analytical results. Also we have defined an information generating function(IGF) whose derivative evaluated at specific points gives the moments of the self information of negation of a probability distribution. The properties of the generating function along with its relationship with the information generating function proposed by S. Golomb[2] has been explored. A closer look at the properties of IGF confirms the existence of markovian structure of Yager's Negation.Mathematics Subject Classification (2010) 90C70 · 90B06 · 90B50 · 90C05