Tazid Ali

Methods to Obtain Basic Probability Assignment in Evidence Theory

Dempster-Shafer Theory (DST) of Evidence is a powerful and flexible mathematical tool for handling uncertainty, impreciseness, and incomplete information. It can be used when both epistemic and aleatory uncertainties are present in the problem under consideration. The fundamental and important object of this theory of evidence is the primitive function called basic probability assignment (bpa). In the absence of empirical data, experts in related fields provide necessary information (bpa). However how to obtain BPA is still an open issue. In this paper, we propose methods to determine BPA when only the minimum, maximum and most likely values of the parameter are known. An example is illustrated to demonstrate and check the efficiency of the proposed methods. We have also developed an extended version of uncertainty measurement in evidence theory in order to calculated total uncertainty in the body of evidence obtained by the proposed methods.

A Hybrid Method to Deal with Aleatory and Epistemic Uncertainty in Risk Assessment

Risk assessment is an important and significant aid in the decision making process. Risk assessment is performed using ‘model’ and a model is a function of parameters which are usually affected by uncertainty. Some model parameters are affected by aleatory uncertainty and some others are affected by epistemic uncertainty. In this paper we propose a hybrid method to deal with propagation of both kinds of uncertainty within the same computation of risk.

Uncertainty Modeling in Risk Analysis: A Fuzzy Set Approach

isk assessment is a popular and important tool in decision making process. Risk assessment is generally performed using models and model is a function of some parameters which are usually affected by uncertainty. Here, we consider that model parameters are affected by epistemic uncertainty. To represent epistemic uncertainty in general triangular fuzzy number or trapezoidal fuzzy numbers are used. In this paper, we study Gaussian fuzzy number to represent epistemic type uncertainty and try to fuse with triangular fuzzy numbers and also risk assessment is carried out under fuzzy environment.

LATTICE STRUCTURE AND DISTANCE MATRIX OF GENETIC CODE

The genetic code is the rule by which DNA stores the genetic information about formation of protein molecule. In this paper, a partial ordering is equipped on the genetic code and a lattice structure has been developed from it. The codon–anticodon interaction, hydrogen bond number and the chemical types of bases play an important role in the partial ordering. We have established some relations between the lattice structure of the genetic code and physico-chemical properties of amino acids. Taking into consideration the evolutionary importance of base positions in codons we have constructed a distance matrix for the amino acids. Further with a real life example we have demonstrated the relationship between frequently occurring mutations and codon distances.

Analysis of Unweighted Amino Acids Network

The analysis of amino acids network is very important to studying the various physicochemical properties of amino acids. In this paper we consider the amino acid network based on mutation of the codons. To analyze the relative importance of the amino acids we have discussed different measures of centrality. The measure of centrality is a powerful tool of graph theory for ranking the vertices and analysis of biological network. We have also investigated the correlation coefficients between various measures of centrality. Also we have discussed clustering coefficient as well as average clustering coefficient of the network. Finally we have discussed the degree of distribution as well as skewness.

Stochastic Model for Genetic Recombination because of Crossing over and Chromatid Exchange

Genetic recombination by crossing over and chromatid exchange in eukaryotes is one of the major events leading to variance, among individuals of a population set. Therefore, quantification of the recombination would be central to the understanding of the genetic diversity, genealogical differences, disease variants and its maintenance within the population. Hence in this article an attempt is made to model genetic recombination stochastically and prove the Haldanes mapping function of genetic recombination by applying exponential series and Poisson process.

Uncertainty Modeling of Radiological Risk using Probability and Possibility Methods

is inherent in almost all aspects of our life. We usually ignore uncertainty to avoid complexity. However solutions so obtained are quite far from the reality and ignoring uncertainty may lead to over (under) estimation. So we need to quantify the uncertainty so as to be aware of the risk involved in any decision making process. Uncertainties can be modeled and analyzed using different theories, viz. Probability theory, Possibility theory, Evidence theory etc. Modeling of an uncertain parameter depends on the nature of the information available. In this paper we have considered uncertainty quantification of parameters in the case of radiological risk assessment. Radiological Risk means, risk associated with the release of radionuclides when radioactive materials are released into the environment. There are various pathways through which radionucliodes can reach human being namely inhalation, ingestion through drinking water and through contaminate food. The main aim of risk assessment is to determine the potential detriment to human health from exposure to a substance or activity that under plausible circumstances can cause to human health. We have analyzed the propagation of the risk both in terms of probability and possibility theory. One advanced method of probabilistic risk assessment (PRAs),viz. P-box method is discussed in this paper. A case study is also carried out with this method and compared with the results taking the parameters of the input distribution of the model as Fuzzy number.

Some Algebraic Aspects and Evolution of Genetic Code

The genetic code is the set of rules by which DNA stores genetic information of organisms. In this paper we discuss an algebraic structure of the genetic code in terms of the four DNA bases (A, C, G, T). Some relations between transition/transversion mutation of codons and algebraic properties of respective codons of the group structure are obtained. A distance matrix of the amino acids is constructed. We establish some relations between the distance matrix and physico-chemical properties of amino acids. Further we argue that the distance matrix reflects evolutionary pattern of amino acids.

Networks in Amino Acids Based on Mutation

Abstract Network theory has a broad spectrum of application including biological science. In the present study, we have analyzed hydrophobic and hydrophilic amino acids’ network based on mutation. To analyze the relative importance of the amino acids, we have discussed different measures of centrality and investigated the correlation coefficients between these measures. We have also dealt with clustering coefficient. Finally, we have discussed the degree of distribution as well as skewness for the networks.

Aleatory and Epistemic Uncertainty Quantification

In this paper, an effort has been made to combine aleatory and epistemic uncertainties in risk models. We have combined probabilistic distributions, generalized fuzzy numbers, and completely generalized interval valued fuzzy numbers.