This volume is the first of two containing selected papers from the International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017 - Volume I. This meeting brought together researchers from around the world to share their work, with the aim of promoting collaboration as a means of solving various problems in modern science and engineering. The authors of each chapter present a research problem, techniques suitable for solving it, and a discussion of the results obtained. These volumes will be of interest to both theoretical- and application-oriented individuals in academia and industry. Papers in Volume I are dedicated to active and open areas of research in algebra, analysis, operations research, and statistics, and those of Volume II consider differential equations, fluid mechanics, and graph theory.

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Part 1: Algebra.- IT-2 Fuzzy Automata and IT-1 Fuzzy Languages.- Level Sets of i_v_Fuzzy -Subalgebras.-Interval-Valued Fuzzy Subalgebra and Fuzzy INK-Ideal in INK-Algebra.- On Dendrites Generated by Symmetric Polygonal Systems: The Case of Regular Polygons.- Efficient Authentication Scheme Based on Twisted Near-ring Root Extraction Problem.- Dimensionality Reduction Technique to Solve E-Crime Motives.- Partially Ordered Gamma Near-Rings.- Novel Digital Signature Scheme with Multiple Private Keys on Non-Commutative Division Semirings.- Cozero Divisor Graph of a Commutative Rough Semiring.- Gorenstein FI-Flat Complexes and (Pre)Envelopes.- Bounds of Extreme Energy of an Intuitionistic Fuzzy Directed Graph.- Part 2: Analysis.- On Ultra Separation Axioms via -open Sets.- Common Fixed Point Theorems in 2-Metric Spaces using Composition of Mappings via A-Contractions.- Coefficient bounds for a Subclass of m-fold Symmetric -pseudo Bi-starlike Functions.- Laplacian and Effective Resistance Metric in Sierpinski Gasket Fractal.- Some Properties of Certain Class of Uniformly Convex Functions defined by Bessel Functions.- A New Subclass of Uniformly Convex Functions defined by Linear Operator.- Coefficient Bounds of Bi-univalent Functions using Faber Polynomial.- Convexity of Polynomials using Positivity of Trigonometric Sums.- Local Countable Iterated Function Systems.-On Intuitionistic Fuzzy C-ends.- Generalized Absolute Riesz Summability of Orthogonal Series.- Holder Inequalities for Analytic Functions defined by Ruschewyh-type q-difference Operator.- Fuzzy Cut Sets Based Filter for Fixed-Value Impulse Noise Reduction.- On (p, q)-quantum calculus involving quasi-subordination.- Part 3: Operations Research.- Sensitivity Analysis for Spanning Tree.- On Solving Bi-objective Fuzzy Transportation Problem.- Nonlinear Programming Problem for an M-Design Multi Skill Call Center with Impatience Basedon Queuing Model Method.- Optimizing a Production Inventory Model with Exponential Demand Rate, Exponential Deterioration, and Shortages.- Analysis of Batch Arrival Bulk Service Queuing System with Breakdown, Different Vacation Policies, and Multi Phase Repair.- An Improvement to One's BCM for the Balanced and Unbalanced Transshipment Problems by Using Fuzzy Numbers.- An Articulation Point Based Approximation Algorithm for Minimum Vertex Cover Problem.- On Bottleneck-Rough Cost Interval Integer Transportation Problems.- Direct Solving Method of Fully Fuzzy Linear Programming Problems with Equality Constraints Having Positive Fuzzy Numbers.- An Optimal Deterministic Two Warehouse Inventory Model for Deteriorating Items.- Analysis on Time to Recruitment in a Three Grade Marketing Organization Having Classified Sources of Depletion of Two Types with an Extended Threshold and Shortage in Manpower forms Geometric Process.- Neutrosophic Assignment Problem via BnB Algorithm.- Part 4: Statistics.- An Approach to Segment the Hippocampus from T2-Weighted MRI of Human Head Scans for the Diagnosis of Alzheimer's Disease Using Fuzzy C-Means Clustering.- Analysis of M^[X]/G_k/1 Retrial Queuing Model and Stand-by.- -Statistically Convergent Mutliple Sequences in Probabilistic Normed Spaces.- A Retrial Queuing Model with Unreliable Server in K Policy.- Two Level Control Policy of an Unreliable Queuing System with Queue Size Dependent Vacation and Vacation Disruption.- Analysis of M/G/1 Priority Retrial G-Queue with Bernoulli Working Vacations.- Time to Recruitment for Organizations having n Types of Policy Decisions with Lag Period for Non-Ideal Wastages.- A Novice's Application of Soft Expert Set: A Case Study on Students' Course Registration.- Dynamics of Stochastic SIRS Model.- Steady State Analysis of Unreliable Preemptive Priority Retrial Queue with Feedback, Two Phase Service under Bernoulli Vacation.- An Unrealizable Optional Stage M^X/G/1 Retrial Queue with Immediate Feedbacks and at most J Vacations.- Weibull Estimates in Reliability - An Order Statistics Approach.- Intuitionistic Fuzzy ANOVA and Its Application using Different Techniques.- A Resolution to Stock Prices Prediction by Developing ANN based Models using PCA.- A Novel Method of Solving Quadratic Programming Problem under Stochastic Conditions.