Ramakant Bhardwaj

In this article we study semi-Markov decision processes (SMDPs) where the pay-off criterion is limiting ratio average, generally known as undiscounted pay-off. Here we consider the action space of the decision maker to be possibly countably infinite. However, we do not put any restriction on the reward function. We prove the existence of a near-optimal or ϵ-optimal strategy of the decision maker which turns out to be a deterministic semi-stationary. An efficient algorithm is discussed to compute a near-optimal pure semi-stationary strategy for such SMDP model. Also under some standard ergodicity conditions, we propose an optimality equation of these SMDP models.

Introduction: Rapid growth of Internet of Things (IoT) sensors in smart cities not only enables fine‐grained demand response but also exposes disparities in connectivity, device capability, and security that undermine equitable and resilient energy management. Problem Statement: Conventional centralized schedulers and standard metaheuristics ignore heterogeneous device constraints, edge‐level security costs, and access inequities; this leads to inefficient energy use, higher peak loads, and exclusion of poorly connected zones. Need for Research: A unified, deployable framework is needed that jointly optimizes energy allocation, enforces lightweight edge security, and explicitly accounts for the digital divide so that underserved clusters receive fair, secure service without large runtime penalties. Proposed Work and Objective: We propose digital divide‐aware secure load balancing (DDASLB), a codesigned framework that fuses hybrid particle swarm optimization (HPSO) with a fairness control engine (FCE) and an adaptive security management layer (SML). Objectives are to (i) optimize real‐time energy distribution across heterogeneous IoT clusters, (ii) embed security costs into scheduling, and (iii) improve fairness for low‐connectivity zones. Novelty: DDASLB uniquely incorporates a fairness coefficient into the optimization loop and models encryption/verification overhead as part of the objective, enabling security‐aware scheduling that treats inclusion as a first‐class constraint rather than a post‐hoc metric. Method: HPSO is extended with simulated‐annealing refinement; particles encode allocation vectors evaluated by a composite objective. The FCE adjusts fitness gradients for underserved clusters, while the SML adaptively tunes encryption strength based on trust scores. Simulations use reinforcement feedback and asynchronous edge/cloud coordination. Dataset: Experiments use the CSE‐CIC‐IDS2018 flows augmented with synthetically generated per‐node energy traces and connectivity classes to emulate urban, semiurban, and rural clusters. Results: In simulation, DDASLB attains higher energy utilization (≈88.9% ± 1.4), Jain fairness (≈0.87 ± 0.02), ≈19.8% peak‐load reduction, and improved secure‐transaction rate (≈84.6% ± .2) versus centralized and baseline PSO methods, with modest encryption overhead. Conclusion and Future Work: DDASLB demonstrates that codesigning fairness and lightweight security into edge‐aware optimization yields measurable gains in efficiency, inclusion, and resilience. Future work will pursue federated/reinforcement schemes, field validation, and real joint energy‐attack labeled datasets to strengthen external validity.

This study presents a comprehensive approach to solving fuzzy multi-objective linear programming problems (FMOLPP) under uncertainty using trapezoidal fuzzy numbers. The authors propose a novel integration of Yager’s ranking method, the Big-M optimization technique, and Chandra Sen’s statistical mean methods to effectively convert fuzzy objectives into crisp values and optimize them. The methodology allows for managing multiple fuzzy objectives by ranking and aggregating them using various statistical means such as arithmetic, geometric, quadratic, harmonic, and Heronian averages. The model is implemented using TORA software and demonstrated through a detailed numerical example. The results validate the robustness and practicality of the proposed approach, showcasing consistent optimal solutions across all statistical methods. This research significantly enhances decision-making processes in uncertain environments by offering a structured, computationally efficient solution strategy for complex real-world optimization problems.

This research paper delves into the application of optimality results in orthogonal fuzzy metric spaces to demonstrate the existence and uniqueness of solutions of nonlinear differential equations with boundary conditions and nonlinear integral equations, emphasizing the importance of orthogonal fuzzy metric spaces in extending fixed-point theory. Through introducing this innovative concept, the study provides a theoretical framework for analyzing mappings in diverse scenarios. In this study, we introduce the concept of best proximity point (BPP) within the framework of orthogonal fuzzy metric spaces by employing orthogonal fuzzy proximal contractive mappings. Moreover, this research explores the implications of the established results, considering both self-mappings and non-self mappings that share the same parameter set. Additionally, some examples are provided to illustrate the practical relevance of the proven results and consequences in various mathematical contexts. The findings of this study can open up avenues for further exploration and application in solving real-world problems.

In this paper, bicomplex parametric partial metric space is discussed. The new contractive condition is discussed for coupled invariant point concerning self-mapping on the said spaces with particular conditions. We support our tracking down through models. Our outcomes sum up the common coupled invariant point in bicomplex valued parametric metric spaces by Saluja (Coupled fixed point results based on control function in complex partial metric spaces, Functional Analysis, Approximation and Computation 15(2) (2023), 1 – 15). Established results generalize previously known results for specified conditions.

Pabitra Kumar Gouri, Bharti Saxena, Rajesh Kedarnath Navandar, Pranoti Prashant Mane, Ramakant Bhardwaj, Jambi Ratna Raja Kumar, Surendra Kisanrao Waghmare, and Antonios Kalampakas. International Journal of Fuzzy Logic and Intelligent Systems 2024;24:93-104. https://doi.org/10.5391/IJFIS.2024.24.2.93