http://repository.ou.ac.lk/handle/94ousl/3637 Sat, 16 May 2026 00:46:08 GMT 2026-05-16T00:46:08Z http://repository.ou.ac.lk/handle/94ousl/3690 ∆-OPEN SETS AND δ-SEMI CLOSED SETS IN FUZZY TOPOLOGICAL SPACES Piriyalucksan, P.; Arunmaran, M. The study of fuzzy topological spaces was introduced by Chang in 1968, following the discovery of fuzzy sets by Zadeh. So far, several types of open sets and closed sets in fuzzy topological spaces have been documented in the literature. Some of them are fuzzy pre-open sets, fuzzy α-open sets, fuzzy β-open sets, fuzzy regular open sets, and fuzzy semi-open sets. In this abstract, we describe two new types of sets, namely fuzzy ∆-open sets and fuzzy δ-semi-closed sets, and discuss the properties of these sets. For a non-empty set X, a fuzzy topology is a family τ of fuzzy subsets in X satisfying the following conditions: 0_X ,1_X∈ Τ ; the finite intersection of members of τ is a member of τ; and the arbitrary union of members of τ is a member of τ. We call the pair (X,Τ) a fuzzy topological space. Also, the elements of τ are called fuzzy open sets. First, we define fuzzy ∆-open set in fuzzy topological spaces. A subset D of a fuzzy topological space X is called fuzzy ∆-open if D=(A∧B^C)∨(B∧A^C), where A and B are fuzzy open sets. When the set D is called fuzzy semi ∆-open, the above equation holds with the fuzzy semi-open sets A and B. Similarly, we can define the following sets: fuzzy pre ∆-open / fuzzy α-∆-open / fuzzy β-∆-open. Next, we show that every fuzzy ∆-open set is fuzzy semi ∆-open. However, the converse need not be true in general. Next, we define fuzzy δ-open sets in fuzzy topological spaces. A subset A is called fuzzy δ-open if for every x∈A, there exists a regular open set G such that x∈G≤A. A subset A is called fuzzy δ-semi closed if there exists a fuzzy δ-closed set F such that int(F)≤A≤F. Next, we show the following: A subset A is called fuzzy δ-semi open if and only if X\A is fuzzy δ-semi closed; every fuzzy δ-closed set is fuzzy δ-semi closed; every fuzzy δ-semi closed set is fuzzy semi-closed; a fuzzy set A is fuzzy δ-semi closed if and only if int(δcl(A))≤A. Finally, we show that the intersection or union of two fuzzy δ-semi closed sets is also fuzzy δ-semi closed. Wed, 01 Jan 2025 00:00:00 GMT http://repository.ou.ac.lk/handle/94ousl/3690 2025-01-01T00:00:00Z http://repository.ou.ac.lk/handle/94ousl/3689 COMPUTING THE ℎ-FUNCTION OF THE COMPLEX PLANE WITH A DELETED LINE SEGMENT, WITH AND WITHOUT USING THE PRIME FUNCTION Piriyalucksan, P.; Arunmaran, M. The likelihood of a particle launched from a fixed point z_0 in a region Ω initially leaving the area within the distance r of z_0 is the harmonic-measure distribution function, or the h-function. This function is non-decreasing, right-continuous, and takes values on the unit interval [0,1]. The objective of this paper is to validate the h-function formula obtained via three different approaches for a simply connected region Ω formed by deleting a line segment [-i,i] from the complex plane with basepoint z_0=1. To evaluate the h-function, we employ various forms of conformal mappings, harmonic functions, and the prime function. These three approaches vary in their utilization of the prime function, both in terms of presence and methodology. In the first approach, we completely avoid employing the prime function. Rather, the conformal mapping from the unit disc is expressed through the combination of a Joukowski map and a Mobius transformation, with the h-function being determined by extracting the correct angle of view in the unit disc. In the second and third approaches, the prime function is utilized. In the second method, we do not employ the prime function in the conformal mapping from the disc to the region Ω, as it is essentially a Joukowski transformation. In the meantime, the main function is utilized in the Cayley-type map R(ζ) from the interior of the unit disc D_ζ to the lower half-plane, which is employed in the creation of the harmonic function Im[W(ζ)]. In the third approach, the prime function is applied twice: initially during the parallel-slit mapping from the unit disc D_ζ to the target region Ω, and subsequently in R(ζ) and consequently in Im[W(ζ)]. All three approaches yield identical h-function graphs. These methods provide a check for our h-function formula. Wed, 01 Jan 2025 00:00:00 GMT http://repository.ou.ac.lk/handle/94ousl/3689 2025-01-01T00:00:00Z http://repository.ou.ac.lk/handle/94ousl/3688 COMPARATIVE ANALYSIS OF EXPONENTIAL SMOOTHING MODELS FOR FORECASTING THE WATER QUALITY INDEX Dissanayake, H.; Punchi-Manage, R. Surface water quality plays a significant role in maintaining healthy ecosystems and supporting both human and aquatic life, making reliable monitoring and forecasting essential due to increasing pollution and environmental changes. The objective of this study is to forecast the Weighted Arithmetic Water Quality Index (WAWQI) at 20 sampling sites along the River Thames using three time series models: Single Exponential Smoothing (SES), Holt’s (Double) Exponential Smoothing (HES), and Holt-Winters (Triple) Exponential Smoothing (HWES), and to evaluate and compare the forecasting performance using three accuracy metrics: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) to identify the most suitable model for sites with varying temporal patterns (stable, trending, or seasonal). Water quality data collected from 20 sampling sites along the River Thames between March 2009 and September 2017 were arranged chronologically. Each model was applied after linearly interpolating missing data and splitting the series into training and testing sets in an 80:20 ratio. The results revealed that model performance varied depending on the temporal patterns of WQI data. SES performed well at sites with stable conditions, such as TC8, TC12, TC13, and TC17. TC8 recorded the lowest RMSE (1.49), MAE (1.12), and MAPE (1.68%), indicating high forecasting accuracy. The HES model accounts for both the level and trend components of time series data and generally does not outperform the SES model for most sites, since most of the sites lack trend components. At TC20, the HES model showed the highest accuracy, with RMSE of 2.11, MAE of 1.38, and MAPE of 1.96%. HWES achieved the best performance across the majority of monitoring sites, particularly those exhibiting clear seasonal patterns in WQI fluctuations. In contrast, volatile sites (TC15) resulted in higher forecast errors (MAPE >15%) regardless of the model applied. These findings suggest that model selection should consider the underlying temporal characteristics of WQI behavior at each site: HWES for seasonal patterns, HES for trending series, and SES for stable conditions. These insights can aid water management authorities in proactive pollution control and sustainable resource planning by enabling accurate water quality forecasting. Wed, 01 Jan 2025 00:00:00 GMT http://repository.ou.ac.lk/handle/94ousl/3688 2025-01-01T00:00:00Z http://repository.ou.ac.lk/handle/94ousl/3687 COMPARATIVE SPATIAL ANALYSIS OF ROAD TRAFFIC ACCIDENTS USING ORDINARY KRIGING AND INVERSE DISTANCE WEIGHTING Sashinka, D.; Yapa, R. D.; Punchi-Manage, R. Road traffic accidents are a significant public safety concern, especially in urban areas where congestion and infrastructural limitations increase the likelihood of collisions. This study investigates road traffic accidents within the Kandy Police Division in Sri Lanka by applying geostatistical interpolation techniques to model the spatial distribution of 2,099 RTAs reported from January 2022 to March 2024. The analysis evaluates the suitability of two interpolation methods: Inverse Distance Weighting (IDW), a deterministic approach, and Ordinary Kriging, a model-based geostatistical method that incorporates spatial autocorrelation. For the Kriging analysis, an empirical semivariogram was developed to quantify the spatial dependence structure of the accident data, and accident counts were log- transformed to approximate normality prior to spatial prediction with Ordinary Kriging. Four theoretical models, Spherical, Exponential, Gaussian, and Matérn, were fitted to the empirical semivariogram. The Spherical model outperformed the others, followed the empirical observed points closely, and reached the sill, with a sum of squared errors of 2.59 between empirical and fitted semivariograms. It was therefore selected as the best fit for spatial prediction using Kriging. Both interpolation methods were applied on a regular 10 × 10 grid across the study area to estimate accident frequencies. The performance of both methods was assessed using cross-validation, and predictive accuracy was evaluated through Mean Error (ME), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). Results showed that Ordinary Kriging provided slightly better predictive accuracy than IDW, with lower values for MAE (24.26 and 35.13), RMSE (40.04 and 52.87), and ME (-4.94 and -6.48), respectively. These findings reveal the effectiveness of geostatistical modeling, particularly Kriging, in identifying high-risk areas and supporting data-driven decision making. The findings of this study will support urban planners, traffic engineers, and policymakers in guiding targeted road safety measures, prioritizing infrastructure improvements, and effectively allocating resources in accident-prone zones. Wed, 01 Jan 2025 00:00:00 GMT http://repository.ou.ac.lk/handle/94ousl/3687 2025-01-01T00:00:00Z