Gamma Operators Research Articles

Fuzzy Logic-Based Landslide Susceptibility Mapping in Earthquake-Prone Areas: A Case Study of the Mila Basin, Algeria

Abstract —This research focuses on analyzing landslides triggered by a moderate earthquake (Mw = 4.9) in the northeastern region of the Mila province, which resulted in significant damage and economic losses in the El Kherba district and Grarem Gouga city. Through an extensive field-based investigation, a comprehensive inventory of landslides has been compiled. To assess the susceptibility to landslides triggered by seismic activity, a GIS-based fuzzy logic model was employed. The model incorporates various input factors, such as lithology, slope angle, normalized difference vegetation index (NDVI), distance from rivers and roads, precipitation, and seismic hazard, which is shown on a map. The study compares the performance of different fuzzy operators and gamma values and determines that using fuzzy gamma operators with a gamma value of 0.8 yields a satisfactory consistency with the distribution of landslides. Moreover, incorporating the map of seismic hazard as a causative factor enhances the accuracy of landslide susceptibility mapping. This study underscores the utility of the fuzzy logic model in disaster management and the planning of development activities.

Spatial multi-criteria approaches for estimating geogenic radon hazard index

The geogenic radon hazard index (GRHI) map plays a crucial role in evaluating radon exposure risks. The construction of this map requires a comprehensive analysis of radon levels in soil gas and some critical factors, such as uranium content in bedrock, soil permeability, and geological inhomogeneities. In this context, the spatial multi-criteria decision analysis is proposed to integrate the GRHI-based criteria for identifying the high-potential radon areas. In particular, the multivariate integration involves the fuzzy gamma operator and a hybrid multi-criteria decision-making technique, namely AHP-TOPSIS, which represents a novel approach in GRHI mapping. Thus, a comparison is provided through the definition of the GRHI map of an unexplored study area, that is the Apulia region, located in Southern Italy. In order to evaluate the output maps, high radon potential areas are identified based on some available indoor radon measurement data. The success-rate curve, as a valid evaluation metric, is employed for the performance assessment and comparison of these two methods. The results demonstrate that although both generated GRHI maps are closely correlated with high-potential radon zones in Apulia, the hybrid AHP-TOPSIS method is preferable in identifying areas with elevated radon potential.

A Review of Integration Techniques of Multi-Geoscience Data-Sets in Mineral Prospectivity Mapping

In every sphere and utility aspects of human life, there is need of metals and construction materials. Minerals which are below the near subsurface is almost explored on the basis of direct geospatial evidences. There is high demand of metals and other materials which are mined below the surface of earth In the current landscape, there's a demand for faster and more precise exploration strategies, particularly emphasizing Greenfield exploration and deep-seated mineralization. This paper conducts a comprehensive review of existing methodologies for integrating multi-geoscience datasets aimed at mineral prognostication, with a focus on identifying the most precise and authentic Artificial Intelligence (AI) - based data integration techniques. Additionally, it offers insights into the current status of mineral exploration in India and the global evolution of data integration practices. Several types of geoscientific datasets i.e. geological, geophysical, geochemical and geospectral data have to be organized in geospatial domain for meaningful mineral exploration outcome. These datasets have been processed to extract exploratory indicator layers for data integration are called Mineral Prospectivity Mapping (MPM). Indeed, MPM is a multiple criterion decision making (MCDM) task which provide a predictive model for categorizing of sought areas in terms of ore mineralization. There after based upon Geological factors i.e. lithology, structure, shear & fault zones, alteration zones etc. of sought mineralized area, selection of drilling parameters (depth, angle, level, type, rpm, feed) is done for resource assessment. Literature survey suggests that minerals exploration by integrated approach on the basis of these datasets is still poorly performed. It has been gathered that knowledge-driven data integration using Fuzzy Gamma Operator and Multiclass Index Overlay method is best suited for mineral exploration. In past, few researchers of other countries have exploited data integration approach with encouraging results. Despite the abundance of data available in India, this approach has not been utilized very successfully and no standard protocols exist even for decision making for drilling operation. Thus, it's evident that employing the Fuzzy Inference System (FIS) algorithm, particularly utilizing the Fuzzy Gamma Operator and Multiclass Index Overlay integration method, remains underutilized in designing standardized operating procedures (SOP) for mineral exploration in India and decision-making for drilling operations. This approach holds promise for minimizing time lag and optimizing resources such as manpower, instruments, and finances.

Asymptotic expansions for variants of the gamma and Post–Widder operators preserving 1 and xj$$ {x}^j $$

Recently, the authors constructed operators acting on a space of functions defined on and preserving 1 and for a given . To this end, they considered suitable modifications of the Post–Widder and gamma operators. They proved convergence results and established the associated Voronovskaja type formulas. In this paper, we give asymptotic expansions for the sequences of these operators.

Mapping Groundwater Resource using Multispectral Sentinel 2 and Fuzzy Logic method, Case Study: Salafchegan, Qom, Iran

Groundwater is one of the essential freshwater sources for human consumption, with the highest reserves of fresh water on earth after glaciers and glaciers. Conservation and maintenance of groundwater quality in a large area require an overview of the status and potential of groundwater resources in that area, which can be applied to potential areas using remote sensing technology. In this study, after extracting the factors influencing the formation of groundwater aquifers from the Sentinel satellite image, appropriate information layers were prepared and integrated into the ArcGIS using different fuzzy operators and potential maps prepared with the location of groundwater wells. The area was validated. The results of combining slope layers, slope direction, lithology, drainage length density, lineament length density, lineament buffer, drainage buffer, and vegetation in the area showed that fuzzy multiplication and gamma operators could be used as suitable operators for Introducing information layers to identify groundwater potential in the area. Also, using the gamma numbers 0.1 gave better results than larger gamma numbers. The research results showed that 15.9% of the studied area has good and very good potential for the presence of underground water in the production map using the fuzzy gamma with gamma 0.1 method. Also, this map was validated by 70.1% of water wells in the region. The normalized ratio of accuracy to validity in the final production model with this method was estimated to be 54%, which is entirely acceptable compared to other methods.

GIS-Based Flood Susceptibility Mapping of Srinagar District, India Using Weights-of-Evidence (WofE), Frequency Ratio (FR) and Fuzzy Gamma Operator (FGO)

GIS-Based Flood Susceptibility Mapping of Srinagar District, India Using Weights-of-Evidence (WofE), Frequency Ratio (FR) and Fuzzy Gamma Operator (FGO)

Site selection modeling of hybrid renewable energy facilities using suitability index in spatial planning

The research focuses on how hybrid renewable energy facilities can be addressed within the spatial planning system by adopting an approach that minimizes the problems related to the sustainability of energy. The study aims to develop a spatial model based on parameters for the site selection processes of hybrid renewable energy facilities relying on wind, solar, and biomass energy sources within the spatial planning system in Turkey. The integration of fuzzy logic approach and Geographic Information Systems (GIS) tools has been proposed to establish a spatially applicable methodological framework. The methodology focuses on the neighborhood scale in terms of planning level and covers the Karatay district, where the hybrid renewable energy potential is high. The research findings indicate that the GAMMA operator used in the methodology provides the most optimal areas with a value of γ = 0.90 and generates site selections for hybrid renewable energy facilities based on the source with the highest suitability index in single-source utilization. Additionally, the operator determines the best alternative in terms of resources in different hybrid scenarios. In this context conducted in Karatay district, it was found that the highest suitability index in terms of hybrid applications is associated with biomass-solar energy combinations.

Strategic landscape analysis relating multicriteria analysis and socioeconomic and environmental context to define potential areas for active restoration in São Paulo, Brazil

To optimize forest restoration initiatives, landscape planning emerges as a strategy. Thus, this work aims to determine the active restoration potential in Vale do Paraíba, a Brazilian region inserted in the Atlantic Forest biome, using multicriteria analysis and analyzing the result in light of socioeconomic and environmental contexts. Land use and land cover (LULC), hydrography, and slope variables were used in the multicriteria analysis, while average municipal income per capita, availability of restoration areas on rural lands, and water supply basins were used as socioeconomic and environmental variables. Analytic Hierarchy Process (AHP) and Fuzzy Inference by the gamma operator were employed as multicriteria analysis methods. Two comparisons were performed with AHP, resulting in weights of 0.6 (LULC) and 0.2 (slope and hydrography) for AHP 1, and 0.5 (LULC) and 0.25 (slope and hydrography) for AHP 2. Values of 0.4, 0.6, and 0.8 were used in the gamma operator in Fuzzy Inference. Comparing results with restoration sites already implemented, AHP 2 was considered the best method. The restoration potential of each municipality was determined. Then, we grouped those with more areas for restoration, as an opportunity to develop common forest restoration programs. Ten water supply basins were identified with more than 40% of region extension with high restoration potential. Municipalities with a lower average per capita income and higher restoration potential were identified, highlighting a potential to generate income through restoration. The study concluded that Vale do Paraíba has a high potential for active restoration.

Windstorm Hazardous Area Mapping Using Multi-Criteria Evaluation Techniques of Fuzzy Logic Approach

The goal of this study to determine the most exposed area to windstorm event using fuzzy logic approach. Respond to the Sustainable Development Goal (SDG) 11 and 13, Sustainable Cities and Communities and Climate Action, this study was conducted to establish the preparedness in high-risk region. To achieve this goal, the influencing indicator was identified based on previous study. The related indicator comprises of wind speed, temperature, relative humidity, precipitation, slope, population, road, and land use. Fuzzy membership model implemented to aggregating the indicator to standard value 0 to 1. A fuzzy model was used as a method to integrate the constructed index values, and a frequency ratio was used to determine the fuzzy membership value. Different fuzzy operators (AND, OR, SUM, PRODUCT, and GAMMA) are applied to generate windstorm hazard map. The fuzzy gamma (γ) operator, with γ equal to 0.9, was used to create wind hazard map into different zones of five relative sensitivity classes: very high, high, moderate, low, and very low. 10.65% of study area has very high sensitivity towards windstorm hazard which distributed at high area (Banjaran titiwangsa), West Coast area (Pahang and West Johor) and north area (Perlis). In addition, some part in the surrounding region of Peninsular Malaysia were also identified as windstorm hazard due to the dense of urban area such at Johor Bharu and Klang Valley area. 7.20% of the study area has very-low windstorm hazard and is mainly located in the middle part.

A form of Gamma operator due to Rathore

A form of Gamma operator due to Rathore

LOCATION OF FUEL STATIONS USING FUZZY MODEL IN GEOSPATIAL INFORMATION SYSTEM (CASE STUDY: 7TH DISTRICT, TEHRAN CITY)

Abstract. In this study, by using the fuzzy method and geospatial information system (GIS), was attempted to locate the fuel station in the 7th district of Tehran. For this purpose, the information was digitized as a shape file by referring to the field and using the existing maps. The distance map was prepared using the Euclidean Distance function. Finally, using ArcGIS 10.8 software, this information was normalized by the fuzzy method and overlapped using the fuzzy gamma operator. It is presented as a map of prone areas for optimal positioning of fuel stations in the 7th district of Tehran. The most important criteria are the distance from the communication network, population density, incompatible users (commercial, industrial, administrative, residential, cultural and religious, health and medical), compatible users (park and green space, sports, fire department), and distance from fuel stations.

A NEW SOFT SET OPERATION: COMPLEMENTARY SOFT BINARY PIECEWISE GAMMA(𝜸) OPERATION

Soft set theory, introduced by Molodtsov, is as an efficacious mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspect. Since its inception, different kinds of soft set operations are defined and used in various types. In this paper, we define a new kind of soft set operation called, complementary soft binary piecewise gamma operation and we investigate its basic algebraic properties. Moreover by examing the distribution rules, it is aimed to contribute to the soft set literature by obtaining the relationships between this new soft set operation and other types of soft set operations such as extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations. This paper can be regarded as a theoritical study of soft set theory.

Rate of convergence of Stancu type modified $ q $-Gamma operators for functions with derivatives of bounded variation

<p style='text-indent:20px;'>Recently, Karsli [<xref ref-type="bibr" rid="b15">15</xref>] estimated the convergence rate of the <inline-formula><tex-math id="M2">\begin{document}$ q $\end{document}</tex-math></inline-formula>-Bernstein-Durrmeyer operators for functions whose <inline-formula><tex-math id="M3">\begin{document}$ q $\end{document}</tex-math></inline-formula>-derivatives are of bounded variation on the interval <inline-formula><tex-math id="M4">\begin{document}$ [0, 1] $\end{document}</tex-math></inline-formula>. Inspired by this study, in the present paper we deal with the convergence rate of a <inline-formula><tex-math id="M5">\begin{document}$ q $\end{document}</tex-math></inline-formula>- analogue of the Stancu type modified Gamma operators, defined by Karsli et al. [<xref ref-type="bibr" rid="b17">17</xref>], for the functions <inline-formula><tex-math id="M6">\begin{document}$ \varphi $\end{document}</tex-math></inline-formula> whose <inline-formula><tex-math id="M7">\begin{document}$ q $\end{document}</tex-math></inline-formula>-derivatives are of bounded variation on the interval <inline-formula><tex-math id="M8">\begin{document}$ [0, \infty ). $\end{document}</tex-math></inline-formula> We present the approximation degree for the operator <inline-formula><tex-math id="M9">\begin{document}$ \left( { \mathfrak{S}}_{n, \ell, q}^{(\alpha , \beta )} { \varphi}\right)(\mathfrak{z}) $\end{document}</tex-math></inline-formula> at those points <inline-formula><tex-math id="M10">\begin{document}$ \mathfrak{z} $\end{document}</tex-math></inline-formula> at which the one sided q-derivatives<inline-formula><tex-math id="M11">\begin{document}$ {D}_{q}^{+}{ \varphi(\mathfrak{z})\; and\; D} _{q}^{-}{ \varphi(\mathfrak{z})} $\end{document}</tex-math></inline-formula> exist.</p>

An asymptotic approach to proving sufficiency of Stein characterisations

In extending Stein's method to new target distributions, the first step is to find a Stein operator that suitably characterises the target distribution. In this paper, we introduce a widely applicable technique for proving sufficiency of these Stein characterisations, which can be applied when the Stein operators are linear differential operators with polynomial coefficients. The approach involves performing an asymptotic analysis to prove that only one characteristic function satisfies a certain differential equation associated to the Stein characterisation. We use this approach to prove that all Stein operators with linear coefficients characterise their target distribution, and verify on a case-by-case basis that all polynomial Stein operators in the literature with coefficients of degree at most two are characterising. For $X$ denoting a standard Gaussian random variable and $H_p$ the $p$-th Hermite polynomial, we also prove, amongst other examples, that the Stein operators for $H_p(X)$, $p=3,4,\ldots,8$, with coefficients of minimal possible degree characterise their target distribution, and that the Stein operators for the products of $p=3,4,\ldots,8$ independent standard Gaussian random variables are characterising (in both settings the Stein operators for the cases $p=1,2$ are already known to be characterising). We leverage our Stein characterisations of $H_3(X)$ and $H_4(X)$ to derive characterisations of these target distributions in terms of iterated Gamma operators from Malliavin calculus, that are natural in the context of the Malliavin-Stein method.

Eigenstructure and Voronovskaja type formula for a sequence of integral operators

Abstract The composition ℱ n of Rathore and Gamma operators was considered in the literature. We introduce a generalization of ℱ n . For it we determine the eigenstructure and establish the corresponding Voronovskaja type formula.

Approximation Properties of a New Type of Gamma Operator Defined with the Help of k -Gamma Function

With the help of the k -Gamma function, a new form of Gamma operator is given in this article. Voronovskaya type theorem, weighted approximation, rates of convergence, and pointwise estimates have been found for approximation features of the newly described operator. Finally, numerical examples have been provided to demonstrate that the operator is approaching the function.

On the approximation of functions in [formula omitted] by a class of positive linear operators

Let I be a finite or infinite interval and ω(f′,δ)=sup|x−y|≤δ|f′(x)−f′(y)| be the modulus of continuity of f′ for f(x)∈C1(I)={f:f′∈C(I)}. Let [a,b]⊂I be a finite close interval. In this paper we derive the best asymptotic constant defined by C=lim supn→∞supf∈C1(I)supx∈[a,b]n|Ln(f,x)−f(x)|ω(f′,1n)where f is not a linear function of x and Ln(f,x) are a class of positive linear operators. The results are applied to some well-known operators including Szász–Mirakyan operator, Gamma operator, Baskakov operator and B-spline operator.

Landslide susceptibility mapping by integrating analytical hierarchy process, frequency ratio, and fuzzy gamma operator models, case study: North of Lorestan Province, Iran.

Identifying landslide-prone areas is an essential step in assessing landslide risk and reducing landslide damage. In this paper, GIS-based spatial analysis has been used to prepare the landslide susceptibility (LS) map in the north of Lorestan province in western Iran. For this purpose, three main criteria and their sub-criteria were identified as causative factors including geology and topography (i.e., distance from the fault, lithology, slope, aspect, and elevation), climate (i.e., rainfall and distance from the river), and environmental parameters (i.e., distance from the road, land-cover, NDVI). One hundred thirty-six known landslides were randomly divided into training ([Formula: see text] 70%) and validation ([Formula: see text] 30%) datasets. This study is based on the integration of popular analytic hierarchy process (AHP), frequency ratio (FR), and the fuzzy gamma operator (FGO) techniques. AHP was utilized to prioritize causal factors and fuzzy technique was applied in two stages of factor map fuzzification and calculation of sub-criteria maps and then overlap of fuzzified map layers. The fuzzy membership (FM) values were determined based on the FR method, which was normalized between the ranges of 0 and 1. Finally, LS zoning maps were estimated in five susceptibility classes (very low, low, moderate, high, and very high). Validation processes by comparing the three output maps with the layer of validation landslides in the study area and area under receiver operating characteristic curve confirm that the gamma value of 0.9 (AUC = 0.88) offers a more accurate LS map compared to other gamma values. The results of this study will be reliable for landslide risk reduction strategies.

An integrated approach for the application of geographical information system and Remote Sensing for prospective groundwater zones in Surat region, India

Sustainable groundwater management is becoming a priority in the context of significant changes in groundwater use patterns, particularly with continuously increasing demand for groundwater due to growing population, expansion of irrigation area, and economic progress. This research contributed to the integration of GIS-RS and a fuzzy technique to delineate groundwater prospective zones for Surat district, India. In this study, nine different fuzzy membership layers of influencing parameters were overlaid using the fuzzy GAMMA operator to generate the prospective zones. The result indicates that 62.53% area of the district falls under the high prospective zone. Sensitivity analysis reveals that lineament density, rainfall distribution, and geomorphology were the most important parameters influencing the region's groundwater potentiality. The RS-GIS-based Fuzzy method is proficient and efficient and can be applied anywhere on the earth to identify and delineate groundwater prospective zones.

Groundwater potential characterisation over the Voltaian basin using geophysical, geological, hydrological and topographical datasets

The delineation of prospective zones of groundwater resources has been carried out over the Voltaian basin as a viable alternative source of potable water resource to complement increasing demand for domestic and industrial consumption, owing to the danger posed to surficial water resources within the basin by various anthropogenic activities. In achieving this objective, the groundwater potential of the area was assessed by generating a groundwater potential map (GPM) derived by integrating nine (9) evidential layers obtained from geological, geophysical, hydrological, and topographical datasets in geospatial setting using geographic information systems (GIS). The integration of these nine evidential layers was preceded by the assignment of a weight to each evidential layer based on the fuzzy analytical hierarchy process (FAHP) multi-criteria decision making (MCDM) technique. The assignment of weights to these 9 layers using the FAHP approach was done by three decision-makers (DMs) and dwelled on their relative relevance to groundwater resource delineation within the Voltaian basin. The three DMs employed in weighting these layers have expertise in applying geophysical, geological, hydrological and topographical datasets in groundwater prospecting. The weights obtained for the various evidential layers were subjected to normalisation and subsequently consolidated to produce the GPM using a fuzzy gamma operator value of 0.9 in GIS. The efficiency of the GPM was tested using the Nash-Sutclliffe efficiency (NSE) test and the Index of Agreement test. In all, 0.095%, 10.57%, 44.879%, 40.973%, and 3.974% of the study area were delineated as very high, good, moderate, poor, and very poor groundwater zones, respectively by the GPM. The NSE test yielded a value of 0.9996, and the Index of Agreement produced a value of 0.9999. In this regard, results obtained show that FAHP-based model produced is efficient and subsequently good for groundwater prediction over the Voltaian basin.