Mathematics Between Source And Trap: Uncertainty In Hydrocarbon Migration Modeling

1994 ◽  
Author(s):  
Marek Kacewicz
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Petroleum Industry ◽  
Petroleum Geology ◽  
Mathematical Geology ◽  
Mathematical Methods ◽  
Additional Tool ◽  
Petroleum Systems ◽  
Primary Migration ◽  
Mathematical Techniques

Petroleum geology provides a wide spectrum of data that differs from frontier to mature areas. Data quality and quantity control which mathematical methods and techniques should be applied. In this paper two mathematical methods are shown: fuzzy-set theory and possibility theory as applied to permeability prediction and stochastic modeling of traps and leaks. Both methods are used in the modeling of hydrocarbon migration efficiency. Examples of how data uncertainty may affect final assessment of oil accumulation are presented. The complexity of petroleum geology and its importance to society stimulate research in different scientific areas including mathematical geology, which is becoming steadily more important. Armed with workstations, mainframes, and supercomputers, research laboratories in the petroleum industry investigate sophisticated mathematical techniques and develop complex mathematical models which can speed and improve exploration and lower total exploration costs. Together with classical analysis of geological, geochemical, and seismic data, mathematics provides an additional tool for basin research. The elements of petroleum systems—maturation, expulsion and primary migration, secondary migration, seals, reservoirs, and traps—may be better described by properly applied mathematical techniques. The complexity of petroleum geology and its importance to society stimulate research in different scientific areas including mathematical geology, which is becoming steadily more important. Armed with workstations, mainframes, and supercomputers, research laboratories in the petroleum industry investigate sophisticated mathematical techniques and develop complex mathematical models which can speed and improve exploration and lower total exploration costs. Together with classical analysis of geological, geochemical, and seismic data, mathematics provides an additional tool for basin research. The elements of petroleum systems—maturation, expulsion and primary migration, secondary migration, seals, reservoirs, and traps—may be better described by properly applied mathematical techniques. The applicability of mathematical methods differs in frontier and mature areas and depends upon the quality and quantity of available information. Frontier areas for which data are mostly qualitative require methods which can handle imprecise and limited information easily. Fuzzy-set theory with fuzzy inference algorithms and artificial intelligence are useful approaches. Cokriging and "soft" geostatistical approaches also may be helpful.

Chemical analysis: Information contribution of results

1991 ◽  
Vol 56 (3) ◽  
pp. 505-559 ◽  
Author(s):  
Karel Eckschlager
Keyword(s):  
Analytical Chemistry ◽  
Information Theory ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Information Gain ◽  
Analytical Signal ◽  
Point Of View ◽  
System A ◽  
Review Analysis ◽  
Theory Point

In this review, analysis is treated as a process of gaining information on chemical composition, taking place in a stochastic system. A model of this system is outlined, and a survey of measures and methods of information theory is presented to an extent as useful for qualitative or identification, quantitative and trace analysis and multicomponent analysis. It is differentiated between information content of an analytical signal and information gain, or amount of information, obtained by the analysis, and their interrelation is demonstrated. Some notions of analytical chemistry are quantified from the information theory and system theory point of view; it is also demonstrated that the use of fuzzy set theory can be suitable. The review sums up the principal results of the series of 25 papers which have been published in this journal since 1971.

Estimating construction waste generation in residential buildings: A fuzzy set theory approach in the Brazilian Amazon

2020 ◽  
Vol 265 ◽  
pp. 121779 ◽  
Author(s):  
Luiz Maurício Furtado Maués ◽  
Brisa do Mar Oliveira do Nascimento ◽  
Weisheng Lu ◽  
Fan Xue
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Residential Buildings ◽  
Brazilian Amazon ◽  
Theory Approach ◽  
Waste Generation ◽  
Construction Waste

scholarly journals Metapopulation Patterns of Iberian Butterflies Revealed by Fuzzy Logic

Insects ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 392
Author(s):  
Antonio Pulido-Pastor ◽  
Ana Luz Márquez ◽  
José Carlos Guerrero ◽  
Enrique García-Barros ◽  
Raimundo Real
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Metapopulation Dynamics ◽  
Butterfly Species ◽  
Dynamics Analysis ◽  
Metapopulation Structure ◽  
Occurrence Data ◽  
Metapopulation Theory ◽  
The Cost

Metapopulation theory considers that the populations of many species are fragmented into patches connected by the migration of individuals through an interterritorial matrix. We applied fuzzy set theory and environmental favorability (F) functions to reveal the metapopulational structure of the 222 butterfly species in the Iberian Peninsula. We used the sets of contiguous grid cells with high favorability (F ≥ 0.8), to identify the favorable patches for each species. We superimposed the known occurrence data to reveal the occupied and empty favorable patches, as unoccupied patches are functional in a metapopulation dynamics analysis. We analyzed the connectivity between patches of each metapopulation by focusing on the territory of intermediate and low favorability for the species (F < 0.8). The friction that each cell opposes to the passage of individuals was computed as 1-F. We used the r.cost function of QGIS to calculate the cost of reaching each cell from a favorable patch. The inverse of the cost was computed as connectivity. Only 126 species can be considered to have a metapopulation structure. These metapopulation structures are part of the dark biodiversity of butterflies because their identification is not evident from the observation of the occurrence data but was revealed using favorability functions.

scholarly journals Application of Rough and Fuzzy Set Theory for Prediction of Stochastic Wind Speed Data Using Long Short-Term Memory

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 924
Author(s):  
Moslem Imani ◽  
Hoda Fakour ◽  
Wen-Hau Lan ◽  
Huan-Chin Kao ◽  
Chi Ming Lee ◽  
...  
Keyword(s):  
Deep Learning ◽  
Wind Speed ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set Theory ◽  
Short Term Memory ◽  
Learning Model ◽  
Short Term ◽  
Long Short Term Memory ◽  
Deep Learning Model

Despite the great significance of precisely forecasting the wind speed for development of the new and clean energy technology and stable grid operators, the stochasticity of wind speed makes the prediction a complex and challenging task. For improving the security and economic performance of power grids, accurate short-term wind power forecasting is crucial. In this paper, a deep learning model (Long Short-term Memory (LSTM)) has been proposed for wind speed prediction. Knowing that wind speed time series is nonlinear stochastic, the mutual information (MI) approach was used to find the best subset from the data by maximizing the joint MI between subset and target output. To enhance the accuracy and reduce input characteristics and data uncertainties, rough set and interval type-2 fuzzy set theory are combined in the proposed deep learning model. Wind speed data from an international airport station in the southern coast of Iran Bandar-Abbas City was used as the original input dataset for the optimized deep learning model. Based on the statistical results, the rough set LSTM (RST-LSTM) model showed better prediction accuracy than fuzzy and original LSTM, as well as traditional neural networks, with the lowest error for training and testing datasets in different time horizons. The suggested model can support the optimization of the control approach and the smooth procedure of power system. The results confirm the superior capabilities of deep learning techniques for wind speed forecasting, which could also inspire new applications in meteorology assessment.

On soft set-valued maps and integral inclusions

2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Mathematical Tool ◽  
Multivalued Maps ◽  
Soft Sets ◽  
Special Cases ◽  
New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

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