Species distribution modelling (SDM), also known as environmental (or ecological) niche modelling (ENM), habitat suitability modelling, predictive habitat distribution modelling, and range mapping uses ecological models to predict the distribution of a species across geographic space and time using environmental data. The environmental data are most often climate data (e.g. temperature, precipitation), but can include other variables such as soil type, water depth, and land cover. SDMs are used in several research areas in conservation biology, ecology and evolution. These models can be used to understand how environmental conditions influence the occurrence or abundance of a species, and for predictive purposes (ecological forecasting). Predictions from an SDM may be of a species' future distribution under climate change, a species' past distribution in order to assess evolutionary relationships, or the potential future distribution of an invasive species. Predictions of current and/or future habitat suitability can be useful for management applications (e.g. reintroduction or translocation of vulnerable species, reserve placement in anticipation of climate change). There are two main types of SDMs. Correlative SDMs, also known as climate envelope models, bioclimatic models, or resource selection function models, model the observed distribution of a species as a function of environmental conditions. Mechanistic SDMs, also known as process-based models or biophysical models, use independently derived information about a species' physiology to develop a model of the environmental conditions under which the species can exist. The extent to which such modelled data reflect real-world species distributions will depend on a number of factors, including the nature, complexity, and accuracy of the models used and the quality of the available environmental data layers; the availability of sufficient and reliable species distribution data as model input; and the influence of various factors such as barriers to dispersal, geologic history, or biotic interactions, that increase the difference between the realized niche and the fundamental niche. Environmental niche modelling may be considered a part of the discipline of biodiversity informatics. == History == A. F. W. Schimper used geographical and environmental factors to explain plant distributions in his 1898 Pflanzengeographie auf physiologischer Grundlage (Plant Geography Upon a Physiological Basis) and his 1908 work of the same name. Andrew Murray used the environment to explain the distribution of mammals in his 1866 The Geographical Distribution of Mammals. Robert Whittaker's work with plants and Robert MacArthur's work with birds strongly established the role the environment plays in species distributions. Elgene O. Box constructed environmental envelope models to predict the range of tree species. His computer simulations were among the earliest uses of species distribution modelling. The adoption of more sophisticated generalised linear models (GLMs) made it possible to create more sophisticated and realistic species distribution models. The expansion of remote sensing and the development of GIS-based environmental modelling increase the amount of environmental information available for model-building and made it easier to use. == Correlative vs mechanistic models == === Correlative SDMs === SDMs originated as correlative models. Correlative SDMs model the observed distribution of a species as a function of geographically referenced climatic predictor variables using multiple regression approaches. Given a set of geographically referred observed presences of a species and a set of climate maps, a model defines the most likely environmental ranges within which a species lives. Correlative SDMs assume that species are at equilibrium with their environment and that the relevant environmental variables have been adequately sampled. The models allow for interpolation between a limited number of species occurrences. For these models to be effective, it is required to gather observations not only of species presences, but also of absences, that is, where the species does not live. Records of species absences are typically not as common as records of presences, thus often "random background" or "pseudo-absence" data are used to fit these models. If there are incomplete records of species occurrences, pseudo-absences can introduce bias. Since correlative SDMs are models of a species' observed distribution, they are models of the realized niche (the environments where a species is found), as opposed to the fundamental niche (the environments where a species can be found, or where the abiotic environment is appropriate for the survival). For a given species, the realized and fundamental niches might be the same, but if a species is geographically confined due to dispersal limitation or species interactions, the realized niche will be smaller than the fundamental niche. Correlative SDMs are easier and faster to implement than mechanistic SDMs, and can make ready use of available data. Since they are correlative however, they do not provide much information about causal mechanisms and are not good for extrapolation. They will also be inaccurate if the observed species range is not at equilibrium (e.g. if a species has been recently introduced and is actively expanding its range). In standard SDMs, the distribution of a single species is often modeled, with unique parameters describing how environmental (abiotic) factors influence its occurrence probability. This allows for differentiated responses to environmental drivers among species, but can be problematic for data-deficient species. In contrast, similarities in environmental responses can be accounted for in multi-species SDMs, which model several species jointly using shared or hierarchically related parameters. However, neither approach explicitly accounts for community-level biotic interactions, which can be important in explaining species diversity patterns. Joint species distribution models (joint SDMs or J-SDMs) address this by modeling species co-occurrence patterns directly. The occurrence probability of a given species is thus influenced not only by abiotic drivers but also by inferred biotic associations with other species. This can improve accuracy for rarer taxa and provide insights into community ecology. Both standard SDMs and J-SDMs can be used to generate community-level metrics, such as species richness, by aggregating outputs across multiple species. These can be important for decision-making such as conservation planning. === Mechanistic SDMs === Mechanistic SDMs are more recently developed. In contrast to correlative models, mechanistic SDMs use physiological information about a species (taken from controlled field or laboratory studies) to determine the range of environmental conditions within which the species can persist. These models aim to directly characterize the fundamental niche, and to project it onto the landscape. A simple model may simply identify threshold values outside of which a species can't survive. A more complex model may consist of several sub-models, e.g. micro-climate conditions given macro-climate conditions, body temperature given micro-climate conditions, fitness or other biological rates (e.g. survival, fecundity) given body temperature (thermal performance curves), resource or energy requirements, and population dynamics. Geographically referenced environmental data are used as model inputs. Because the species distribution predictions are independent of the species' known range, these models are especially useful for species whose range is actively shifting and not at equilibrium, such as invasive species. Mechanistic SDMs incorporate causal mechanisms and are better for extrapolation and non-equilibrium situations. However, they are more labor-intensive to create than correlational models and require the collection and validation of a lot of physiological data, which may not be readily available. The models require many assumptions and parameter estimates, and they can become very complicated. Dispersal, biotic interactions, and evolutionary processes present challenges, as they aren't usually incorporated into either correlative or mechanistic models. Correlational and mechanistic models can be used in combination to gain additional insights. For example, a mechanistic model could be used to identify areas that are clearly outside the species' fundamental niche, and these areas can be marked as absences or excluded from analysis. See for a comparison between mechanistic and correlative models. == Niche models (correlative) == There are a variety of mathematical methods that can be used for fitting, selecting, and evaluating correlative SDMs. Models include "profile" methods, which are simple statistical techniques that use e.g. environmental distance to known sites of occurrence such as
Granular computing
Granular computing is an emerging computing paradigm of information processing that concerns the processing of complex information entities called "information granules", which arise in the process of data abstraction and derivation of knowledge from information or data. Generally speaking, information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like. At present, granular computing is more a theoretical perspective than a coherent set of methods or principles. As a theoretical perspective, it encourages an approach to data that recognizes and exploits the knowledge present in data at various levels of resolution or scales. In this sense, it encompasses all methods which provide flexibility and adaptability in the resolution at which knowledge or information is extracted and represented. == Types of granulation == As mentioned above, granular computing is not an algorithm or process; there is no particular method that is called "granular computing". It is rather an approach to looking at data that recognizes how different and interesting regularities in the data can appear at different levels of granularity, much as different features become salient in satellite images of greater or lesser resolution. On a low-resolution satellite image, for example, one might notice interesting cloud patterns representing cyclones or other large-scale weather phenomena, while in a higher-resolution image, one misses these large-scale atmospheric phenomena but instead notices smaller-scale phenomena, such as the interesting pattern that is the streets of Manhattan. The same is generally true of all data: At different resolutions or granularities, different features and relationships emerge. The aim of granular computing is to try to take advantage of this fact in designing more effective machine-learning and reasoning systems. There are several types of granularity that are often encountered in data mining and machine learning, and we review them below: === Value granulation (discretization/quantization) === One type of granulation is the quantization of variables. It is very common that in data mining or machine-learning applications the resolution of variables needs to be decreased in order to extract meaningful regularities. An example of this would be a variable such as "outside temperature" (temp), which in a given application might be recorded to several decimal places of precision (depending on the sensing apparatus). However, for purposes of extracting relationships between "outside temperature" and, say, "number of health-club applications" (club), it will generally be advantageous to quantize "outside temperature" into a smaller number of intervals. ==== Motivations ==== There are several interrelated reasons for granulating variables in this fashion: Based on prior domain knowledge, there is no expectation that minute variations in temperature (e.g., the difference between 80–80.7 °F (26.7–27.1 °C)) could have an influence on behaviors driving the number of health-club applications. For this reason, any "regularity" which our learning algorithms might detect at this level of resolution would have to be spurious, as an artifact of overfitting. By coarsening the temperature variable into intervals the difference between which we do anticipate (based on prior domain knowledge) might influence number of health-club applications, we eliminate the possibility of detecting these spurious patterns. Thus, in this case, reducing resolution is a method of controlling overfitting. By reducing the number of intervals in the temperature variable (i.e., increasing its grain size), we increase the amount of sample data indexed by each interval designation. Thus, by coarsening the variable, we increase sample sizes and achieve better statistical estimation. In this sense, increasing granularity provides an antidote to the so-called curse of dimensionality, which relates to the exponential decrease in statistical power with increase in number of dimensions or variable cardinality. Independent of prior domain knowledge, it is often the case that meaningful regularities (i.e., which can be detected by a given learning methodology, representational language, etc.) may exist at one level of resolution and not at another. For example, a simple learner or pattern recognition system may seek to extract regularities satisfying a conditional probability threshold such as p ( Y = y j | X = x i ) ≥ α . {\displaystyle p(Y=y_{j}|X=x_{i})\geq \alpha .} In the special case where α = 1 , {\displaystyle \alpha =1,} this recognition system is essentially detecting logical implication of the form X = x i → Y = y j {\displaystyle X=x_{i}\rightarrow Y=y_{j}} or, in words, "if X = x i , {\displaystyle X=x_{i},} then Y = y j {\displaystyle Y=y_{j}} ". The system's ability to recognize such implications (or, in general, conditional probabilities exceeding threshold) is partially contingent on the resolution with which the system analyzes the variables. As an example of this last point, consider the feature space shown to the right. The variables may each be regarded at two different resolutions. Variable X {\displaystyle X} may be regarded at a high (quaternary) resolution wherein it takes on the four values { x 1 , x 2 , x 3 , x 4 } {\displaystyle \{x_{1},x_{2},x_{3},x_{4}\}} or at a lower (binary) resolution wherein it takes on the two values { X 1 , X 2 } . {\displaystyle \{X_{1},X_{2}\}.} Similarly, variable Y {\displaystyle Y} may be regarded at a high (quaternary) resolution or at a lower (binary) resolution, where it takes on the values { y 1 , y 2 , y 3 , y 4 } {\displaystyle \{y_{1},y_{2},y_{3},y_{4}\}} or { Y 1 , Y 2 } , {\displaystyle \{Y_{1},Y_{2}\},} respectively. At the high resolution, there are no detectable implications of the form X = x i → Y = y j , {\displaystyle X=x_{i}\rightarrow Y=y_{j},} since every x i {\displaystyle x_{i}} is associated with more than one y j , {\displaystyle y_{j},} and thus, for all x i , {\displaystyle x_{i},} p ( Y = y j | X = x i ) < 1. {\displaystyle p(Y=y_{j}|X=x_{i})<1.} However, at the low (binary) variable resolution, two bilateral implications become detectable: X = X 1 ↔ Y = Y 1 {\displaystyle X=X_{1}\leftrightarrow Y=Y_{1}} and X = X 2 ↔ Y = Y 2 {\displaystyle X=X_{2}\leftrightarrow Y=Y_{2}} , since every X 1 {\displaystyle X_{1}} occurs iff Y 1 {\displaystyle Y_{1}} and X 2 {\displaystyle X_{2}} occurs iff Y 2 . {\displaystyle Y_{2}.} Thus, a pattern recognition system scanning for implications of this kind would find them at the binary variable resolution, but would fail to find them at the higher quaternary variable resolution. ==== Issues and methods ==== It is not feasible to exhaustively test all possible discretization resolutions on all variables in order to see which combination of resolutions yields interesting or significant results. Instead, the feature space must be preprocessed (often by an entropy analysis of some kind) so that some guidance can be given as to how the discretization process should proceed. Moreover, one cannot generally achieve good results by naively analyzing and discretizing each variable independently, since this may obliterate the very interactions that we had hoped to discover. A sample of papers that address the problem of variable discretization in general, and multiple-variable discretization in particular, is as follows: Chiu, Wong & Cheung (1991), Bay (2001), Liu et al. (2002), Wang & Liu (1998), Zighed, Rabaséda & Rakotomalala (1998), Catlett (1991), Dougherty, Kohavi & Sahami (1995), Monti & Cooper (1999), Fayyad & Irani (1993), Chiu, Cheung & Wong (1990), Nguyen & Nguyen (1998), Grzymala-Busse & Stefanowski (2001), Ting (1994), Ludl & Widmer (2000), Pfahringer (1995), An & Cercone (1999), Chiu & Cheung (1989), Chmielewski & Grzymala-Busse (1996), Lee & Shin (1994), Liu & Wellman (2002), Liu & Wellman (2004). === Variable granulation (clustering/aggregation/transformation) === Variable granulation is a term that could describe a variety of techniques, most of which are aimed at reducing dimensionality, redundancy, and storage requirements. We briefly describe some of the ideas here, and present pointers to the literature. ==== Variable transformation ==== A number of classical methods, such as principal component analysis, multidimensional scaling, factor analysis, and structural equation modeling, and their relatives, fall under the genus of "variable transformation." Also in this category are more modern areas of study such as dimensionality reduction, projection pursuit, and independent component analysis. The common goal of these methods in general is to find a representation of the data in terms of new variables, which are a linear or nonlinear transformation of the original variables, and in which important stati
Defuzzification
Defuzzification is the process of producing a quantifiable result in crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems. These systems will have a number of rules that transform a number of variables into a fuzzy result, that is, the result is described in terms of membership in fuzzy sets. For example, rules designed to decide how much pressure to apply might result in "Decrease Pressure (15%), Maintain Pressure (34%), Increase Pressure (72%)". Defuzzification is interpreting the membership degrees of the fuzzy sets into a specific decision or real value. The simplest but least useful defuzzification method is to choose the set with the highest membership, in this case, "Increase Pressure" since it has a 72% membership, and ignore the others, and convert this 72% to some number. The problem with this approach is that it loses information. The rules that called for decreasing or maintaining pressure might as well have not been there in this case. A common and useful defuzzification technique is center of gravity. First, the results of the rules must be added together in some way. The most typical fuzzy set membership function has the graph of a triangle. Now, if this triangle were to be cut in a straight horizontal line somewhere between the top and the bottom, and the top portion were to be removed, the remaining portion forms a trapezoid. The first step of defuzzification typically "chops off" parts of the graphs to form trapezoids (or other shapes if the initial shapes were not triangles). For example, if the output has "Decrease Pressure (15%)", then this triangle will be cut 15% the way up from the bottom. In the most common technique, all of these trapezoids are then superimposed one upon another, forming a single geometric shape. Then, the centroid of this shape, called the fuzzy centroid, is calculated. The x coordinate of the centroid is the defuzzified value. == Methods == There are many different methods of defuzzification available, including the following: AI (adaptive integration) BADD (basic defuzzification distributions) BOA (bisector of area) CDD (constraint decision defuzzification) COA (center of area) COG (center of gravity) ECOA (extended center of area) EQM (extended quality method) FCD (fuzzy clustering defuzzification) FM (fuzzy mean) FOM (first of maximum) GLSD (generalized level set defuzzification) ICOG (indexed center of gravity) IV (influence value) LOM (last of maximum) MeOM (mean of maxima) MOM (middle of maximum) QM (quality method) RCOM (random choice of maximum) SLIDE (semi-linear defuzzification) WFM (weighted fuzzy mean) The maxima methods are good candidates for fuzzy reasoning systems. The distribution methods and the area methods exhibit the property of continuity that makes them suitable for fuzzy controllers.
Degree of truth
In classical logic, propositions are typically unambiguously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition one is equal to one is regarded as simply true, by the Law of Identity. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than wholly true or wholly false. Consider this pizza is hot. In mathematics, this idea can be developed in terms of fuzzy logic. In computer science, it has found application in artificial intelligence. In philosophy, the idea has proved particularly appealing in the case of vagueness. Degrees of truth is an important concept in law. The term is an older concept than conditional probability. Instead of determining the objective probability, only a subjective assessment is defined. In adjudicative processes, 'substantive truth' is distinct from 'formal legal truth' which comes in four degrees: hearsay, balance of probabilities, proven beyond reasonable doubt and absolute truth (knowledge reserved unto God).
Supreme Commander (video game)
Supreme Commander (sometimes SupCom) is a 2007 real-time strategy video game designed by Chris Taylor and developed by his company, Gas Powered Games. The game is considered to be a spiritual successor, not a direct sequel, to Taylor's 1997 game Total Annihilation. First announced in the August 2005 edition of PC Gamer magazine, the game was released in Europe on February 16, 2007, and in North America on February 20. The standalone expansion Supreme Commander: Forged Alliance was released on November 6 of the same year. The sequel, Supreme Commander 2, was released in 2010. Nowadays, the original Supreme Commander is played through the community client called Forged Alliance Forever; the game has been further developed and balanced, and offers a wide variety of community mods. The gameplay of Supreme Commander focuses on using a giant bipedal mech called an Armored Command Unit (ACU), the so-called "Supreme Commander", to build a base, upgrading units to reach higher technology tiers, and conquering opponents. The player can command one of three factions: the Aeon Illuminate, the Cybran Nation, or the United Earth Federation (UEF). The expansion game added the Seraphim faction. Supreme Commander was highly anticipated in pre-release previews, and was well received by critics, with a Metacritic average of 86 out of 100. == Gameplay == Supreme Commander, like its spiritual predecessors, Total Annihilation and Spring, begins with the player solely possessing a single, irreplaceable construction unit called the "Armored Command Unit," or ACU, the titular Supreme Commander. Normally the loss of this unit results in the loss of the game (Skirmish missions can be set for a variety of victory conditions). These mech suits are designed to be transported through quantum gateways across the galaxy and contain all the materials and blueprints necessary to create an army from a planet's native resources in hours. All standard units except Commanders and summoned Support Commanders (sACU) are self-sufficient robots. All units and structures belong to one of four technology tiers, or "Tech" levels, each tier being stronger and/or more efficient than the previous. Certain lower-tier structures can be upgraded into higher ones without having to rebuild them. The first tier is available at the start of the game and consists of small, relatively weak units and structures. The second tier expands the player's abilities greatly, especially in terms of stationary weapons and shielding, and introduces upgraded versions of tier one units. The third tier level has very powerful assault units designed to overcome the fortifications of the most entrenched player. The fourth tier is a limited range of "experimental" technology. These are usually massive units which take a lot of time and energy to produce, but provide a significant tactical advantage. Supreme Commander features a varied skirmish AI. The typical Easy' and Normal modes are present, but the Hard difficulty level has four possible variants. Horde AI will swarm the player with hordes of lower level units, Tech AI will upgrade its units as fast as possible and assault the player with advanced units, the Balanced AI attempts to find a balance between the two, and the Supreme AI decides which of the three hard strategies is best for the map. The single player campaign consists of eighteen missions, six for each faction. The player is an inexperienced Commander who plays a key role in their faction's campaign to bring the "Infinite War" to an end. Despite the low number of campaign missions, each mission can potentially last hours. At the start of a mission, objectives are assigned for the player to complete. Once the player accomplishes them, the map is expanded, sometimes doubling or tripling in size, and new objectives are assigned. As the mission is commonly divided into three segments, the player will often have to overcome several enemy positions to achieve victory. === Resource management === Because humans have developed replication technology, making advanced use of rapid prototyping and nanotechnology, only two types of resources are required to wage war: Energy and Mass. Energy is obtained by constructing power generators on any solid surface (except fuel generators, which can only be built on fuel deposits), while Mass is obtained either by placing mass extractors on limited mass deposit spots (the most efficient method, although it requires map control) or by building mass fabricators to convert energy into mass. Constructor units can gather energy by "reclaiming" it from organic debris such as trees and mass from rocks and wrecked units. Each player has a certain amount of resource storage, which can be expanded by the construction of storage structures. This gives the player reserves in times of shortage or allows them to stockpile resources. If the resource generation exceeds the player's capacity, the material is wasted. On the contrary, if the storages are depleted and the demand of one of the resources exceeds the production, then all the productions speed is reduced. In addition, if an energy deficit occurs, shields will stop working. An adjacency system allows certain structures to benefit from being built directly adjacent to others. Energy-consuming structures will use less energy when built adjacent to power generators and power generators will produce more energy when built adjacent to power storage structures. The same applies to their mass-producing equivalents. Likewise, factories will consume less energy and mass when built adjacent to power generators and mass fabricators/extractors, respectively. However, by placing structures in close proximity, they become more vulnerable to collateral damage if an adjacent structure is destroyed. Furthermore, most resource generation structures can cause chain reactions when destroyed (especially Tier III structures, which produce large amounts of resources but often have large detonations that can wipe out a nearby army). === Warfare === Supreme Commander uses a "strategic zoom" system that allows the player to seamlessly zoom from a detailed close up view of an individual unit all the way out to a view of the entire map, at which point it resembles a fullscreen version of the minimap denoting individual units with icons. The camera also has a free movement mode and can be slaved to track a selected unit and there is a split screen mode which also supports multiple monitors. This system allows Supreme Commander to use vast maps up to 80 km x 80 km, with players potentially controlling a thousand units each. Units in Supreme Commander are built to scale as they would be in the real world. For example, battleships dwarf submarines. Late into the game, the larger "experimental" units, such as the Cybran Monkeylord, an enormous spider-shaped assault unit, can actually crush smaller enemy units by stepping on them. Because of the wide range of planets colonized by humanity in the setting, the theatres of war range from desert to arctic, and all battlespaces are employed. Technologies emerging in modern warfare are frequently employed in Supreme Commander. For example, stealth technology and both tactical and strategic missile and missile defense systems can be used. Supreme Commander introduced several innovations designed to reduce the amount of micromanagement inherent in many RTS games. Engineers units have the command "assist", that will help follow other engineers and help them finish their orders or improve production rate of factories. In addition, engineers with the order "patrol" will repair units, buildings and recycle wrecks in their along their patrol route. Holding the shift key causes any orders given to a unit (or group of units) to be queued. In this manner a unit may be ordered to attack several targets in succession, or to make best speed to a given point on the map and then attack towards a specified location engaging any hostiles it encounters along the way. After orders have been issued, holding the shift key causes all issued orders to be displayed on the map where they can be subsequently modified to accommodate a change of plan. Further, when a unit is ordered to attack a target, the player can issue an order to perform a coordinated attack to another unit. This order coordinates the arrival time of the units at the target automatically by adjusting the speed of the units involved. As in other RTS games, air transports can be used to convey units to specified destinations, in Supreme Commander though by shift queuing orders a transport containing several units can be ordered to drop specific units at subsequent waypoints. An air transport can also be ordered to create a ferry route, an airbridge wherein any land units ordered to the start of the ferry route will be conveyed by the air transport to the specified destination. The output from a production factory can be routed to a ferry route causing all units co
Generative design
Generative design is an iterative design process that uses software to generate outputs that fulfill a set of constraints iteratively adjusted by a designer. Whether a human, test program, or artificial intelligence, the designer algorithmically or manually refines the feasible region of the program's inputs and outputs with each iteration to fulfill evolving design requirements. By employing computing power to evaluate more design permutations than a human alone is capable of, the process is capable of producing an optimal design that mimics nature's evolutionary approach to design through genetic variation and selection. The output can be images, sounds, architectural models, animation, and much more. It is, therefore, a fast method of exploring design possibilities that is used in various design fields such as art, architecture, communication design, and product design. Generative design has become more important, largely due to new programming environments or scripting capabilities that have made it relatively easy, even for designers with little programming experience, to implement their ideas. Additionally, this process can create solutions to substantially complex problems that would otherwise be resource-exhaustive with an alternative approach, making it a more attractive option for problems with a large or unknown solution set. It is also facilitated with tools in commercially available CAD packages. Not only are implementation tools more accessible, but also tools leveraging generative design as a foundation. Recent advancements have led to the development of Deep Generative Design, a framework that integrates topology optimization with deep learning models, such as Generative Adversarial Networks (GANs). Unlike traditional evolutionary methods that primarily focus on engineering performance, this approach uses deep generative models to enhance aesthetic diversity and novelty while simultaneously satisfying engineering constraints. For instance, research by Oh et al. (2019) proposed a framework using Boundary Equilibrium GANs (BEGAN) to generate diverse design options which are then refined through density-based topology optimization, allowing for the exploration of complex design spaces that balance structural integrity with visual variation. In practice, generative design does not solely aim to produce a single optimal solution, but involves iteratively refining the design problem by modifying parameters, constraints, and evaluation criteria within a computational model, resulting in multiple design alternatives from which the designer selects. == Use in architecture == Generative design in architecture is an iterative design process that enables architects to explore a wider solution space with more possibility and creativity. Architectural design has long been regarded as a wicked problem. Compared with traditional top-down design approach, generative design can address design problems efficiently, by using a bottom-up paradigm that uses parametric-defined rules to generate complex solutions. The solution itself then evolves to a good, if not optimal, solution. The advantage of using generative design as a design tool is that it does not construct fixed geometries, but take a set of design rules that can generate an infinite set of possible design solutions. The generated design solutions can be more sensitive, responsive, and adaptive to the problem. Generative design involves rule definition and result analysis that are integrated with the design process. By defining parameters and rules, the generative approach is able to provide optimized solution for both structural stability and aesthetics. Possible design algorithms include cellular automata, shape grammar, genetic algorithm, space syntax, and most recently, artificial neural network. Due to the high complexity of the solution generated, rule-based computational tools, such as finite element method and topology optimisation, are preferred to evaluate and optimise the generated solution. The iterative process provided by computer software enables the trial-and-error approach in design, and involves architects interfering with the optimisation process. Historically precedent work includes Antoni Gaudí's Sagrada Família, which used rule based geometrical forms for structures, and Buckminster Fuller's Montreal Biosphere where the rules were designed to generate individual components, rather than the final product. More recent generative-design cases include Foster and Partners' Queen Elizabeth II Great Court, where the tessellated glass roof was designed using a geometric schema to define hierarchical relationships, and then the generated solution was optimized based on geometrical and structural requirements. == Use in sustainable design == Generative design in sustainable design is an effective approach addressing energy efficiency and climate change at the early design stage, recognizing buildings contribute to approximately one-third of global greenhouse gas emissions and 30%-40% of total building energy use. It integrates environmental principles with algorithms, enabling exploration of countless design alternatives to enhance energy performance, reduce carbon footprints, and minimize waste. A key feature of generative design in sustainable design is its ability to incorporate Building Performance Simulations (BPS) into the design process. Simulation programs such as EnergyPlus, Ladybug Tools,, and so on, combined with generative algorithms, can optimize design solutions for cost-effective energy use and zero-carbon building designs. For example, the GENE_ARCH system used a Pareto algorithm with building energy simulation for the whole building design optimization. Generative design has improved sustainable facade design, as illustrated by the algorithm of cellular automata and daylight simulations in adaptive facade design. In addition, genetic algorithms were used with radiation simulations for energy-efficient photo-voltaic (PV) modules on high-rise building facades. Generative design is also applied to life cycle analysis (LCA), as demonstrated by a framework using grid search algorithms to optimize exterior wall design for minimum environmental impact. Multi-objective optimization embraces multiple diverse sustainability goals, such as interactive kinetic louvers using biomimicry and daylight simulations to enhance daylight, visual comfort, and energy efficiency. The study of PV and shading systems can maximize on-site electricity, improve visual quality, and daylight performance. Artificial intelligence (AI) and machine learning (ML) further improve computation efficiency in complex climate-responsive sustainable design. One study employed reinforcement learning to identify the relationship between design parameters and energy use for a sustainable campus, while other studies tried hybrid algorithms, such as using the genetic algorithm and GANs to balance daylight illumination and thermal comfort under different roof conditions. Other popular AI tools were also integrated, including deep reinforcement learning (DRL) and computer vision (CV), to generate an urban block according to direct sunlight hours and solar heat gains. These AI-driven generative design methods enable faster simulations and design decision making, resulting in designs that are environmentally responsible. == Use in additive manufacturing == Additive manufacturing (AM) is a process that creates physical models directly from three-dimensional (3D) data by joining materials layer by layer. It is used in industries to produce a variety of end-use parts, which are final components designed for direct application in products or systems. AM provides design flexibility and enables material reduction in lightweight applications, such as aerospace, automotive, medical, and portable electronic devices, where minimizing weight is critical for performance. Generative design, one of the four key methods for lightweight design in AM, is commonly applied to optimize structures for specific performance requirements. Generative design can help create optimized solutions that balance multiple objectives, such as enhancing performance while minimizing cost. In design for additive manufacturing (DfAM), multi-objective topology optimization is used to generate a set of candidate solutions. Designers then assess these options using their expertise and key performance indicators (KPIs) to select the best option for implementation. However, integrating AM constraints (e.g., speed of build, materials, build envelope, and accuracy) into generative design remains challenging, as ensuring all solutions are valid is complex. Balancing multiple design objectives while limiting computational costs adds further challenges for designers. To overcome these difficulties, researchers proposed a generative design method with manufacturing validation to improve decision-making efficiency. This method starts with a cons
Degree of truth
In classical logic, propositions are typically unambiguously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition one is equal to one is regarded as simply true, by the Law of Identity. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than wholly true or wholly false. Consider this pizza is hot. In mathematics, this idea can be developed in terms of fuzzy logic. In computer science, it has found application in artificial intelligence. In philosophy, the idea has proved particularly appealing in the case of vagueness. Degrees of truth is an important concept in law. The term is an older concept than conditional probability. Instead of determining the objective probability, only a subjective assessment is defined. In adjudicative processes, 'substantive truth' is distinct from 'formal legal truth' which comes in four degrees: hearsay, balance of probabilities, proven beyond reasonable doubt and absolute truth (knowledge reserved unto God).