Biopython is an open-source collection of non-commercial Python modules for computational biology and bioinformatics. It makes robust and well-tested code easily accessible to researchers. Python is an object-oriented programming language and is a suitable choice for automation of common tasks. The availability of reusable libraries saves development time and lets researchers focus on addressing scientific questions. Biopython is constantly updated and maintained by a large team of volunteers across the globe. Biopython contains parsers for diverse bioinformatic sequence, alignment, and structure formats. Sequence formats include FASTA, FASTQ, GenBank, and EMBL. Alignment formats include Clustal, BLAST, PHYLIP, and NEXUS. Structural formats include the PDB, which contains the 3D atomic coordinates of the macromolecules. It has provisions to access information from biological databases like NCBI, Expasy, PBD, and BioSQL. This can be used in scripts or incorporated into their software. Biopython contains a standard sequence class, sequence alignment, and motif analysis tools. It also has clustering algorithms, a module for structural biology, and a module for phylogenetics analysis. == History == The development of Biopython began in 1999, and it was first released in July 2000. First "semi-complete" and "semi-stable" release was done in March 2001 and December 2002 respectively. It was developed during a similar time frame and with analogous goals to other projects that added bioinformatics capabilities to their respective programming languages, including BioPerl, BioRuby and BioJava. Early developers on the project included Jeff Chang, Andrew Dalke and Brad Chapman, though over 100 people have made contributions to date. In 2007, a similar Python project, namely PyCogent, was established. The initial scope of Biopython involved accessing, indexing and processing biological sequence files. The retrieved data from common biological databases will then be parsed into a python data structure. While this is still a major focus, over the following years added modules have extended its functionality to cover additional areas of biology. The key challenge in the design of parsers for bioinformatics file formats is the frequency at which the data formats change. This is due to inadequate curation of the structure of the data, and changes in the database contents. This problem is overcome by the application of a standard event-oriented parser design (see Key features and examples). As of version 1.77, Biopython no longer supports Python 2. The current stable release of Biopython version 1.85 was released on 15 January 2025. It only supports Python 3 and the recent releases of Biopython require NumPy (and not Numeric). == Design == Wherever possible, Biopython follows the conventions used by the Python programming language to make it easier for users familiar with Python. For example, Seq and SeqRecord objects can be manipulated via slicing, in a manner similar to Python's strings and lists. It is also designed to be functionally similar to other Bio projects, such as BioPerl. It is organized into modular sub-packages, e.g., Bio.Seq, Bio.Align, Bio.PDB, Bio.Entrez each of them useful in a different bioinformatics domain. It used principles, like encapsulation and polymorphism, notably in classes Seq, SeqRecord, and Bio.PDB.Structure. It can also interoperate with other Python tools (Pandas, Matplotlib and SciPy). Biopython can read and write most common file formats for each of its functional areas, and its license is permissive and compatible with most other software licenses, which allows Biopython to be used in a variety of software projects. == Requirements == Biopython is currently supported and tested with the following Python implementations: Python 3 or PyPy3 NumPy == Key features and examples == === Input and output === Biopython can read and write to a number of common formats. When reading files, descriptive information in the file is used to populate the members of Biopython classes, such as SeqRecord. This allows records of one file format to be converted into others. Very large sequence files can exceed a computer's memory resources, so Biopython provides various options for accessing records in large files. They can be loaded entirely into memory in Python data structures, such as lists or dictionaries, providing fast access at the cost of memory usage. Alternatively, the files can be read from disk as needed, with slower performance but lower memory requirements. === Sequences === A core concept in Biopython is the biological sequence, and this is represented by the Seq class. A Biopython Seq object is similar to a Python string in many respects: it supports the Python slice notation, can be concatenated with other sequences and is immutable. This object includes both general string-like and biological sequence-specific methods. It is best to store information about the biological type (DNA, RNA, protein) separately from the sequence, rather than using an explicit alphabet argument. === Sequence annotation === The SeqRecord class describes sequences, along with information such as name, description and features in the form of SeqFeature objects. Each SeqFeature object specifies the type of the feature and its location. Feature types can be ‘gene’, ‘CDS’ (coding sequence), ‘repeat_region’, ‘mobile_element’ or others, and the position of features in the sequence can be exact or approximate. === Accessing online databases === Through the Bio.Entrez module, users of Biopython can download biological data from NCBI databases. Each of the functions provided by the Entrez search engine is available through functions in this module, including searching for and downloading records. === Phylogeny === The Bio.Phylo module provides tools for working with and visualising phylogenetic trees. A variety of file formats are supported for reading and writing, including Newick, NEXUS and phyloXML. Common tree manipulations and traversals are supported via the Tree and Clade objects. Examples include converting and collating tree files, extracting subsets from a tree, changing a tree's root, and analysing branch features such as length or score. Rooted trees can be drawn in ASCII or using matplotlib (see Figure 1), and the Graphviz library can be used to create unrooted layouts (see Figure 2). === Genome diagrams === The GenomeDiagram module provides methods of visualising sequences within Biopython. Sequences can be drawn in a linear or circular form (see Figure 3), and many output formats are supported, including PDF and PNG. Diagrams are created by making tracks and then adding sequence features to those tracks. By looping over a sequence's features and using their attributes to decide if and how they are added to the diagram's tracks, one can exercise much control over the appearance of the final diagram. Cross-links can be drawn between different tracks, allowing one to compare multiple sequences in a single diagram. === Macromolecular structure === The Bio.PDB module can load molecular structures from PDB and mmCIF files, and was added to Biopython in 2003. The Structure object is central to this module, and it organises macromolecular structure in a hierarchical fashion: Structure objects contain Model objects which contain Chain objects which contain Residue objects which contain Atom objects. Disordered residues and atoms get their own classes, DisorderedResidue and DisorderedAtom, that describe their uncertain positions. Using Bio.PDB, one can navigate through individual components of a macromolecular structure file, such as examining each atom in a protein. Common analyses can be carried out, such as measuring distances or angles, comparing residues and calculating residue depth. === Population genetics === The Bio.PopGen module adds support to Biopython for Genepop, a software package for statistical analysis of population genetics. This allows for analyses of Hardy–Weinberg equilibrium, linkage disequilibrium and other features of a population's allele frequencies. This module can also carry out population genetic simulations using coalescent theory with the fastsimcoal2 program. === Wrappers for command line tools === Biopython previously included command-line wrappers for tools such as BLAST, Clustal, EMBOSS, and SAMtools. This option allowed users to run external tool commands from within the code using specialized Biopython classes. However, Bio.Application modules and their wrappers have deprecated and will be removed in future Biopython releases. The main reason for this is the high maintenance burden of updating them with the evolving external tools. The recommended approach is to directly construct and execute command-line tool commands using Python’s built-in subprocess module. This method provides flexibility and removes the dependency on the Biopython wrappers. subprocess is a native Python module useful for running ext
Super app
A super app or super-app (also known as an everything app) is a mobile or web application that can provide multiple services including payment and instant messaging services, effectively becoming an all-encompassing, self-contained, commerce and communication online platform that embraces many aspects of personal and commercial life. Notable examples of super apps include Tencent's WeChat in China, Tata Neu in India, Grab in Southeast Asia and Max in Russia. For end users, a super app is an application that provides a set of core features while also giving access to independently developed miniapps. For app developers, a super app is an application integrated with the capabilities of platforms and ecosystems that allows third-parties to develop and publish miniapps. == History == The super app term was first used to describe WeChat when it combined the instant messaging service with the digital wallet function. Recognition of WeChat as a super app stems from its combination of messaging, payments, e-commerce, and much more within a single application, making it indispensable for many users. WeChat's establishment of the super app model has led companies like Meta to try to build similar applications outside of China. In India, Tata Group has announced that it is currently developing a super app named Tata Neu. Major Indian companies like Paytm, PhonePe, and ITC Maars also have apps in development that might constitute super apps. In Southeast Asia, Grab and Gojek lay claim to the super app classification despite lacking many of the features offered by WeChat. Accordingly, growth-stage companies like Shopee, Traveloka, and AirAsia have also expanded the range of services offered by their respective applications. == Notable examples == === Alipay === Alipay is a third-party mobile and online payment platform established in Hangzhou, China in February 2004 by Alibaba Group and its founder Jack Ma. It operates in association with Ant Group, an affiliate company of the Chinese Alibaba Group. === Gojek === Gojek is an Indonesian on-demand multiservice digital platform and fintech payment super app. Established in Jakarta in 2010, as a call center to connect consumers to courier delivery and two-wheeled ride-hailing services, it launched its mobile app in 2015 with four services: GoRide, GoSend, GoShop, and GoFood, which has since expanded to offer over 20 services. In 2021, it merged with another Indonesian unicorn, Tokopedia, forming the decacorn GoTo Gojek Tokopedia. === Grab === Grab is a Southeast Asian technology company headquartered in Singapore and Indonesia. Founded in 2012 as the MyTeksi app in Kuala Lumpur, Malaysia, it expanded the following year as GrabTaxi, before moving its headquarters to Singapore in 2014 and rebranding officially as Grab. In addition to ride-hailing and transportation services, the company's mobile app also offers food delivery and digital payment services. === Max === Max is a messenger from the Russian company VK, positioned as a super app. The application combines messaging, calls, and channels features with the integration of additional services: payments, miniapps, taxi ordering, deliveries, and other everyday services are available within a single interface. The goal is to unite communication and routine tasks in a unified ecosystem. === Tata Neu === Tata Neu is a multipurpose super app, developed in India by the Tata Group. It is the country's first super app. The app was launched to coincide with the start of a 2022 Indian Premier League cricket match. === WeChat === WeChat is a Chinese multipurpose instant messaging, social media and mobile payment app. First released in 2011, it became the world's largest standalone mobile app in 2018, with over 1 billion monthly active users. WeChat provides text messaging, hold-to-talk voice messaging, broadcast (one-to-many) messaging, video conferencing, video games, the sharing of photographs and videos and location sharing. === X === X is an American social network, originally known as Twitter from its launch through 2023. Prior to his acquisition of the service, new owner Elon Musk stated that he planned for Twitter to become an "everything app" known as "X"; in 2023, the service added an AI chatbot known as "Grok" as well as integrated job search tools known as "X Hiring". In January 2025, X announced its intent to offer a digital wallet service in the future. Later in the year, X revamped its direct messaging system as "Chat". == Criticism == Although apps that fit the super app classification can offer users a wider variety of services in comparison to single-purpose alternatives, internet regulators in regions such as the US and Europe have become more concerned about the overall power of the technology industry and have become more critical of companies developing such apps. In China, WeChat and other local firms have been ordered to open up their platforms to rivals by local regulators. There are also reports that suggest it might be difficult to replicate WeChat's super app model. This stems partly from the peaking of smartphone penetration rates in many regions worldwide, which has led to overcrowded app stores and tighter restrictions on targeted advertising as regulators assert more control over the companies. From a technical viewpoint, single-purpose apps are comparatively faster, more responsive and easier to navigate than super apps, which helps improve the overall user experience. Super-apps are also likelier to store larger amounts of personal data to facilitate the delivery of their services, so users run a greater risk of becoming victims of severe data breaches. In 2020, this unfolded with Tokopedia, which had the data of 91 million of its users stolen and shared by crackers. It has also been noted that a user who loses access to their account or is banned from a super app generally loses access to multiple real-life services and digital applications; the Chinese government has used this approach to penalize people who shared the photos of the Sitong Bridge protest.
Computer-automated design
Design Automation usually refers to electronic design automation, or Design Automation which is a Product Configurator. Extending Computer-Aided Design (CAD), automated design and Computer-Automated Design (CAutoD) are more concerned with a broader range of applications, such as automotive engineering, civil engineering, composite material design, control engineering, dynamic system identification and optimization, financial systems, industrial equipment, mechatronic systems, steel construction, structural optimisation, and the invention of novel systems. The concept of CAutoD perhaps first appeared in 1963, in the IBM Journal of Research and Development, where a computer program was written. to search for logic circuits having certain constraints on hardware design to evaluate these logics in terms of their discriminating ability over samples of the character set they are expected to recognize. More recently, traditional CAD simulation is seen to be transformed to CAutoD by biologically-inspired machine learning, including heuristic search techniques such as evolutionary computation, and swarm intelligence algorithms. == Guiding designs by performance improvements == To meet the ever-growing demand of quality and competitiveness, iterative physical prototyping is now often replaced by 'digital prototyping' of a 'good design', which aims to meet multiple objectives such as maximised output, energy efficiency, highest speed and cost-effectiveness. The design problem concerns both finding the best design within a known range (i.e., through 'learning' or 'optimisation') and finding a new and better design beyond the existing ones (i.e., through creation and invention). This is equivalent to a search problem in an almost certainly, multidimensional (multivariate), multi-modal space with a single (or weighted) objective or multiple objectives. == Normalized objective function: cost vs. fitness == Using single-objective CAutoD as an example, if the objective function, either as a cost function J ∈ [ 0 , ∞ ) {\displaystyle J\in [0,\infty )} , or inversely, as a fitness function f ∈ ( 0 , 1 ] {\displaystyle f\in (0,1]} , where f = J 1 + J {\displaystyle f={\tfrac {J}{1+J}}} , is differentiable under practical constraints in the multidimensional space, the design problem may be solved analytically. Finding the parameter sets that result in a zero first-order derivative and that satisfy the second-order derivative conditions would reveal all local optima. Then comparing the values of the performance index of all the local optima, together with those of all boundary parameter sets, would lead to the global optimum, whose corresponding 'parameter' set will thus represent the best design. However, in practice, the optimization usually involves multiple objectives and the matters involving derivatives are a lot more complex. == Dealing with practical objectives == In practice, the objective value may be noisy or even non-numerical, and hence its gradient information may be unreliable or unavailable. This is particularly true when the problem is multi-objective. At present, many designs and refinements are mainly made through a manual trial-and-error process with the help of a CAD simulation package. Usually, such a posteriori learning or adjustments need to be repeated many times until a ‘satisfactory’ or ‘optimal’ design emerges. == Exhaustive search == In theory, this adjustment process can be automated by computerised search, such as exhaustive search. As this is an exponential algorithm, it may not deliver solutions in practice within a limited period of time. == Search in polynomial time == One approach to virtual engineering and automated design is evolutionary computation such as evolutionary algorithms. === Evolutionary algorithms === To reduce the search time, the biologically-inspired evolutionary algorithm (EA) can be used instead, which is a (non-deterministic) polynomial algorithm. The EA based multi-objective "search team" can be interfaced with an existing CAD simulation package in a batch mode. The EA encodes the design parameters (encoding being necessary if some parameters are non-numerical) to refine multiple candidates through parallel and interactive search. In the search process, 'selection' is performed using 'survival of the fittest' a posteriori learning. To obtain the next 'generation' of possible solutions, some parameter values are exchanged between two candidates (by an operation called 'crossover') and new values introduced (by an operation called 'mutation'). This way, the evolutionary technique makes use of past trial information in a similarly intelligent manner to the human designer. The EA based optimal designs can start from the designer's existing design database, or from an initial generation of candidate designs obtained randomly. A number of finely evolved top-performing candidates will represent several automatically optimized digital prototypes. There are websites that demonstrate interactive evolutionary algorithms for design. allows you to evolve 3D objects online and have them 3D printed. allows you to do the same for 2D images.
A.I. Insight forums
The Artificial Intelligence Insight forums, also known as the A.I. Insight forums, are a series of forums to build consensus on how the United States Congress should craft A.I. legislation. Organized by Senate Majority Leader Charles "Chuck" Schumer, the first of nine closed-door forums convened on September 13, 2023. == Background == Amid a surge in the popularity and advancement of artificial intelligence, senator Chuck Schumer launched an effort to establish a framework for the regulation of A.I. in April 2023. By the end of June, a preliminary framework – dubbed the "SAFE Innovation Framework" – was established and presented to Congress. Schumer also announced a series of forums wherein tech leaders who were well-acquainted with A.I. would help to "educate" Congress on the risks and problems that A.I. poses. Many tech leaders including Sam Altman, Elon Musk, and Sundar Pichai were set to attend the meetings. Many U.S. lawmakers and senators such as Mike Rounds and Todd Young were also set to attend. == September 13 forum == The overarching consensus following the conclusion of the September 13 forum was that there "should be" regulations regarding the use and advancement of A.I., but it should not be made "too fast". Many tech executives who attended the forum also warned senators of the risks and threats that A.I. could pose. Musk, who attended the forum, stated afterwards that there was "overwhelming consensus" on the regulation of A.I. === Invitees === This is a list of people who were invited to attend the September 13 forum. Elon Musk (Tesla, SpaceX, X Corp.) Sam Altman (OpenAI) Bill Gates (ex–Microsoft) Jensen Huang (Nvidia) Alex Karp (Palantir) Satya Nadella (Microsoft) Arvind Krishna (IBM) Sundar Pichai (Alphabet Inc., Google) Eric Schmidt (ex–Google) Mark Zuckerberg (Meta) Charles Rivkin (Motion Picture Association) Liz Shuler (AFL-CIO) Meredith Stiehm (Writers Guild of America) Randi Weingarten (American Federation of Teachers) Maya Wiley (LCCHR) == October 24 forum == The second of nine forums was hosted on October 24, 2023, as federal A.I. regulation drew nearer. According to Schumer's office, the forum was centered mainly on how A.I. could "enable innovation", and the innovation that is needed for the safe progression of A.I. At the forum, Senators Brian Schatz and John Kennedy introduced the "Schatz-Kennedy A.I. Labeling Act", a new piece of A.I. legislation that would provide "more transparency on A.I.-generated content". Following the forum, Senator Rounds stated that in order to fuel the development of A.I., a total estimated $56 billion would be needed for the next three years. Rounds, alongside Senator Young and Schumer, also highlighted the need to outcompete China and workforce initiatives. === Invitees === 21 people were invited to attend the forum, and were composed largely of venture capitalists, academics, civil rights campaigners, and industry figures. Some key figures included venture capitalists Marc Andreessen and John Doerr. == Future == Over the course of fall 2023, there is slated to be a total of nine forums on the topic of A.I., with the first hosted on September 13.
Mario Klingemann
Mario Klingemann (born 1970 in Laatzen, Lower Saxony) is a German artist best known for his work involving neural networks, code, and algorithms. Klingemann was a Google Arts and Culture resident from 2016 to 2018, and he is considered as a pioneer in the use of computer learning in the arts. His works examine creativity, culture, and perception through machine learning and artificial intelligence, and have appeared at the Ars Electronica Festival, the Museum of Modern Art New York, the Metropolitan Museum of Art New York, the Photographers’ Gallery London, the Centre Pompidou Paris, and the British Library. Today he lives in Munich, where, in addition to his art under the name "Dog & Pony", he still runs a creative free space between gallery and Wunderkammer with the paper artist Alexandra Lukaschewitz. In 2018 his work The Butcher's Son won the Lumen Prize Gold Award 2018 by working with figurative visual input. Mario Klingemann is part of ONKAOS, the new media artist support programme of SOLO. In collaboration with ONKAOS he has created works such as Memories of Passerby I, the first work made with AI to be auctioned at Sotheby's in 2019. In 2020, Mario Klingemann won an Honorary Mention in the Prix Ars Electronica with his AI installation Appropriate Response. In 2023, Klingemann presented A.I.C.C.A., a performative sculpture in the form of a dog capable of elaborating art critiques thanks to AI programming.
Qloo
Qloo (pronounced "clue") is a company that uses artificial intelligence (AI) to understand taste and cultural correlations. It provides companies with an application programming interface (API). It received funding from Leonardo DiCaprio, Elton John, Barry Sternlicht, Pierre Lagrange and others. Qloo establishes consumer preference correlations via machine learning across data spanning cultural domains including music, film, television, dining, nightlife, fashion, books, and travel. The recommender system uses AI to predict correlations for further applications. == History == Qloo was founded in 2012 by chief executive officer Alex Elias and chief operating officer Jay Alger. Qloo initially launched an app designed for consumers, allowing them to understand their own tastes and receive personalized recommendations. The company amassed several million users and built a large catalog of cultural entities and corresponding user sentiment. In 2012, Qloo raised $1.4 million in seed funding from investors including Cedric the Entertainer, and venture capital firm Kindler Capital. Qloo had a public beta release in November 2012 after its initial funding. In 2013, the company raised an additional $1.6 million from Cross Creek Pictures founding partner Tommy Thompson, and Samih Toukan and Hussam Khoury, founders of Maktoob, an Internet services company purchased by Yahoo! for $164 million in 2009. On November 14, 2013, a website and an iPhone app were announced. The company later released an Android app, and tablet versions, in mid-2014. In 2015, Twitter approached Qloo about powering personalized social feeds and targeted eCommerce ads on the platform based on what users were posting. Qloo developed an enterprise-grade API to support Twitter’s needs. Twitter ended up pivoting to enable brands to use the social platform for customer service and support, but Qloo was able to sell access to its cultural intelligence via API to many other enterprise clients, marking the official transition from a B2C company to a B2B company. In 2016, Qloo secured $4.5 million in venture capital investment. The $4.5 million was split between a number of investors, including Barry Sternlicht, Pierre Lagrange, and Leonardo DiCaprio. In July 2017, Qloo raised $6.5 million in funding rounds from AXA Strategic Ventures, and Elton John. Following the investment, the founders stated in an interview with Tech Crunch that they would use the investment to expand Qloo's database. They hoped the move would secure larger contracts with corporate clients. At the time, clients already included Fortune 500 companies such as Twitter, PepsiCo, and BMW. In 2019, the company announced that it had acquired cultural recommendation service TasteDive, with Alex Elias becoming chairman of TasteDive. In September 2019, Qloo was named among the Top 14 Artificial Intelligence APIs by ProgrammableWeb. In 2022, Qloo raised $15M in Series B funding from Eldridge and AXA Venture Partners, enabling the privacy-centric AI leader to expand its team of world-class data scientists, enrich its technology, and build on its sales channels in order to continue to offer premier insights into global consumer taste for Fortune 500 companies across the globe. Qloo was recognized as the "Best Decision Intelligence Company" at the 2023 AI Breakthrough Awards. Also in 2023, the company was awarded a Top Performer Award by SourceForge. As of 2024, Qloo is a three-time Inc. 5000 honoree: No. 360 (2022), No. 344 (2021), No. 187 (2020). Qloo raised $25 million Series C round on February 21, 2024. The round was led by AI Ventures with participation from AXA Venture Partners, Eldridge, and Moderne Ventures, allowing Qloo to address new commercial surface areas for Taste AI, including on-device learning and foundational models leveraging Qloo, as well as introduce self-service platform to make consumer and taste analytics available to small and mid-sized enterprises and individuals. Qloo also announced pursuing opportunistic M&A using its balance sheet along the lines of the TasteDive acquisition completed, which expanded Qloo's first-party data moat and corpus of cultural learning. This latest financing brought the total amount raised since the company's founding in 2012 to over $56 million. == Services and features == Qloo calls itself a cultural AI platform to provide real-time correlation data across domains of culture and entertainment including: film, music, television, dining, nightlife, fashion, books, and travel. Each category contains subcategories. Qloo’s knowledge of a user's taste in one category can be utilized to offer suggestions in other categories. Users then rate the suggestions, providing it with feedback for future suggestions. Qloo has partnerships with companies such as Expedia and iTunes. == Technology == Qloo’s Taste AI technology uses machine learning to decode and predict consumers’ interests, maintaining user anonymity. It is powered by 3.7 billion lifestyle entities (brands, music, film, TV, dining, nightlife, fashion, books, travel, and more) and trillions of anonymized consumer behavioral signals. Through AI, Qloo identifies patterns in these data signals, making predictions about how much interest a person or group has in a concept or thing. Central to Qloo’s technology are algorithms designed to detect and mitigate biases within datasets and models, allowing Qloo to assess the fairness of its AI systems with a focus on attributes such as age, gender, and race, enabling the company to fine-tune its AI models to align with their ethical standards. They also use visualization tools to probe the behavior of their AI models for conducting counterfactual analyses and for comparing the performances of the AI models across diverse demographic segments. Qloo’s Taste AI doesn’t collect or use any Personally Identifiable Information (PII). Instead, it derives recommendations for audience segments based on co-occurrences between lifestyle entities and anonymized behavioral signals. == Applications == Starbucks uses Qloo to create in-store music playlists tailored to specific neighborhoods. Hershey’s uses Qloo to customize the content of assorted candy bags. Michelin uses Qloo to serve recommendations in its Michelin Guide app. Netflix leverages Qloo’s technology to enhance merchandising by identifying actors who resonate with certain demographics. Qloo also works with PepsiCo, Samsung, The New York Mets, BuzzFeed, and Ticketmaster, Universal Music Group, and OOH advertising company JCDecaux.
Fuzzy pay-off method for real option valuation
The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real option). The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem. == Method == The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the three cash-flow scenarios a corresponding definition with regards to a fuzzy number (triangular fuzzy number for three scenarios and a trapezoidal fuzzy number for four scenarios). This means that the pay-off distribution is created without any simulation whatsoever. This makes the procedure easy and transparent. The scenarios used are a minimum possible scenario (the lowest possible outcome), the maximum possible scenario (the highest possible outcome) and a best estimate (most likely to happen scenario) that is mapped as a fully possible scenario with a full degree of membership in the set of possible outcomes, or in the case of four scenarios used - two best estimate scenarios that are the upper and lower limit of the interval that is assigned a full degree of membership in the set of possible outcomes. The main observations that lie behind the model for deriving the real option value are the following: The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers. The mean value of the positive values of the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values. Real option value, ROV, calculated from the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The real option formula can then be written simply as: R O V = A ( P o s ) A ( P o s ) + A ( N e g ) × E [ A + ] {\displaystyle \mathrm {ROV} ={\frac {A(\mathrm {Pos} )}{A(\mathrm {Pos} )+A(\mathrm {Neg} )}}\times E[A_{+}]} where A(Pos) is the area of the positive part of the fuzzy distribution, A(Neg) is the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+]. As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. At the same time, simulation is not an absolutely necessary step in the Datar–Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar–Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different. == Use of the method == The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options). The method has been taken into use in some large international industrial companies for the valuation of research and development projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments. The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology and at the Tampere University of Technology in Finland.