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Image analysis is a fundamental task for extracting information from images acquired across a range of different devices. Since reliable quantitative results are requested, image analysis requires highly sophisticated numerical and analytical methods—particularly for applications in medicine, security, and remote sensing, where the results of the processing may consist of vitally important data. The contributions to this book provide a good overview of the most important demands and solutions concerning this research area. In particular, the reader will find image analysis applied for feature extraction, encryption and decryption of data, color segmentation, and in the support new technologies. In all the contributions, entropy plays a pivotal role.

keyframes --- time-delay --- whale optimization algorithm --- multilevel thresholding --- multi-exposure image fusion --- additive manufacturing --- patch structure decomposition --- ultra-sound images --- 3D scanning --- Arimoto entropy --- contrast enhancement --- spatial filling factor --- depth maps --- image processing --- 3D prints --- differential evolution --- field of experts --- normalized divergence measure --- image privacy --- multiscale top-hat transform --- q-exponential --- texture information entropy --- diffusion --- hybrid algorithm --- Weibull statistics --- adaptive selection --- nonextensive entropy --- computer aided diagnostics --- fatty liver --- random forest --- DNA encoding --- low contrast --- entropy --- Minkowski island --- fuzzy entropy --- free-form deformations --- person re-identification --- chaotic system --- DNA computing --- pavement --- information entropy --- discrete entropy --- Tsallis statistics --- video skimming --- prime-indexed primes --- natural scene statistics (NSS) --- Hénon map --- q-sigmoid --- image entropy --- Shannon entropy --- macrotexture --- Shannon’s entropy --- binary image --- multi-feature fusion --- image analysis --- uncertainty assessment --- non-rigid registration --- hash layer --- Cantor set --- dynamic filtering --- deep neural network --- security analysis --- multiple-image encryption --- Hamming distance --- blind image quality assessment (BIQA) --- q-Gaussian --- remote sensing --- decay trend --- chaotic cryptography --- chaotic strategy --- cross-entropy loss --- random insertion --- metabolic syndrome --- sign languages --- generalized entropies --- relevance feedback --- image retrieval --- two-dimensional chaotic economic map --- cryptanalysis --- infrared images --- 3D Latin cube --- SHA-256 hash value --- gradient distributions --- structural entropy --- discrete cosine transform (DCT) --- chaotic map --- hepatic steatosis --- machine vision --- electromagnetic field optimization --- security --- image segmentation --- quantization loss --- colonoscopy --- video summarization --- permutation --- Kapur’s entropy --- surface quality assessment --- permutation-diffusion --- Ramanujan primes --- Rényi entropies --- chosen-plaintext attack --- image encryption --- dynamic index --- color image segmentation --- ultrasound --- Otsu method --- sigmoid --- reconstruction --- image information entropy --- 3-D digital imaging --- positron emission tomography --- medical imaging

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This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences.

Research & information: general --- Mathematics & science --- Bonferroni means --- prioritized aggregation operators --- induced aggregation operators --- OWA operator --- transparency --- fuzzy sets --- fuzzy numbers --- linguistic variables --- fuzzy data analysis --- correlation between fuzzy variables --- poverty policy --- efficiency --- Debreu–Farrell productivity index --- cryptocurrencies --- bitcoin --- blockchain --- fintech --- unified theory of acceptance and use of technology --- intention to use --- fuzzy set qualitative comparative analysis --- bonus-malus system --- fuzzy number --- fuzzy transition probability --- fuzzy Markov chain --- fuzzy stationary state --- SDGs --- The Quintuple Helix of Innovation Model --- sustainability --- Latin America --- knowledge systems --- Forgotten Effects Theory --- Fuzzy Logic --- tourist destination competitiveness --- experton theory --- forgotten effects theory --- Hamming distance --- decision making --- expert group --- neuro-fuzzy assessment --- evaluation of specialists --- smart city --- assessment risk --- smart transport --- mobility --- transparent selection --- public financial resources --- recovery plan --- selection of quality methods --- manufacturing process --- intuitionistic fuzzy sets --- genetic algorithm --- adoption of environmental practices --- human resource costs --- organizational learning capability --- information technology support --- size --- education level --- experience --- university ranking --- unsupervised pattern recognition --- clustering techniques --- corruption perception --- corruption normalization --- gender --- entrepreneurial intention --- STEM --- family entrepreneurial background --- fsQCA --- household income --- pythagorean membership --- financial knowledge --- decision-making --- fuzzy logic --- fuzzy arithmetic --- extension principle --- economic models --- Harrod’s growth --- enhancement strategy --- brand attachment --- convenience stores --- fuzzy quality function deployment --- audit team leader --- audit risk assessment --- small- and medium-sized audit firms --- planification --- fuzzy theory

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This book is a Printed Edition of the Special Issue that covers research on symmetric and asymmetric data that occur in real-life problems. We invited authors to submit their theoretical or experimental research to present engineering and economic problem solution models that deal with symmetry or asymmetry of different data types. The Special Issue gained interest in the research community and received many submissions. After rigorous scientific evaluation by editors and reviewers, seventeen papers were accepted and published. The authors proposed different solution models, mainly covering uncertain data in multicriteria decision-making (MCDM) problems as complex tools to balance the symmetry between goals, risks, and constraints to cope with the complicated problems in engineering or management. Therefore, we invite researchers interested in the topics to read the papers provided in the book.

Information technology industries --- COVID-19 --- criteria importance through inter-criteria correlation (CRITIC) --- combined compromise solution (CoCoSo) --- gray values --- temporary hospital --- location selection --- ARAS --- interval-valued triangular fuzzy numbers --- e-learning courses --- MCDM --- neutrosophic sets --- quadripartitioned bipolar neutrosophic sets --- similarity measure --- decision making --- multiple-criteria decision-making --- neutrosophic --- single-valued neutrosophic sets --- TOPSIS --- Hamming distance --- Euclidean distance --- e-commerce development strategies --- Symmetry --- bibliometric analysis --- Web of Science --- co-citation --- burst detection analysis --- supply chain --- DANP-mV model --- performance analysis --- asymmetric underactuated --- rehabilitation --- robotic exoskeleton --- symmetric and asymmetric trajectory --- Bowden cable --- video processing data --- EOQ --- Wilson’s formulation --- lot size --- reordering time --- visual analogue scales (VAS) --- criteria weighting --- matrix question --- survey --- WASPAS-SVNS --- entropy --- direct rating --- rehabilitation device --- electromyogram --- symmetry --- window parameters --- feature extraction --- pattern recognition --- sensitivity analysis --- reliability --- failure probability --- quantile --- civil engineering --- limit states --- mathematical model --- uncertainty --- cost overrun --- construction project --- fuzzy sets --- earned value management (EVM) --- artificial neural networks (ANNs) --- multiple regression analysis --- road industry --- buckling --- safety --- superquantile --- subquantile --- aerial imagery --- lossy compression --- qualitative evaluation --- WASPAS --- neutrosophic set --- Analytic Hierarchy Process --- fuzzy Analytic Hierarchy Process --- symmetric and asymmetric fuzzy numbers --- stability --- landscape --- micro factor --- macro factor --- real estate market --- Big Data analysis --- Big Data --- land price --- R and Python --- land Big Data --- symmetric data --- asymmetric data --- solution models

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This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences.

Bonferroni means --- prioritized aggregation operators --- induced aggregation operators --- OWA operator --- transparency --- fuzzy sets --- fuzzy numbers --- linguistic variables --- fuzzy data analysis --- correlation between fuzzy variables --- poverty policy --- efficiency --- Debreu–Farrell productivity index --- cryptocurrencies --- bitcoin --- blockchain --- fintech --- unified theory of acceptance and use of technology --- intention to use --- fuzzy set qualitative comparative analysis --- bonus-malus system --- fuzzy number --- fuzzy transition probability --- fuzzy Markov chain --- fuzzy stationary state --- SDGs --- The Quintuple Helix of Innovation Model --- sustainability --- Latin America --- knowledge systems --- Forgotten Effects Theory --- Fuzzy Logic --- tourist destination competitiveness --- experton theory --- forgotten effects theory --- Hamming distance --- decision making --- expert group --- neuro-fuzzy assessment --- evaluation of specialists --- smart city --- assessment risk --- smart transport --- mobility --- transparent selection --- public financial resources --- recovery plan --- selection of quality methods --- manufacturing process --- intuitionistic fuzzy sets --- genetic algorithm --- adoption of environmental practices --- human resource costs --- organizational learning capability --- information technology support --- size --- education level --- experience --- university ranking --- unsupervised pattern recognition --- clustering techniques --- corruption perception --- corruption normalization --- gender --- entrepreneurial intention --- STEM --- family entrepreneurial background --- fsQCA --- household income --- pythagorean membership --- financial knowledge --- decision-making --- fuzzy logic --- fuzzy arithmetic --- extension principle --- economic models --- Harrod’s growth --- enhancement strategy --- brand attachment --- convenience stores --- fuzzy quality function deployment --- audit team leader --- audit risk assessment --- small- and medium-sized audit firms --- planification --- fuzzy theory

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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.

similarity measure --- generalized partitioned Bonferroni mean operator --- normal distribution --- school administrator --- complex neutrosophic set --- expert set --- neutrosophic classification --- multi-attribute decision-making (MADM) --- multi-criteria decision-making (MCDM) techniques --- criterion functions --- matrix representation --- possibility degree --- quantum computation --- typhoon disaster evaluation --- NT-subgroup --- generalized neutrosophic ideal --- three-way decisions --- decision-making --- G-metric --- multiple attribute group decision-making (MAGDM) --- SVM --- semi-neutrosophic triplets --- LA-semihypergroups --- power operator --- fuzzy graph --- neutrosophic cubic graphs --- LNGPBM operator --- neutrosophic c-means clustering --- (commutative) ideal --- region growing --- clustering algorithm --- Neutrosophic cubic sets --- forecasting --- vector similarity measure --- totally dependent-neutrosophic soft set --- Fenyves identities --- TODIM model --- similarity measures --- CI-algebra --- Dice measure --- de-neutrosophication methods --- DSmT --- semigroup --- VIKOR model --- multigranulation neutrosophic rough set (MNRS) --- simplified neutrosophic linguistic numbers --- Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) --- multi-criteria group decision making --- multi-attribute group decision-making (MAGDM) --- exponential operational laws of interval neutrosophic numbers --- simplified neutrosophic weighted averaging operator --- neutro-epimorphism --- Choquet integral --- fixed point theory (FPT) --- computability --- neutrosophic triplet set --- interval-valued neutrosophic set --- simplified neutrosophic sets (SNSs) --- totally dependent-neutrosophic set --- Maclaurin symmetric mean --- recursive enumerability --- loop --- photovoltaic plan --- intersection --- neutrosophic bipolar fuzzy set --- big data --- inclusion relation --- dual aggregation operators --- Hamming distance --- neutro-automorphism --- neutrosophic set theory --- multiple attribute decision-making --- multicriteria decision-making --- pseudo primitive elements --- medical diagnosis --- neutrosophic G-metric --- bipolar fuzzy set --- NC power dual MM operator (NCPDMM) operator --- neutrosophic sets (NSs) --- emerging technology commercialization --- neutrosophic triplet groups --- probabilistic rough sets over two universes --- neutrosophic triplet set (NTS) --- neutrosophic triplet cosets --- MM operator --- TOPSIS --- cloud model --- extended ELECTRE III --- extended TOPSIS method --- 2ingle-valued neutrosophic set --- dual domains --- probabilistic single-valued (interval) neutrosophic hesitant fuzzy set --- Jaccard measure --- data mining --- BE-algebra --- neutrosophic soft set --- aggregation operators --- image segmentation --- multiple attribute decision making (MADM) --- neutrosophic duplets --- fundamental neutro-homomorphism theorem --- neutro-homomorphism --- power aggregation operator --- linear and non-linear neutrosophic number --- multi-attribute decision making --- first neutro-isomorphism theorem --- MCGDM problems --- neutrosophic bipolar fuzzy weighted averaging operator --- Bonferroni mean --- analytic hierarchy process (AHP) --- quasigroup --- action learning --- weak commutative neutrosophic triplet group --- generalized aggregation operators --- single valued neutrosophic multiset (SVNM) --- sustainable supplier selection problems (SSSPs) --- LNGWPBM operator --- skin cancer --- oracle computation --- fault diagnosis --- interval valued neutrosophic support soft sets --- neutrosophic triplet normal subgroups --- soft set --- multi-criteria decision-making --- neutrosophic triplet --- generalized group --- neutrosophic multiset (NM) --- two universes --- algorithm --- multi-attribute decision making (MADM) --- PA operator --- BCI-algebra --- neutrosophic triplet group (NTG) --- single valued trapezoidal neutrosophic number --- quasi neutrosophic triplet loop --- neutrosophy --- complex neutrosophic graph --- S-semigroup of neutrosophic triplets --- and second neutro-isomorphism theorem --- MADM --- dermoscopy --- linguistic neutrosophic sets --- defuzzification --- construction project --- potential evaluation --- neutrosophic big data --- decision-making algorithms --- neutosophic extended triplet subgroups --- applications of neutrosophic cubic graphs --- fuzzy time series --- TFNNs VIKOR method --- two-factor fuzzy logical relationship --- oracle Turing machines --- grasp type --- interval neutrosophic sets --- multi-criteria group decision-making --- interval neutrosophic weighted exponential aggregation (INWEA) operator --- power aggregation operators --- neutrosophic triplet group --- MGNRS --- 2-tuple linguistic neutrosophic sets (2TLNSs) --- computation --- filter --- multi-valued neutrosophic set --- integrated weight --- Bol-Moufang --- prioritized operator --- interval number --- logic --- pseudo-BCI algebra --- interval neutrosophic set (INS) --- neutrosophic rough set --- soft sets --- Q-neutrosophic --- Linguistic neutrosophic sets --- fuzzy measure --- homomorphism theorem --- commutative generalized neutrosophic ideal --- neutrosophic association rule --- shopping mall --- dependent degree --- Q-linguistic neutrosophic variable set --- quasi neutrosophic loops --- symmetry --- neutrosophic sets --- neutrosophic logic --- neutrosophic cubic set --- complement --- robotic dexterous hands --- neutro-monomorphism --- group --- analytic network process --- Muirhead mean --- maximizing deviation --- classical group of neutrosophic triplets --- neutrosophic triplet quotient groups --- generalized neutrosophic set --- multi-criteria group decision-making (MCGDM) --- support soft sets --- decision making --- generalized De Morgan algebra --- multiple attribute group decision making (MAGDM) --- single-valued neutrosophic multisets --- 2TLNNs TODIM method --- membership --- grasping configurations --- single valued neutrosophic set (SVNS) --- multiple attribute decision making problem --- SWOT analysis --- neutrosophic clustering --- hesitant fuzzy set --- interval neutrosophic numbers (INNs) --- quasi neutrosophic triplet group --- triangular fuzzy neutrosophic sets (TFNSs) --- interdependency of criteria --- aggregation operator --- cosine measure --- neutrosophic set --- neutrosophic computation --- decision-making trial and evaluation laboratory (DEMATEL) --- partial metric spaces (PMS) --- NCPMM operator --- clustering