There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

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The concept of mind

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

This paper proposes novel skin lesion detection based on neutrosophic clustering and adaptive region growing algorithms applied to dermoscopic images, called NCARG. First, the dermoscopic images are mapped into a neutrosophic set domain using the shearlet transform results for the images. The images are described via three memberships: true, indeterminate, and false memberships. An indeterminate filter is then defined in the neutrosophic set for reducing the indeterminacy of the images. A neutrosophic c-means clustering algorithm is applied to segment the dermoscopic images. With the clustering results, skin lesions are identified precisely using an adaptive region growing method. To evaluate the performance of this algorithm, a public data set (ISIC 2017) is employed to train and test the proposed method. Fifty images are randomly selected for training and 500 images for testing. Several metrics are measured for quantitatively evaluating the performance of NCARG. The results establish that the proposed approach has the ability to detect a lesion with high accuracy, 95.3% average value, compared to the obtained average accuracy, 80.6%, found when employing the neutrosophic similarity score and level set (NSSLS) segmentation approach.

A Novel Skin Lesion Detection Approach Using Neutrosophic Clustering and Adaptive Region Growing in Dermoscopy Images

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic commutative N-ideal are discussed. Characterizations of a neutrosophic commutative N-ideal are considered.

/pdf/neutrosophic-commutative-n-ideals-in-bck-algebras-27cu397eba.pdf

Neutrosophic Commutative N -Ideals in BCK-Algebras

La toma de decisiones de criterios multiples (MCDM) se preocupa por organizar y ocuparse de las cuestiones de eleccion y planificacion, incluidos los criterios multiples. Cuando los atributos son mas de uno y se bifurcan aun mas, el entorno de softset neutrosofico no se puede utilizar para abordar este tipo de problemas. Por lo tanto, existia una necesidad imperiosa de definir un nuevo enfoque para resolver este tipo de problemas, por lo que, para este proposito, se define un nuevo entorno llamado Neutrosophic Hypersoft set (NHSS). Este articulo incluye operadores basicos como union, interseccion, complemento, subconjunto, conjunto nulo, conjunto igual, de conjunto Neutrosofico Hypersoft (NHSS). La validez y la implementacion se presentan junto con ejemplos adecuados. Para mayor decisiones y exactitud, en el futuro, las operaciones propuestas desempenaran un papel vital en la toma de como la seleccion personal, problemas de gestion y muchos otros.

Aggregate Operators of Neutrosophic Hypersoft Set

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and effectiveness of the two proposed strategies. Sensitivity analysis with the variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the results obtained from the proposed strategies with the results obtained from the existing strategies in the literature.

/pdf/nn-harmonic-mean-aggregation-operators-based-mcgdm-strategy-irwu6zgw29.pdf

NN-Harmonic Mean Aggregation Operators-Based MCGDM Strategy in a Neutrosophic Number Environment

Combining the single valued neutrosophic set with graph theory, a new graph model emerges, called single valued neutrosophic graph. This model allows attaching the truth-membership (t), indeterminacy–membership (i) and falsity- membership degrees (f) both to vertices and edges. Combining the interval valued neutrosophic set with graph theory, a new graph model emerges, called interval valued neutrosophic graph. This model generalizes the fuzzy graph, intuitionistic fuzzy graph and single valued neutrosophic graph. In this paper, the authors define operations of Cartesian product, composition, union and join on interval valued neutrosophic graphs, and investigate some of their properties, with proofs and examples.

Florentin Smarandache

Papers

A Novel Skin Lesion Detection Approach Using Neutrosophic Clustering and Adaptive Region Growing in Dermoscopy Images

Neutrosophic Commutative N -Ideals in BCK-Algebras

Aggregate Operators of Neutrosophic Hypersoft Set

NN-Harmonic Mean Aggregation Operators-Based MCGDM Strategy in a Neutrosophic Number Environment

Operations on Interval Valued Neutrosophic Graphs