Positive bases with maximal cosine measure

Abstract We show that if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one that gives a positive basis.

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Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

Journal of Intelligent Systems ◽

10.1515/jisys-2014-0001 ◽

2015 ◽

Vol 24 (1) ◽

pp. 23-36 ◽

Cited By ~ 48

Author(s):

Jun Ye

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Multiple Attribute Decision Making ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Neutrosophic Set ◽

Fuzzy Environment ◽

Cosine Measure ◽

Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

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The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making

Symmetry ◽

10.3390/sym10050154 ◽

2018 ◽

Vol 10 (5) ◽

pp. 154 ◽

Cited By ~ 12

Author(s):

Changxing Fan ◽

En Fan ◽

Jun Ye

Keyword(s):

Decision Making ◽

Multiple Attribute Decision Making ◽

Cosine Measure ◽

Multiple Attribute

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Totally positive bases and progressive iteration approximation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2005.01.023 ◽

2005 ◽

Vol 50 (3-4) ◽

pp. 575-586 ◽

Cited By ~ 55

Author(s):

Hong-Wei Lin ◽

Hu-Jun Bao ◽

Guo-Jin Wang

Keyword(s):

Totally Positive ◽

Positive Bases

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Similarity Learning Algorithm Selection for Chronic Renal Failure Patients Treatment Strategy Optimization

INFORMACIONNYE TEHNOLOGII ◽

10.17587/it.26.701-705 ◽

2020 ◽

Vol 26 (12) ◽

pp. 701-705

Author(s):

I. Lakman ◽

◽

R. Akhmetvaleev ◽

D. Enikeev ◽

R. Khaziakhmetov ◽

...

Keyword(s):

Learning Algorithm ◽

Rank Order ◽

Calcium Balance ◽

Similarity Learning ◽

Algorithm Selection ◽

Specific Patient ◽

Cosine Measure ◽

Measure Of Similarity ◽

Personalized Approach

One of the main methods on which the personalized approach in medicine is based is finding a pair of patients who are similar in the properties of the disease. The objective of the study is to select the most effective similarity learning instrument amongst three options anaemia treatment and phosphorus-calcium balance recovery in dialysis patients, ranked according to the highest similarity to the particular patient. As soon as methods for comparing instruments will achieve the goal, the algorithm of weight tagging is used, modified by the authors by adding more weights values to important features — the cosine measure, the soft cosine measure, considering the similarity of drug alternative and their bioavailability. As a metric that evaluates the quality of algorithms, a combined metric is used that takes into account the quality of treatment classification as effective and the rank order of the greatest correspondence of therapy to a specific patient. As a result, using the opinions of nephrologists as experts, it was shown that the best measure of similarity is the soft cosine measure.

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A Novel Kernel for RBF Based Neural Networks

Abstract and Applied Analysis ◽

10.1155/2014/176253 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 7

Author(s):

Wasim Aftab ◽

Muhammad Moinuddin ◽

Muhammad Shafique Shaikh

Keyword(s):

Basis Function ◽

Distance Measures ◽

Gaussian Kernel ◽

Phase Shift Keying ◽

Multiple Phase ◽

Cosine Measure ◽

Symbol Detection ◽

Shift Keying ◽

Rbf Kernel ◽

Artificial Neural Network Ann

Radial basis function (RBF) is well known to provide excellent performance in function approximation and pattern classification. The conventional RBF uses basis functions which rely on distance measures such as Gaussian kernel of Euclidean distance (ED) between feature vector and neuron’s center, and so forth. In this work, we introduce a novel RBF artificial neural network (ANN) where the basis function utilizes a linear combination of ED based Gaussian kernel and a cosine kernel where the cosine kernel computes the angle between feature and center vectors. Novelty of the proposed work relies on the fact that we have shown that there may be scenarios where the two feature vectors (FV) are more prominently distinguishable via the proposed cosine measure as compared to the conventional ED measure. We discuss adaptive symbol detection for multiple phase shift keying (MPSK) signals as a practical example to show where the angle information can be pivotal which in turn justifies our proposed RBF kernel. To corroborate our theoretical developments, we investigate the performance of the proposed RBF for the problems pertaining to three different domains. Our results show that the proposed RBF outperforms the conventional RBF by a remarkable margin.

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