Two Different Approaches for Consistency of Intuitionistic Multiplicative Preference Relation using Directed Graph

Consistency is an important issue that causes wide public concern of decision-makers in the decision-making process. The lack of consistency in preference relations results in a vague solution. The main goal of this paper is to achieve the consistent intuitionistic multiplicative preference relation using a graphical approach. We have proposed two different characterizations of the consistency for intuitionistic multiplicative preference relation(IMPR). In the first approaches, we propose an algorithm to achieve the consistency of IMPR by using the cycles of various length in a directed graph. The second approach proves isomorphism between the set of IMPRs and the set of asymmetric multiplicative preference relations. That result is explored to use the methodologies developed for asymmetric multiplicative preference relations to the case of IMPRs and achieve the consistency of asymmetric multiplicative preference relation using a directed graph. Sometimes the decision maker may not be able to provide the complete relation. So the above-said method is applied for an incomplete IMPR also, here consistency plays an important role. The examples are provided to illustrate both the methods in all cases.

A quaternion-group knowledge graph embedding model

Capturing the composite embedding representation of a multi-hop relation path is an extremely vital task in knowledge graph completion. Recently, rotation-based relation embedding models have been widely studied to embed composite relations into complex vector space. However, these models make some over-simplified assumptions on the composite relations, resulting the relations to be commutative. To tackle this problem, this paper proposes a novel knowledge graph embedding model, named QuatGE, which can provide sufficient modeling capabilities for complex composite relations. In particular, our method models each relation as a rotation operator in quaternion group-based space. The advantages of our model are twofold: (1) Since the quaternion group is a non-commutative group (i.e., non-Abelian group), the corresponding rotation matrices of composite relations can be non-commutative; (2) The model has a more expressive setting with stronger modeling capabilities, which is flexible to model and infer the complete relation patterns, including: symmetry/anti-symmetry, inversion and commutative/non-commutative composition. Experimental results on four benchmark datasets show that the proposed method outperforms the existing state-of-the-art models for link prediction, especially on composite relations.

Singular Values, Eigenvalues and Diagonal Elements Of The Commutator Of 2x2 Rank One Matrices

We determine the region of singular values of the commutator XY-YX for 2x2 rank one complex matrices X and Y. This answers in affirmative a conjecture raised in [Wenzel 2015] when 2x2 matrices are concerned. Our approach and proofs also lead to a complete relation between the singular values, eigenvalues and diagonal elements of the commutator under consideration.

AS CAMADAS POPULARES E O REMO NO RIO DE JANEIRO DA TRANSIÇÃO DOS SÉCULOS XIX/XX

No Brasil, ainda não são fartos os estudos sobre a apreensão do esporte pelas camadas populares. O objetivo deste estudo é discutir a presença, a participação e o relacionamento das camadas populares com o esporte, especificamente o remo, no Rio de Janeiro da transição dos séculos XIX/XX, momento de estruturação do campo esportivo no país. Ao final, sugere-se que não seja adequado afirmar que as camadas populares apreenderam o remo, mas por certo deve-se considerar que tiveram uma participação ativa na consolidação e organização dessa prática esportiva. In Brazil, we don't have a significant number of studies about the relation between sport and the working class. This article has for purpose to argue about the presence and the participation of working class members in sporting events, specifically of rowing, in the 19th/20th century culture of Rio de Janeiro. In that moment, we could observe the first moments oí modern sport in Brazil. At the final, I conclude that it is no possible to assert that working class had a complete relation with rowing clubs, but certainlly they had an active participation in development and organization of that sporting practice.