let $g$ be a simple graph with vertex set $v(g) = {v_1, v_2,ldots, v_n}$ and edge set $e(g) = {e_1, e_2,ldots , e_m}$. similar tothe randi'c matrix, here we introduce the randi'c incidence matrixof a graph $g$, denoted by $i_r(g)$, which is defined as the$ntimes m$ matrix whose $(i, j)$-entry is $(d_i)^{-frac{1}{2}}$ if$v_i$ is incident to $e_j$ and $0$ otherwise. naturally, therandi'c incidenc...

We investigate the thermodynamics of ideal gas on the spacetime with noncommutative fuzzy geometry. We first find that the heat capacity of the ideal boson and fermion on the fuzzy two-sphere have different values, contrast to that on the commutative geometry, and see that the heat capacity approaches to zero in high-temperature limit. We next evaluate the heat capacity of the ideal boson and f...

Fuzzy Cognitive Maps (FCMs) have been proposed to represent causal reasoning by using numeric processing. They graphically represent uncertain causal reasoning. In the resonant states, there emerges a limit cycle or a hidden pattern, which is a FCM inference. However, there are some shortcomings concerned with knowledge representation in the conventional FCMs. In this paper, we propose Extended...

Rough set theory has been extensively discussed in machine learning and pattern recognition. It provides us another important theoretical tool for feature selection. In this paper, we construct a novel rough set model for feature subset selection. First, we define the fuzzy decision of a sample by using the concept of fuzzy neighborhood. A parameterized fuzzy relation is introduced to character...