The main features of the fuzzy sets and their corresponding membership functions were presented in terms fuzzification process further by de-fuzzification operation. convexity α -(alfa) cuts is used decomposition sets. alfa defined precisely pair lowest upper greatest lower bounds. convex combination intervals sub-regions function considered as points defuzzified values methods to crisp formula...

where B = d 4 I− A 2 and Ei is a matrix whose i th diagonal entry is 1 and the others are 0. From now on let’s assume G is d-regular (i.e. each vertex has degree exactly d). Then the adjacency matrix A has at most d non-zero entries, each equal to 1/2, in every row, so ‖A‖ ≤ d/2 and 0 B d 2 I. Note that if α is the optimal value for the SDP we have |E| 2 = nd 4 ≤ α ≤ |E| = nd 2 . The first ineq...

In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of α on any edge, there exists an online prediction algorithm with mistake bound α times the cut size, which is the size of the cut induced by the label partitioning ...

We introduce the concept of a fuzzy total preorder. Then we analyze its numerical representability through a real-valued order-preserving function defined for each α-cut.

We show that for the regularized exponential interaction λ : e : in d space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field if d>2 for all α or if d = 2 for all α such that |α| >α0. 1. Notations and Results In this paper we study the space-time cut-off exponential interaction in d spacetime dimensions VΛ = λ§:d* :dx, where A is a bounded subset of ...

We introduce a new familiy of random compact metric spaces Sα for α∈(1,2), which we call stable shredded spheres. They are constructed from excursions α-stable Lévy processes on [0,1] possessing no negative jumps. Informally, viewing the graph excursion in plane, each jump process is “cut open” and replaced by circle, then all points at equal height, not separated jump, identified. show that sp...

The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using α-cuts. based on (FDEA) and considers two objectives, solution method ranking system are provided. Generally, score obtained for DMU α-cut an interval. Intervals partially ordered sets, due which intervals...