Xinshang You

Let P be a planar point set with no three points collinear; k points of P form a k-hole of P if these k points are the vertices of a convex polygon whose interior contains no points of P. Inthis...

In this article, we transform intuitionsitic multiplicative preference relation into interval fuzzy preference relation and propose the concept of geometric index based on multiplicative and fuzzy aspects. In order to deal with the incomplete group decision making problems, we give a simple method to calculate the missing values and weight values with respect to the geometric consistency degree. Depending on these studies, we introduce a novel approach to group decision making with incomplete information. An illustrative numerical example is followed to demonstrate.

This paper proposes a novel approach to cope with the multi-criteria group decision-making problems. We give the pairwise comparisons based on the best-worst-method (BWM), which can decrease comparison times. Additionally, our comparison results are determined with the positive and negative aspects. In order to deal with the decision matrices effectively, we consider the elimination and choice translation reality (ELECTRE III) method under the intuitionistic multiplicative preference relations environment. The ELECTRE III method is designed for a double-automatic system. Under a certain limitation, without bothering the decision-makers to reevaluate the alternatives, this system can adjust some special elements that have the most influence on the group’s satisfaction degree. Moreover, the proposed method is suitable for both the intuitionistic multiplicative preference relation and the interval valued fuzzy preference relations through the transformation formula. An illustrative example is followed to demonstrate the rationality and availability of the novel method.

Let n(k, l,m), k ≤ l ≤ m, be the smallest integer such that any finite planar point set of at least n(k, l,m) points in general position, contains an empty convex k-hole; an empty convex l-hole and an