Common fixed soft element results in soft complex valued b-metric spaces

In this paper, firstly, on the base of the soft complex numbers suggested by Das and Samanta, we introduce the concept of a soft complex valued b-metric space and investigate some of its properties. Also, we compare it to a soft complex valued metric space and a soft topological space. Next, we establish some fixed soft element theorems in the context of soft complex valued b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature.Publisher's Versio

Soft cooperation systems and games

A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. In order to obtain this allocation, a characteristic function is known. It establishes the profit of each coalition of agents if this coalition decides to act alone. Originally players are considered symmetric and then the allocation only depends on the characteristic function; this paper is about cooperative games with an asymmetric set of agents. We introduced cooperative games with a soft set of agents which explains those parameters determining the asymmetry among them in the cooperation. Now the characteristic function is defined not over the coalitions but over the soft coalitions, namely the profit depends not only on the formed coalition but also on the attributes considered for the players in the coalition. The best known of the allocation rules for cooperative games is the Shapley value. We propose a Shapley kind solution for soft games. © 2017 Informa UK Limited, trading as Taylor & Francis Group