A new approach utilizing addition-min composition in two-sided fuzzy relation

In this study, we focus on investigating the two-sided fuzzy relation inequalities with addition-min composition in the context of P۲P network systems, taking into account the bilateral requirements of the terminals. The solutions derived from such a two-sided fuzzy relation system represent viable flow control strategies for the respective P۲P network system. The primary objectives encompass: (i) identifying a minimal solution that is either less than or equal to a specified solution; (ii) identifying a maximal solution that is either more than or equal to a specified solution; and (iii) outlining the structure of the solution set for the fuzzy relation system. The aim of (i) and (ii) is to pinpoint specific minimal or maximal solutions within the two-sided system.We introduce two resolution algorithms, denoted as Algorithm I and II, designed to ascertain these specific minimal and maximal solutions. It is observed that the complete solution set of the two-sided system can be exhaustively determined by considering all minimal and maximal solutions, with the potential for the solution set to exhibit non-convex characteristics.

کلیدواژه ها:

Fuzzy relation inequality ، Two-sided ، Addition-min composition.