Abstract
To avoid unoccupied base stations, we introduce the concept of a strong solution to max-product fuzzy relation inequalities in this paper. Such a strong solution enables all base stations take part in wireless communication activities. The structure of the set of all strong solutions is discussed. The strong solution set is composed of a finite number of closed intervals. To decrease the damage caused by electromagnetic radiation, one always aims to find an optimal strong solution, in which each component reaches its minimum value. However, this is generally impossible. Hence, finding an optimal strong solution with a specific objective function is more feasible. In this work, we investigate the optimization, minimizing the largest component of a strong solution. A detailed algorithm is developed to find an optimal strong solution. The experimental results show that our proposed algorithm is efficient. In addition, we further discuss the structure of the complete optimal strong solution set.
Highlights
IntroductionJ∈J where aij, xj, bi ∈ [0, 1] and I and J are two conventional index sets
There have been many works investigating fuzzy relation equations with max-min composition [1], [2], i.e.,(aij ∧ xj) = bi, i ∈ I . (1)j∈J where aij, xj, bi ∈ [0, 1] and I and J are two conventional index sets
To make all base stations take part in the communication activities, i.e., every base station serves at least one testing point, we aim to investigate the so-called strong solution of system (5) in this work
Summary
J∈J where aij, xj, bi ∈ [0, 1] and I and J are two conventional index sets. The max-min was the first proposed composition and the most commonly used one. It has been found that the max-min composition was not always effective in describing real world models [3]. When applying the max-min operator, the values of a solution vector are not allowed to compensate for each other. In some application cases, compensation among the components of the solution vector should be allowed [5]. In such cases, the max-product composition surpasses the max-min one [5]
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