Fuzzy inference has played a significant role in many applications. Although the simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed a "single input rule modules connected fuzzy inference method" (SIRMs method) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Seki et al. have shown that the simplified fuzzy inference method and the SIRMs method are equivalent when the sum of diagonal elements in rules of the simplified fuzzy inference method is equal to that of cross diagonal elements. This paper clarifies the conditions for the infimum and supremum of the fuzzy inference method using the single input type fuzzy inference method, from the view point of fuzzy inference.

Providing a fair allocation of bandwidth among different connections over the Internet without affecting link efficiency has been a challenging issue in the area of network performance improvement. Congestion signaling is essential for the purpose. Conventional TCP uses packet loss as an implicit indication of congestion. Several enhancements to TCP have been proposed for faster congestion recovery and thus to improve the network performance. However, packet loss reduces TCP goodput and adds large delay. Also the variance in the share of bandwidth obtained by each connection may become unaccepatbly high. To the contrary, Explicit Congestion Notification (ECN) indicates a congestion explicitly before it actually occurs. Therefore, ECN facilitates a faster congestion detection and contributes to the network performance improvement. In this paper, we consider the performance implications of employing different ECN strategies along with several TCP enhancement schemes. We also introduce a new ECN packet marking strategy FIM and evaluate its relative performance and suitability for deployment along with different TCP enhancements. Simulation results show the superiority of FIM over other existing marking strategies with different TCP enhancement schemes by providing the best fairness without hampering link efficiency. We also observe FIM maintains a more consistent delay bound than other strategies and as such, is more suitable for application in practical purposes.