Fuzzychain: An Equitable Consensus Mechanism for Blockchain Networks

TL;DR

Fuzzychain addresses centralization concerns in proof-of-stake by representing stake with fuzzy sets and linguistic labels, introducing a degree-of-membership mechanism to select validators. The method comprises three stages—scaling stake into fuzzy sets, selecting validators from each set based on reputation and randomization, and voting to accept blocks—followed by rewards and penalties to shape future participation. Empirical results from simulations show that Fuzzychain achieves comparable functionality to PoS while distributing validator selection more equitably, evidenced by lower Gini coefficients and broader participation across stake groups. The approach enhances decentralization and security of blockchain networks, with future work on dynamic fuzzy representations and computing-with-words to further improve resilience.

Abstract

Blockchain technology has become a trusted method for establishing secure and transparent transactions through a distributed, encrypted network. The operation of blockchain is governed by consensus algorithms, among which Proof of Stake (PoS) is popular yet has its drawbacks, notably the potential for centralising power in nodes with larger stakes or higher rewards. Fuzzychain, our proposed solution, introduces the use of fuzzy sets to define stake semantics, promoting decentralised and distributed processing control. This system selects validators based on their degree of membership to the stake fuzzy sets rather than just the size of their stakes. As a pioneer proposal in applying fuzzy sets to blockchain, Fuzzychain aims to rectify PoS's limitations. Our results indicate that Fuzzychain not only matches PoS in functionality but also ensures a fairer distribution of stakes among validators, leading to more inclusive validator selection and a better-distributed network.

Figures (13)

• Figure 1: The figure depicts the elliptic curve defined by $y^2=x^3-x$.
• Figure 2: The figure depicts four fuzzy membership functions.
• Figure 3: The figure shows the blockchain process explained in three stages. Stage 1: Initialise the transaction, generate a new block, and send it to the participating network. Stage 2: Block validation and consensus process. In this stage, three phases are executed: scaling, selection and voting. Stage 3: The new block was added to the blockchain and transaction finalisation.
• Figure 4: The figure illustrates an overview of the scaling, selection, and voting phases employed in the development of the equitable consensus algorithm. These phases are applied during the second stage, where block validation and consensus occur.
• Figure 5: The figure displays the scaling phase in the equitable consensus algorithm used in Stage 2. The items $x$ in the set of Participant's stakes are scaled through the fuzzy membership function $\mu_{T_i}(x)$ into fuzzy sets $T_i$ on the universe of discourse defined from $l$ to $r$ for the linguistic variable "Participant's stake". The degree of membership for $x$ is the highest membership degree function (HMDF)

Theorems & Definitions (11)

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