As the data resources grow, providing recommendations that best meet the demands has become a vital requirement in business and life to overcome the information overload problem. However, building a system suggesting relevant recommendations has always been a point of debate. One of the most cost-efficient techniques in terms of producing relevant recommendations at a low complexity is Product Quantization (PQ). PQ approaches have continued developing in recent years. This system's crucial challenge is improving product quantization performance in terms of recall measures without compromising its complexity. This makes the algorithm suitable for problems that require a greater number of potentially relevant items without disregarding others, at high-speed and low-cost to keep up with traffic. This is the case of online shops where the recommendations for the purpose are important, although customers can be susceptible to scoping other products. This research proposes a fuzzy approach to perform norm-based product quantization. Type-2 Fuzzy sets (T2FSs) define the codebook allowing sub-vectors (T2FSs) to be associated with more than one element of the codebook, and next, its norm calculus is resolved by means of integration. Our method finesses the recall measure up, making the algorithm suitable for problems that require querying at most possible potential relevant items without disregarding others. The proposed method outperforms all PQ approaches such as NEQ, PQ, and RQ up to +6%, +5%, and +8% by achieving a recall of 94%, 69%, 59% in Netflix, Audio, Cifar60k datasets, respectively. More and over, computing time and complexity nearly equals the most computationally efficient existing PQ method in the state-of-the-art.

翻译：随着数据资源的增长，提供最符合需求的推荐已成为商业和生活中克服信息过载问题的关键要求。然而，构建能够提供相关推荐的系统始终存在争议。在低复杂度下生成相关推荐方面，最具成本效益的技术之一是乘积量化（PQ）。近年来，PQ方法持续发展。该系统的关键挑战在于在不增加复杂度的前提下，通过召回率指标提升乘积量化性能。这使得算法适用于需要以高速、低成本方式获取大量潜在相关项目且不遗漏其他项目的问题场景，从而满足流量需求。在线商店正是此类典型案例：虽然顾客可能倾向于浏览其他产品，但针对性推荐仍然至关重要。本研究提出了一种基于模糊理论的范数乘积量化方法。通过采用二型模糊集（T2FSs）定义码本，使得子向量（T2FSs）可与码本中多个元素关联，进而通过积分求解其范数计算。我们的方法显著提升了召回率指标，使算法能够在不忽略其他项目的前提下，最大程度地查询潜在相关项目。在Netflix、Audio和Cifar60k数据集上，所提方法分别实现了94%、69%和59%的召回率，较NEQ、PQ和RQ等现有PQ方法提升幅度最高达+6%、+5%和+8%。此外，其计算时间与复杂度几乎与当前最先进的最高效PQ方法持平。