The growing popularity of the Internet and information technology continues to flourish. In such a background, the use of mobile (web) sites are growing every year. According to the latest information on Internet World Stats, as of June 2008, the global online population has reached 1.46 billion, of which Asia accounted for 40%, 26% in Europe, and 17% in North America. Penetration of the global Internet population has surpassed into two, which in North America up to 74%, 60% in Oceania, and 48% in Europe. Global Internet population from 2000 to 2008 grew at a rate of more than 300%, and the countries of the world strive to improve the information penetration of the case. Therefore, the global Internet population will show a more rapid population growth in the future¹. In addition, in investigation results from International Telecommunication Union, twice the world's online population has grown over the past 5 years, and will include more than 20 million people this year². Then according to the Institute for Information Industry statistics, at the end of June 2010 in Taiwan, total broadband subscribers were 4.98 million, an increase over the previous quarter's fifty thousand users³. The global Internet used by the rapid rise in population could reflect how network usage and daily life have been inextricably linked.

With the rapid development of Internet, along with the number of people e-shopping has continued to grow in recent years. According to a Market Intelligence Center study, global e-shopping market grew from in 2006 at U.S. 640 billion dollars to U.S. 782 billion dollars in 2008. And the forecasts for 2009 and 2010, respectively, are up to U.S. 830 billion dollars and U.S. 951 billion dollars. Although the development of Taiwan's e-shopping is late, after a strong government and private investment in information and communication building, the Internet use of the environment has matured, and Taiwan's e-shopping market will reach U.S. 105 billion dollars in 2009⁴.

Compared to physical stores, online stores possess lower spatial and temporal costs, low barriers to construct, and are coupled with media reports. Therefore, attracting many people into the online store to entrepreneurship, making the online store has become the most popular emerging industry. But also because of the relatively low barriers to entry, online store competition is fierce; therefore, to enhance the performance of online stores becomes even more important, and the online store's performance depends on many factors. For example, the characteristics of goods, the smoothness of the website, the way of transactions, distribution, and other factors (Troy and Shaw, 1997) will affect the online store crowds and the money flows, and also the online store's performance in the operating performance. Since the influencing factors are complex, it is difficult to control the online store's business strategy. In fact, for such decision problems with uncertainty and ambiguity, we should be able to use fuzzy set theory to deal effectively and make the appropriate decisions (Bellman and Zadeh, 1970; Chen and Hwang, 1992; Akhter et al., 2003).

In this study, we use the linguistic variables to express the subjective assessment value of the evaluators in order to reduce the ambiguity. We then use the combination of fuzzy logic theory and neural algorithm to assess a proper decision to construct a decision model for the performance of the online store. In this way, we can quickly and effectively grasp the operation of the online store for the consumers and enterprises through the online store performance of decision-making. Based on the above, the main purposes of this study are the following two points:

In recent years, because of the rapid development of Internet applications and Information Technology, online shopping adopted information system use to create a competitive advantage. In this study, DeLone and McLean (2003) proposed information system success model. They measure the loyalty of the e-shopping, whether it has significant impact on the information quality, service quality, and system quality. This study takes the fuzzy with three inputs and one output as an example. The architecture of fuzzy is shown in Figure 3. Table 1 presents the respective linguistic members of the summarized variables. Decision rules can usually be represented in the form “If … Then …” Figure 4 shows partial decision rules in spreadsheet format. The membership functions of respective decision variables are depicted in Figure 5.

Compared to other e-shopping studies (Zhang, 2006; Khalifa and Liu, 2007; Zhou et al., 2007), which mainly use the complex mathematical formulas to solve the problem, this study uses the Fuzzy logic rule to represent the human mind, and more and more studies use Fuzzy logic to represent the human mind (Akhter et al., 2005; Lu and Sy, 2009; Liu, 2010). Increasing choices for consumers is obvious in the context of online shopping with diverse products. In this study, the vendor would benefit from the survey data aggregated over time to refine existing rule-sets. The vendor can also utilize the data to ascertain the loyalty of the site as per user's perception and rectify if needed. Figure 6 presents that the highest gradient for loyalty is when information is “very-high” and service is “medium” to “high.” This suggests that when consumers somewhat have information with online shopping, then a small increase in service from medium to high will boost their loyalty in a significant way. Figure 7 presents that the highest gradient for loyalty is when system is “very-high” and service is “medium” to “high.” This suggests that the system quality for loyalty is influenced. So to simplify, an easy to operate system for consumers is a very important factor. Figure 8 presents that the highest gradient for loyalty is when system is “very-high” and information is “very-high.” This suggests that consumers have high quality for system and information. Easy to use and with good information quality is a very important factor for e-commerce.

Many existing studies have found that the system, information, and service quality of online commerce has a significant positive impact on customers' continuous use behavior (DeLone and McLean, 1992, 2003; Van Dyke et al., 1997; Tankovic and Benazic, 2018; Cachero-Martínez and Vázquez-Casielles, 2021), however, does the highest system/information/service online quality necessarily lead to the highest customer loyalty behavior? Our study results show that we cannot make a simple affirmative answer to this. From Figures 6, 7, we can find that when the quality of online service is medium to high, and the quality of information and system is very high, which leads to the highest customer loyalty, thus we believe that the relationship between system/information/service quality and loyalty is non-linear and uncertain, nor is it that the higher the quality of online services, the higher the loyalty, and there may exist the best combination of system-information-service quality that has the best impact on online customer loyalty. Therefore, our study is a further improvement and supplement to the related theoretical research on the influencing factors for customer loyalty in e-shopping.

In addition, our study also has important practical applications. First, vendors can use survey data to build a multi-dimensional graph of the relationship between system-information-service quality and customer loyalty behavior. Second, vendors can analyze and determine the spatial position of their system/information/service quality in the multi-dimensional relationship diagram. Finally, based on the spatial position, vendors can make the best decisions to increase customer loyalty. For example, with limited resources and capabilities, if the vendor's service quality is below the medium level and the information/system quality is below the high level, then the vendor can choose the method that has the least investment but the biggest effect on improving customer loyalty. For another example, if the vendor's service quality is very high, but the system/information quality is below very high, the vendor can appropriately reduce the service quality investment and increase the system/information quality investment, which can improve customer loyalty.

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.

L-XG conceived and designed the research and provided guidance throughout the entire research process and made main revisions to the original manuscript during the interactive process of submission. C-CL and P-FH wrote and supplemented the English paper. S-YJ participated in data processing. S-CC and F-ST reviewed and edited the paper and are responsible for all R&R works. All authors contributed to the article and approved the submitted version.

This research was partially funded by the Jiangsu Province Social Science Foundation Project, grant number: 17SHB006 (Research results of Jiangsu Social Science Fund Project, http://jspopss.jschina.com.cn/).

S-YJ is employed by China Life Insurance Co., Ltd., Taiwan. He joined the research when he was a graduate student in a master's program. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.