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This paper aims to propose a mathematical model for describing and clarifying the relationships among the indicators governing the social values of special customers in business-to-consumer (B2C) e-commerce systems. This mathematical model is also able to describe the degree of adaptability of e-commerce systems to the social values of specific clients, and commercial firms are able to use the parameters described in this paper to increase the versatility and has the power to trade with special customers in different areas.

In this paper, while analyzing the issue of trading from the point of view of the customer as an element of trading, the affecting factors the trading space have been extracted. These affecting factors are categorized in three major groups: culture, technology and customers. This classification is based on the e-commerce and developing the traditional commerce. Using the mapping functions, the effects of each element in these three spaces on the concept of social values have been analyzed. The result of this analysis is the mathematical model governing each parameter and its semantic relation with the concept of social value.

The presence of a mathematical model between the indicators influencing the model adaptability and social values space allows e-commerce system designers to be able to make decisions on the adaptability of the model with a quantitative approach. To examine the proposed mathematical models, important frameworks and patterns in the field of e-commerce have been analyzed with an Islamic approach, as one of the adaptations of B2C e-commerce model.

Regarding the innovation of the work, the case has been made, and the concept of social value and the model governing the elements of social values in this paper, in a B2C e-commerce model, has been discussed in general; the problem is parametric solved.

One of the key concepts in commerce is the ability of the commerce model to adapt to the requirements of special customers. This is more important in costumer-based e-commerce models. In these types of systems, if the commerce cannot match the customer’s characteristics, it will not be accepted and used by customers. This is especially more important in the field of social values for customers.

In this paper, a mathematical model is presented to examine the adaptability of e-commerce systems to the social values of special customers. In examining this model, the relationship between each element affecting the social value of specific customers and the factors affecting trade has been studied.