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Virtual marketplaces on the Web provide people with great facilities to buy and sell goods similar to conventional markets. In traditional business, reputation is subjectively built for known persons and companies as the deals are made in the course of time. As it is important to do business with trustful individuals and companies, there is a need to survive the reputation concept in virtual markets. Auction sites generally employ reputation systems based on feedbacks that provide a global view to a cyber dealer. In contrast to global trust, people usually infer their personal trust about someone whose reputation is completely or partially unknown by asking their trusted friends. Personal reputation is what makes a person trusted for some people and untrusted for others. There should be a facility for users in a virtual market to specify how much they trust a friend and also a mechanism that infers the trust of a user to another user who is not directly a friend of her. There are two main issues that should be addressed in trust inference. First, the trust modeling and aggregation problem needs to be challenged. Second, algorithms should be introduced to find and select the best paths among the existing trust paths from a source to a sink. First, as trust to a person can be stated more naturally using linguistic expressions, this work suggests employing linguistic terms for trust specification. To this end, corresponding fuzzy sets are defined for trust linguistic terms and a fuzzy trust aggregation method is also proposed. Comparing the fuzzy aggregation method to the existing aggregation methods shows superiority of fuzzy approach especially at aggregating contradictory information. Second, this paper proposes an incremental trust inference algorithm. The results show improvement in preciseness of inference for the proposed inference algorithm over the existing and recently proposed algorithm named TidalTrust. [ABSTRACT FROM AUTHOR]