The Internet becomes an enormous source of information containing billions of documents. Users deal with an overwhelming number of alternatives, and continuously make decisions anytime they want to obtain meaningful information. The paper describes an approach for a simple yet effective selection of the most suitable information that fits user's needs. The novelty of the approach is twofold: the concept of lexicographical-like preferences used for a multi-criteria decision-making with elements of fuzziness and OWA operator; a simple fuzzy number based mechanism for estimating user's degrees of acceptance of criterion satisfaction. The lexicographic preferences allow for mimicking user's attitude that some criteria should be satisfied before other criteria are considered. The acceptance of criterion satisfaction levels are defined with a single threshold that represents a boundary value between acceptable and unacceptable values of attributes of alternatives. The paper includes results of a simple case study preformed on a prototype of a web selection system built using the proposed approach.