Abstract�Real world problems don't always come with sufficient, complete, and precise data; classical algorithms are facing some limitations like inefficiency of handling imprecise data or uncertain information. Therefore there is a need for finding powerful techniques to handle such situations. The main objective of this research is to introduce a new version of ant algorithm that can solve the problems, which contain uncertain information or imprecise data. To achieve this objective, the research integrates fuzzy logic and ant algorithm for better handling of such problems.

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When a quantity is measured, the outcome depends on several factors like the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. In case of inexact quantity the outcome may also depends on the uncertainty representation.Recently inexact numbers got a lot of attention from many researchers in different fields. In this paper, we have tried to give an overview for the different representations of the inexact granular numbers. The objective of this overview is providing a certain insight into the essence of granular data representation being regarded as a framework of representing and manipulation of inexact information, and introduce a new representation of granular uncertain number to be as step in formulate a general form for all uncertain numbers.

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