Khamirrudin Md  Derus, J.  Kavikumar, Nor Shamsidah Amir  Hamzah, 
    Decomposition of Bipolar Fuzzy Finite State Machines and
Transformation Semigroups,
    Journal of Engineering and Applied Sciences,
    Volume 12,Issue 3,
    2017,
    Pages 679-683,
    ISSN 1816-949x,
    jeasci.2017.679.683,
    (https://makhillpublications.co/view-article.php?doi=jeasci.2017.679.683)
    Abstract: Bipolar fuzzy sets are the generalization of fuzzy sets. In many domains dealing with bipolar
information is an essential. In this study, we deal with bipolar information and introduce the concept of
decomposition of fuzzy finite state machines and transformation semigroups and investigated some of their
algebraic properties.
    Keywords: Bipolar fuzzy sets;finite state machines;decomposition;transformation semigroups;algebraic properties