APPLICATIONS OF BIPOLAR FUZZY THEORY TO HEMIRINGS

In our real life, bipolar fuzzy theory is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. In this paper, we provide a general algebraic framework for handling bipolar information by combining the theory of bipolar fuzzy sets with hemirings. First, we present the concepts of bipolar fuzzy h-ideals and normal bipolar fuzzy h-ideals. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in the present paper. Second, the characterizations of bipolar fuzzy h-ideals are investigated by means of positive t-cut, negative s-cut, homomorphism and equivalence relation. Third, we give the range of the values of the non-constant maximal element of all normal bipolar fuzzy h-ideals.

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