| Summary: | There are many symmetries in <i>L</i>-fuzzy algebras. In this paper, a novel approach to the fuzzification of a field is introduced. We define a mapping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>:</mo><msup><mi>L</mi><mi>X</mi></msup><mo>→</mo><mi>L</mi></mrow></semantics></math></inline-formula> from the family of all the <i>L</i>-fuzzy sets on a field <i>X</i> to <i>L</i> such that each <i>L</i>-fuzzy set is an <i>L</i>-fuzzy subfield to some extent. Some equivalent characterizations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></semantics></math></inline-formula> are given by means of cut sets. It is proved that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula> is <i>L</i>-fuzzy convex structure on <i>X</i>, hence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>X</mi><mo>,</mo><mi mathvariant="script">F</mi><mo>)</mo></mrow></semantics></math></inline-formula> forms an <i>L</i>-fuzzy convexity space. A homomorphism between fields is exactly an <i>L</i>-fuzzy convexity preserving mapping and an <i>L</i>-fuzzy convex-to-convex mapping. Finally, we discuss some operations of <i>L</i>-fuzzy subsets.
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