Representations on Raised Very Thin Hv-fields

Transactions on Fuzzy Sets and Systems

مقاله 7، دوره 1، شماره 1، مرداد 2022، صفحه 88-105   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2022.690402

نویسنده

Thomas Vougiouklis^*

School of Science and Education, Democritus University of Thrace, Greece.

چکیده

The hyperstructures have applications in mathematics and other sciences such as‎ ‎biology‎, ‎physics‎, ‎linguistics‎, ‎sociology‎, ‎to mention but a few‎. ‎For this‎, ‎mainly‎, ‎the‎ ‎largest class of the hyperstructures‎, ‎the  $H_v$-structures‎, ‎is used‎, ‎which satisfy the‎  weak axioms  where the non-empty intersection replaces the equality and they are‎ ‎straightly related to fuzzy set theory‎. ‎The fundamental relations connect the $H_v$-structures with the classical ones‎, ‎moreover‎, ‎they reveal new concepts as the  $H_{v}$-fields‎.  $H_{v}$-numbers are called the elements of an $H_v$-field and they are used in‎ ‎representation theory‎. ‎We introduce the  raised finite $H_{v}$-fields‎, ‎and present some‎ ‎results and examples on $2\times 2$ representations on them‎.

کلیدواژه‌ها

Hyperstructure؛ Hope؛ Hv-structure؛ Hv-group Hv-ring؛ Hv-field

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