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Monadic algebras of an involutive monoidal t-norm based logic | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 13، دوره 19، شماره 3، مرداد و شهریور 2022، صفحه 187-202 اصل مقاله (206.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6951 | ||
| نویسندگان | ||
| J. T. Wang* 1؛ X. L. Xin2 | ||
| 1School of Science, Xi'an Shiyou University, Xi'an 710065, Shaanxi, China | ||
| 2School of Science, Xi'an Polytechnic University, Xi'an 710048, Shaanxi, China | ||
| چکیده | ||
| The main goal of this paper is to study universal and existential quantifiers on involutive monoidal t-norm based algebras, which are algebraic semantics for the logic of involutive left-continuous t-norms and their residua, and the resulting class of algebras will be called monadic IMTL-algebras. First we study some of their related algebraic properties and prove that the variety of monadic IMTL-algebras is the equivalent algebraic semantics of monadic predicate fuzzy logic $\mathbf{mMTL_{\forall}}$, which is equivalent to the modal fuzzy logic $\mathbf{S5(IMTL)}$, and show the completeness for $\mathbf{IMTL_{\forall}}$ via functional monadic IMTL-algebras. Moreover we start a systematic study of monadic algebraic structures that related to the monadic IMTL-algebras, some of which constitute the monadic MTL-algebras, monadic WNM-algebras, monadic NM-algebras, monadic BL-algebras, monadic MV-algebras and monadic Boolean algebras. Finally we give some representations of monadic IMTL-algebras. In particular, we character representable and directly indecomposable monadic IMTL-algebras by monadic filters. | ||
| کلیدواژه‌ها | ||
| Mathematical fuzzy logic؛ monadic predicate fuzzy logic؛ monadic IMTL-algebra؛ functional monadic IMTL-algebra؛ representation | ||
| مراجع | ||
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