http://hdl.handle.net/11089/44032 Mon, 06 Apr 2026 05:09:47 GMT 2026-04-06T05:09:47Z https://dspace.uni.lodz.pl:443/bitstream/id/618fbfe5-a984-45de-be8a-a0999086b2bb/ http://hdl.handle.net/11089/44032 http://hdl.handle.net/11089/44041 Complete Representations and Neat Embeddings Sayed Ahmed, Tarek Let \(2<n<\omega\). Then \({\sf CA}_n\) denotes the class of cylindric algebras of dimension \(n\), \({\sf RCA}_n\) denotes the class of representable \(\sf CA_n\)s, \({\sf CRCA}_n\) denotes the class of completely representable \({\sf CA}_n\)s, and \({\sf Nr}_n{\sf CA}_{\omega}(\subseteq {\sf CA}_n\)) denotes the class of \(n\)-neat reducts of \({\sf CA}_{\omega}\)s. The elementary closure of the class \({\sf CRCA}_n\)s (\(\mathbf{K_n}\)) and the non-elementary class \({\sf At}({\sf Nr}_n{\sf CA}_{\omega})\) are characterized using two-player zero-sum games, where \({\sf At}\) is the operator of forming atom structures. It is shown that \(\mathbf{K_n}\) is not finitely axiomatizable and that it coincides with the class of atomic algebras in the elementary closure of \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{\omega}\) where \(\mathbf{S_c}\) is the operation of forming complete subalgebras. For any class \(\mathbf{L}\) such that \({\sf At}{\sf Nr}_n{\sf CA}_{\omega}\subseteq \mathbf{L}\subseteq {\sf At}\mathbf{K_n}\), it is proved that \({\bf SP}\mathfrak{Cm}\mathbf{L}={\sf RCA}_n\), where \({\sf Cm}\) is the dual operator to \(\sf At\); that of forming complex algebras. It is also shown that any class \(\mathbf{K}\) between \({\sf CRCA}_n\cap \mathbf{S_d}{\sf Nr}_n{\sf CA}_{\omega}\) and \(\mathbf{S_c}{\sf Nr}_n{\sf CA}_{n+3}\) is not first order definable, where \(\mathbf{S_d}\) is the operation of forming dense subalgebras, and that for any \(2<n<m\), any \(l\geq n+3\) any any class \(\mathbf{K}\) (such that \({\sf At}({\sf Nr}_n{\sf CA}_{m})\cap {\sf CRCA}_n\subseteq \mathbf{K}\subseteq {\sf At}\mathbf{S_c}{\sf Nr}_n{\sf CA}_{l}\), \(\mathbf{K}\) is not not first order definable either. Fri, 09 Sep 2022 00:00:00 GMT http://hdl.handle.net/11089/44041 2022-09-09T00:00:00Z http://hdl.handle.net/11089/44040 An (α,β)-Hesitant Fuzzy Set Approach to Ideal Theory in Semigroups Yiarayong, Pairote The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of \((\alpha,\beta)\)-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study \((\alpha,\beta)\)-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of \((\alpha,\beta)\)-hesitant fuzzy ideal generated by a hesitant fuzzy ideal in a semigroup. In addition, we also introduce the concepts of \((\alpha,\beta)\)-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of \((\alpha,\beta)\)-hesitant fuzzy left ideals and \((\alpha,\beta)\)-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of \((\alpha,\beta)\)-hesitant ideals are given. Wed, 14 Sep 2022 00:00:00 GMT http://hdl.handle.net/11089/44040 2022-09-14T00:00:00Z http://hdl.handle.net/11089/44039 Constructing a Hoop Using Rough Filters Borzooei, Rajab Ali; Babaei, Elham When it comes to making decisions in vague problems, rough is one of the best tools to help analyzers. So based on rough and hoop concepts, two kinds of approximations (Lower and Upper) for filters in hoops are defined, and then some properties of them are investigated by us. We prove that these approximations- lower and upper- are interior and closure operators, respectively. Also after defining a hyper operation in hoops, we show that by using this hyper operation, set of all rough filters is monoid. For more study, we define the implicative operation on the set of all rough filters and prove that this set with implication and intersection is made a hoop. Fri, 09 Sep 2022 00:00:00 GMT http://hdl.handle.net/11089/44039 2022-09-09T00:00:00Z http://hdl.handle.net/11089/44038 Unification and Finite Model Property for Linear Step-Like Temporal Multi-Agent Logic with the Universal Modality Bashmakov, Stepan I.; Zvereva, Tatyana Yu. This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality \(\mathcal{LTK}.sl_U\) based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic. Fri, 09 Sep 2022 00:00:00 GMT http://hdl.handle.net/11089/44038 2022-09-09T00:00:00Z