http://hdl.handle.net/11089/39678 2026-04-06T20:39:21Z http://hdl.handle.net/11089/39689 Neighbourhood Semantics for Graded Modal Logic Chen, Jinsheng; van Ditmarsch, Hans; Greco, Giuseppe; Tzimoulis, Apostolos We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation. 2021-07-14T00:00:00Z http://hdl.handle.net/11089/39688 A General Model of Neutrosophic Ideals in BCK/BCI-algebras Based on Neutrosophic Points Bordbar, Hashem; Borzooei, Rajab Ali; Smarandache, Florentin; Jun, Young Bae More general form of (∈, ∈ ∨q)-neutrosophic ideal is introduced, and their properties are investigated. Relations between (∈, ∈)-neutrosophic ideal and (∈, ∈ ∨q(kT ,kI ,kF ))-neutrosophic ideal are discussed. Characterizations of (∈, ∈∨q(kT ,kI,kF ))-neutrosophic ideal are discussed, and conditions for a neutrosophic set to be an (∈, ∈∨q(kT ,kI ,kF ))-neutrosophic ideal are displayed. 2020-08-15T00:00:00Z http://hdl.handle.net/11089/39687 Falling Shadow Theory with Applications in Hoops Borzooei, Rajab Ali; Rezaei, Gholam Reza; Kologhani, Mona Aaly; Jun, Young Bae The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy filter are provided. Also conditions for a falling shadow of a random set to be a falling fuzzy filter are displayed. 2021-01-20T00:00:00Z http://hdl.handle.net/11089/39685 Tense Operators on BL-algebras and Their Applications Paad, Akbar In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided. 2021-05-28T00:00:00Z