In this paper, newly defined level operators and modal-like operators over extensional generalized intuitionistic fuzzy sets (GIFSB) are proposed. Some of the basic properties of the new operators are discussed.

In this work, four modal-like operators on Boolean lattices are introduced and their theory is presented from lattice-theoretical, topological and algebraic point of view. It is also shown how rough set approximation operators, modal operators in temporal logic, and linguistic modifiers determined by L-sets can be interpreted as modal-like operators.

Intuitionistic Fuzzy Modal Operator was defined by Atanassov in cite{at3}in 1999. In 2001, cite{at4}, he introduced the generalization of thesemodal operators. After this study, in 2004, Dencheva cite{dencheva} definedsecond extension of these operators. In 2006, the third extension of thesewas defined in cite{at6} by Atanassov. In 2007,cite{gc1}, the authorintroduced a new operator over Intuit...

An extension of the concept description language ACC used in KL-ONE-like terminological reasoning is presented. The extension includes multi-modal operators that can either stand for the usual role quantifications or for modalities such as belief, time etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an inst...

An extension of the concept description language ALC used in kl-one-like terminological reasoning is presented. The extension includes multi{modal operators that can either stand for the usual role quanti cations or for modalities such as belief, time etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an insta...

We enrich Kleene algebra by domain and codomain operators. These abstractions of relational notions give rise to four modal operators. The boxes and diamonds enjoy various symmetries via Galois connections and dualities. Lifting modal statements to modal operator semirings yields a further abstraction and thus a more elegant and concise “statefree” reasoning about modalities. We use this modal ...

Any strict partial order R on a nonempty set X defines a function θR which associates to each strict partial order S ⊆ R on X the strict partial order θR(S) = R ◦ S on X. Owing to the strong relationships between Alexandroff TD derivative operators and strict partial orders, this paper firstly calls forth the links between the CantorBendixson ranks of Alexandroff TD topological spaces and the g...

Terminological knowledge representation formalisms can be used to represent objective, time-independent facts about an application domain. Notions like belief, intentions, and t ime which are essential for the representation of mult i-agent environments can only be expressed in a very l imi ted way. For such not i ons, modal logics w i th possible worlds semantics provides a formal ly well-foun...

Categorial characterizations are given of both unconstrained and constrained bring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison with model theoretic parchments is included.

We describe the embedding of the semantic notions and modal operators of a fir st-order temporal logic based on time intervals in a multivalued setting. Truth values will be realized as functions from time intervals to "ordinary" truth values like t and f . The main emphasis lies on the realization of the various modal operators contained in the temporal logic as operations on the functional tr...