In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.
In this paper, the ordinal sum construction methods of implications on bounded lattices are studied. Necessary and sufficient conditions of an ordinal sum for obtaining an implication are presented. New ordinal sum construction methods on bounded lattices which generate implications are discussed. Some basic properties of ordinal sum implications are studied.
A partial order on a bounded lattice is called t-order if it is defined by means of the t-norm on . It is obtained that for a t-norm on a bounded lattice the relation iff for some is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of and a complete lattice on the subset of all elements of which are the supremum of a subset of atoms.
In this paper, an equivalence on the class of uninorms on a bounded lattice is discussed. Some relationships between the equivalence classes of uninorms and the equivalence classes of their underlying t-norms and t-conorms are presented. Also, a characterization for the sets admitting some incomparability w.r.t. the U-partial order is given.
In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.
In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on from the t-norm on a subinterval of need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction...
In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice are given and a...
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