This paper proposes to study the lattice properties of two closed binary operations in the set of discrete fuzzy numbers. Using these operations to represent the meet and the join, we prove that the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers is a distributive lattice. Finally, we demonstrate that the subsets of discrete fuzzy numbers, which have the same...

It is well known that the only simple distributive lattice is the twoelement chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices. “COMPLETE-SIMPLE” DISTRIBUTIVE LATTICES G. GRÄTZER A...

We study the serial and parallel computation of Γ (Gamma), a comprehensive data summarization matrix for linear machine learning models widely used in big data analytics. We prove that computing Gamma can be reduced to a single matrix multiplication with the data set, where such multiplication can be evaluated as a sum of vector outer products, which enables incremental and parallel computation...

Distributive justice concerns the fair, just or equitable distribution of benefits and burdens. These benefits and burdens span all dimensions of social life and assume all forms, including income, economic wealth, political power, taxation, work obligations, education, shelter, health care, military service, community involvement and religious activities. Thus, justice arguments are often invo...

We study the serial and parallel computation of Γ (Gamma), a comprehensive data summarization matrix for linear Gaussian models, widely used in big data analytics. Computing Gamma can be reduced to a single matrix multiplication with the data set, where such multiplication can be evaluated as a sum of vector outer products, which enables incremental and parallel computation, essential features ...

In this paper, we introduce and study the stable topology on the set of prime filters of a bounded 0-distributive lattice. The stable topology is a subtopology of the hull kernel topology on the set of prime filters of a bounded 0-distributive lattice. Sufficient condition is given under which the hull kernel topology and stable topology coincide on the set of prime filters (the set of maximal ...

We prove that the skeleton of a product of finitely many finite distributive lattices is isomorphic to the product of skeletons of its factors. Thus, it is possible to construct finite distributive lattices with a given directly reducible skeleton by reducing the problem to the skeleton factors. Although not all possible lattices can be obtained this way, we show that it works for the smallest ...

We give a representation of distributive lattices with the existential quantifier in terms of spectral spaces, which is an alternative to Cignoli’s representation in terms of Priestley spaces. Then we describe dual spectral spaces of subdirectly irreducible and simple Q-distributive lattices and prove that the variety QDist of Q-distributive lattices does not have the congruence extension prope...

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the ca...