In this paper we present some Boolean algebras in the form of lattice by using the fuzzy implication. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature. KeywordsFuzzy logic connectives, Fuzzy implication, Algebras, Lattice.

We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra E is separable and modular then there exists a faithful state on E. Further, if an atomic lattice effect algebra is densely embeddable into a c...

B. Bájnok and S. Shahriari proved that in 2, the Boolean lattice of order n, the width (the maximum size of an antichain) of a non-trivial cutset (a collection of subsets that meets every maximal chain and does not contain ∅ or [n]) is at least n− 1. We prove that, for n ≥ 5, in the Boolean lattice of order n, given ⌈n2 ⌉− 1 disjoint long chains, we can enlarge the collection to a cutset of wid...

The triply periodic minimal surface lattice structure is innovatively introduced into the design of flexure hinges in this paper. Four types lattices are generated by approximate mathematical expressions. compliance characteristics these four simulated finite element analysis (FEA), and it found that primitive (P-lattice) most suitable for hinges. Simplified model single P-lattice one-dimension...

There are few Romanian mathematicians (computer scientists) having seven books published by important international publishers. Professor Sergiu Rudeanu is one of them. He has several titles published by Springer, North-Holland, World Scientific, Dunod (Paris), Kogaku Tosho (Tokyo) and Bentham (eBooks). As well as several others books printed by wellknown Romanian publishers. Their titles refle...

We are interested in maximizing the number of pairwise unrelated copies of a poset P in the family of all subsets of [n]. For instance, Sperner showed that when P is one element, ( n bn2 c ) is the maximum number of copies of P . Griggs, Stahl, and Trotter have shown that when P is a chain on k elements, 1 2k−1 ( n bn2 c ) is asymptotically the maximum number of copies of P . We prove that for ...

Let [n] = {1, 2, . . . , n} be a set with n elements, and let 2[n] denote the poset of all subsets of [n] ordered by inclusion. In other words, 2[n] is the Boolean lattice of order n or the n-dimensional hypercube. It is easy (for example using a symmetric chain decomposition [1, Theorem 3.1.1]) to find n disjoint skipless (saturated) symmetric chains of length n − 2, that is n disjoint chains ...

In the Diffusion Limited Aggregation (DLA) process on on Z, or more generally Z, particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a fractal with dimension strictly less than d. Very little has been shown rigorously about the process, however. We study an analogous process on the Boolean lattice {0, 1}, in which pa...

In this paper we investigate an extended version of modal dependence logic by allowing arbitrary Boolean connectives. Modal dependence logic was recently introduced by Jouko Väänänen by extending modal logic by a the dependence atom dep(·). In this paper we study the computational complexity of the model checking problem. For a complete classification of arbitrary Boolean functions we are using...