In this paper we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the modeltheoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts bei...

We prove that several problems concerning congruences on algebras are complete for nondeterministic log-space. These problems are: determining the congruence on a given algebra generated by a set of pairs, and determining whether a given algebra is simple or subdirectly irreducible. We also consider the problem of determining the smallest fully invariant congruence on a given algebra containing...

We investigate the algebra of an ample groupoid, introduced by Steinberg, over a semifield S. In particular, we obtain complete characterization congruence-simpleness for Steinberg algebras second-countable groupoids, extending well-known characterizations when S is field. apply our congruence-simplicity results to tight groupoids inverse semigroup representations associated self-similar graphs.

<abstract><p>Among the triangle congruence axioms, side-side-angle (SsA) axiom states that two triangles are congruent if and only pairs of corresponding sides angles opposite longer equal. We construct sequences in which items satisfy a modified condition. require shorter be The locus intersection points other is derived to hyperbola, generalized form defined by complete quadrilate...

By using a special t-level relation U(μ, t) = {(x, y) ∈ S × S|(μ(x) ∧ μ(y)) ∨ IdS(x, y) ≥ t} based on a fuzzy ideal μ of a semigroup S, which is a congruence relation, we study the roughness of soft semigroups under this special ideal of S, such as rough soft subsemigroups, rough soft ideals and rough soft prime ideals.

in this paper, we shall introduce the fuzzyw-distance, then prove a common fixed point theorem with respectto fuzzy w-distance for two mappings under the condition ofweakly compatible in complete fuzzy metric spaces.

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

We perform a complete ρ-integration of the GHP equations for all spacetimes that admit a geodesic shear-free expanding null congruence, whose Ricci spinor is aligned to the congruence and whose Ricci scalar is constant. We also deduce the system of GHP equations after the integration is completed, and discuss a few applications.