M. Konstantinidou

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The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an L-fuzzy valued relation between fuzzy sets. This relation is(More)
In this paper we present an example of a lattice-ordered join space, i.e. a structure (L, ≤, ·) where (L, ≤) is a lattice, (L, ·) is a join space and the · hyperoperation is compatible with the ≤ order. Our example is obtained from a join hyperoperation which is frequently used in machine learning applications. We study the basic properties of the join(More)
Caratheodory has formulated an important theorem regarding the behavior of convex sets in Euclidean spaces [1]. In this paper we discuss a generalization of convexity which is applicable to lattices. This generalization involves a join hyperoperation; we show that associativity of this hyperoperation is equivalent to several attractive properties. In(More)
In this paper we explore the Nakano superlattice (H, ,), where , are the Nakano hyperop-erations x y = {z : x ∨ z = y ∨ z = x ∨ y}, x y = {z : x ∧ z = y ∧ z = x ∧ y}. In particular, we study the properties of congruences on the Nakano superlattice and the associated quotients. New hyperoperations are introduced on the quotient and their properties studied.
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