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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)

- Ath Kehagias, M Konstantinidou
- 2000

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)

- Ath Kehagias, M Konstantinidou
- 2000

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 study the L-fuzzy hyperoperation , which generalizes the crisp Nakano hyperoperation 1. We construct using a family of crisp p hyperoperations as its p-cuts. The hyperalgebra (X, , ∧) can be understood as an L-fuzzy hyperlattice.

- Ath Kehagias, K Serafimidis, M Konstantinidou
- 2001

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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