Huisik Kim

The purpose of this study was to assess the extent to which a battery of 24 activities of daily living (ADL) performance tasks could be used to determine functional age in a sample of older women. The subjects were 253 older adult Korean women, aged 60 to 91 years. All subjects completed a comprehensive battery of 24 performance tests related to common activities of daily living. Correlations between the measures were computed, and principal component analysis was applied to the 24 × 24 correlat

The notions of hesitant fuzzy translations and hesitant fuzzy extensions of a hesitant fuzzy set on BCK / BCI -algebras are introduced, and related properties are investigated. We prove that every hesitant fuzzy translation of a hesitant fuzzy subalgebra (ideal) is a hesitant fuzzy subalgebra (ideal). Conditions for a hesitant fuzzy set to be a hesitant fuzzy subalgebra (ideal) are provided. We show that if a hesitant fuzzy set is a hesitant fuzzy subalgebra (ideal), then its support is a subalg

Abstract In this paper we consider Fibonacci functions on the real numbers R , i.e. , functions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>R</mml:mi> <mml:mo>→</mml:mo> <mml:mi>R</mml:mi> </mml:math> such that for all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>x</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>R</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>f</mml:mi> <mml:mo>(</mml:

Abstract In this article, we consider several properties of Fibonacci sequences in arbitrary groupoids (i.e., binary systems). Such sequences can be defined in a left-hand way and a right-hand way. Thus, it becomes a question of interest to decide when these two ways are equivalent, i.e., when they produce the same sequence for the same inputs. The problem has a simple solution when the groupoid is flexible. The Fibonacci sequences for several groupoids and for the class of groups as special cas

The notions of int-soft semigroups and int-soft left (resp., right) ideals are introduced, and several properties are investigated. Using these notions and the notion of inclusive set, characterizations of subsemigroups and left (resp., right) ideals are considered. Using the notion of int-soft products, characterizations of int-soft semigroups and int-soft left (resp., right) ideals are discussed. We prove that the soft intersection of int-soft left (resp., right) ideals (resp., int-soft semigr

Reliability optimization is a critical aspect of modern engineering systems and products, particularly with the growing complexity and interconnectedness of systems. This paper delves into the significance of reliability optimization and the techniques employed to achieve it. It highlights the benefits of optimizing reliability, including reduced costs, enhanced customer retention, and a competitive advantage. The paper discusses the challenges of balancing performance, cost, and reliability, es

In this paper, we generalize the notion of an implicativity discussed in B C K -algebras, and apply it to some groupoids and B C K -algebras. We obtain some relations among those axioms in the theory of groupoids.

In this paper, we introduce the notions of generalized commutative laws in algebras, and investigate their relations by using Smarandache disjointness. Moreover, we show that every pre-commutative B C K -algebra is bounded.

In this paper, we consider a theory of elements u of a groupoid ( X , ∗ ) that are associated with certain functions u ^ : X → X , pseudo-inverse functions, which are generalizations of the inverses associated with units of groupoids with identity elements. If classifying the elements u as special of one of twelve types, then it is possible to do a rather detailed analysis of certain cases, leftoids, rightoids and linear groupoids included, which demonstrates that it is possible to develop a suc

In this paper we introduce the notion of a (pre-)Coxeter algebra and show that a Coxeter algebra is equivalent to an abelian group all of whose elements have order 2, i.e., a Boolean group. Moreover, we prove that the class of Coxeter algebras and the class of B-algebras of odd order are Smarandache disjoint. Finally, we show that the class of pre-Coxeter algebras and the class of BCK-algebras are Smarandache disjoint.

In this paper, we define the concepts of ( ∈ , ∈ ) and ( ∈ , ∈ ∨ q ) -fuzzy filters of hoops, discuss some properties, and find some equivalent definitions of them. We define a congruence relation on hoops by an ( ∈ , ∈ ) -fuzzy filter and show that the quotient structure of this relation is a hoop.

In this paper, the authors extend the theory of groupoids already developed for semigroups ( Bin ( X ) , □) in a growing number of research papers with X a set and Bin ( X ) the set of groupoids (binary systems) defined on X to the generalizations: fuzzy (sub)groupoids (largely known as used here) and hyperfuzzy (sub)groupoids (largely novel as used here), showing (1) there are natural processes and (2) new results of interest can be obtained, including the existence of new parameters which on t

In this paper, we define the Fibonacci-norm [Formula: see text] of a natural number n to be the smallest integer k such that n|F k , the kth Fibonacci number. We show that [Formula: see text] for m ≥ 5. Thus by analogy we say that a natural number n ≥ 5 is a local-Fibonacci-number whenever [Formula: see text]. We offer several conjectures concerning the distribution of local-Fibonacci-numbers. We show that [Formula: see text], where [Formula: see text] provided F m+k ≡ F m (mod n) for all natura