Keon Chang Lee

INTUITIONISTIC FUZZY WEAK CONGRUENCES ON A SEMIRING

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

The Lattice of Interval-Valued Intuitionistic Fuzzy Relations

By using the notion of interval-valued intuitionistic fuzzy relations, we form the poset (IVIR(X), ≤ ) of intervalvalued intuitionistic fuzzy relations on a given set X. In particular, we form the subposet (IVIE(X), ≤ ) of interval-valued intuitionistic fuzzy equivalence relations on a given set X and prove that the poset (IVIE(X), ≤ ) is a complete lattice with the least element and greatest element.

Interval-Valued H-Fuzzy Sets

We introduce the category IVSet(H) of interval-valued H-fuzzy sets and show that IVSet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study some relations among IVSet(H), ISet(H) and Set(H).

FUZZY EQUIVALENCE RELATIONS AND FUZZY FUNCTIONS

In this paper, by using the definition of fuzzy equivalence relations introduced by Dib and Youssef, we obtain fuzzy analogues of many results concerning ordinary equivalence relations. Moreover, we investigate fuzzy analogues of many results concerning relationships between ordinary equivalence relations and ordinary functions. In particular, we obtain the fuzzy canonical decomposition of a fuzzy function.

Interval-Valued Fuzzy Ideals of a Ring

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and intervalvalued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.

Interval-Valued Fuzzy Cosets

First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

THE LATTICE OF INTERVAL-VALUED FUZZY IDEALS OF A RING

We investigate the lattice structure of various sublat- tices of the lattice of interval-valued fuzzy subrings of a given ring. We prove that a special class of interval-valued fuzzy ideals of a ring. Finally, we show that the lattice of interval-valued fuzzy ideals of R is not complemented(resp. has no atoms(dual atoms)).

Intuitionistic Fuzzy G-Equivalence Relations and G-Congruences on a Groupoid

We investigate the images and preimages of intuitionistic fuzzy G-equivalence relations and G-congruences under product mappings.

A NEW APPROACH TO FUZZY CONGRUENCES

First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ρ ο ∈ FC(S) for any two fuzzy congruences and on a fuzzy groupoid (S, ⊙). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.