• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.363-371
• /
• 2018

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.6
• /
• pp.771-779
• /
• 2005

We introduce two concepts of intuitionistic fuzzy Rees congruence on a semigroup and intuitionistic fuzzy Rees con-gruence semigroup. As an important result, we prove that for a intuitionistic fuzzy Rees congruence semigroup S, the set of all intuitionistic fuzzy ideals of S and the set of all intuitionistic fuzzy congruences on S are lattice isomorphic. Moreover, we show that a homomorphic image of an intuitionistic fuzzy Rees congruence semigroup is an intuitionistic fuzzy Rees congruence semigroup.

• Kyungpook Mathematical Journal
• /
• v.45 no.4
• /
• pp.527-537
• /
• 2005

The intuitionistic fuzzification of the notion of a bi-ideal in ordered semigroups is considered. In terms of intuitionistic fuzzy set, conditions for an ordered semigroup to be completely regular is provided. Characterizations of intuitionistic fuzzy bi-ideals in ordered semigroups are given. Using a collection of bi-ideals with additional conditions, an intuitionistic fuzzy bi-ideal is constructed. Natural equivalence relations on the set of all intuitionistic fuzzy bi-ideals of an ordered semigroup are investigated.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.3
• /
• pp.207-219
• /
• 2008

We give some properties of intuitionistc fuzzy left, right, and two-sided ideals and bi-ideals of a semigroup. And we characterize a regular semigroup, a semigroup that is a lattice of left(right) simple semigroups, a semigroup that is a semilattice of left(right) groups and a semigroup that is a semilattice of groups in terms of intuitionistic fuzzy ideals and intuitionistic fuzzy bi-ideals.

• Korean Journal of Mathematics
• /
• v.21 no.2
• /
• pp.171-180
• /
• 2013

We consider a fuzzy semigroup S in a right (or left) reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ and find a faithful representation (or anti-representation) of S by transformations of S. Also we show that a fuzzy semigroup S in a weakly reductive semigroup X such that $S(k)=1$ for some $k{\in}X$ is isomorphic to the semigroup consisting of all pairs of inner right and left translations of S and that S can be embedded into the semigroup consisting of all pairs of linked right and left translations of S with the property that S is an ideal of the semigroup.

• Korean Journal of Mathematics
• /
• v.19 no.3
• /
• pp.321-330
• /
• 2011

We characterize the fuzzy bi-ideal generated by a fuzzy subset in a semigroup and the fuzzy bi-ideal generated by a fuzzy subset A such that $A{\subseteq}A^2$ in a semigroup with an identity element. Our work generalizes the characterization of fuzzy bi-ideals by Mo and Wang ([8]).

• Korean Journal of Mathematics
• /
• v.22 no.2
• /
• pp.367-381
• /
• 2014

The notion of ${\Gamma}$-semigroups was introduced by Sen in 1981 and that of fuzzy sets by Zadeh in 1965. Any semigroup can be reduced to a ${\Gamma}$-semigroup but a ${\Gamma}$-semigroup does not necessarily reduce to a semigroup. In this paper, we study the coincidences of fuzzy generalized bi-ideals, fuzzy bi-ideals, fuzzy interior ideals and fuzzy ideals in regular, left regular, right regular, intra-regular, semisimple ordered ${\Gamma}$-semigroups.

• The Pure and Applied Mathematics
• /
• v.19 no.1
• /
• pp.23-35
• /
• 2012

Given a set ${\Omega}$ and the notion of bipolar valued fuzzy sets, the concept of a bipolar ${\Omega}$-fuzzy sub-semigroup in semigroups is introduced, and related properties are investigated. Using bipolar ${\Omega}$-fuzzy sub-semigroups, bipolar fuzzy sub-semigroups are constructed. Conversely, bipolar ${\Omega}$-fuzzy sub-semigroups are established by using bipolar fuzzy sub-semigroups. A characterizations of a bipolar ${\Omega}$-fuzzy sub-semigroup is provided, and normal bipolar ${\Omega}$-fuzzy sub-semigroups are discussed. How the homomorphic images and inverse images of bipolar ${\Omega}$-fuzzy sub-semigroups become bipolar ${\Omega}$-fuzzy sub-semigroups are considered.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.13 no.3
• /
• pp.231-244
• /
• 2013

We introduce the concept of interval-valued fuzzy congruences on a semigroup S and we obtain some important results: First, for any interval-valued fuzzy congruence $R_e$ on a group G, the interval-valued congruence class Re is an interval-valued fuzzy normal subgroup of G. Second, for any interval-valued fuzzy congruence R on a groupoid S, we show that a binary operation * an S=R is well-defined and also we obtain some results related to additional conditions for S. Also we improve that for any two interval-valued fuzzy congruences R and Q on a semigroup S such that $R{\subset}Q$, there exists a unique semigroup homomorphism g : S/R${\rightarrow}$S/G.

• Communications of the Korean Mathematical Society
• /
• v.27 no.3
• /
• pp.465-475
• /
• 2012

We characterize the fuzzy ideal generated by a fuzzy subset in a semigroup and the fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our work generalizes the characterizations ([8]) of those fuzzy ideals generated by fuzzy subsets in semigroups with an identity element.