arXiv subjects

Young Bae Jun

Publications and source records attributed to Young Bae Jun.

5 recordsLinked to original sources

arXiv2026

Fuzzy normed BCK-algebras and BCI-algebras

In this paper, we introduce and study the notion of fuzzy normed BCK-algebras and fuzzy normed BCI-algebras as a natural extension of clas sical normed algebraic structures into the fuzzy setting. A fuzzy norm on a BCK/BCI-algebra is defined as a mapping from the algebra and a positive real parameter into the unit interval satisfying suitable axioms analogous to those of fuzzy normed linear spaces. Several examples are presented to illustrate the validity of the axioms. Fundamental properties of fuzzy normed BCK/BCI algebras are established, including monotonicity, chained triangle inequalities, and order-related behaviors. It is shown that every BCK/BCI-algebra admits a fuzzy norm, and the behavior of fuzzy norms under algebra homomorphisms is investigated. Necessary and sufficient conditions are obtained for the transfer of fuzzy norms via injective, surjective, and bijective homomorphisms. A charac terization theorem is proved showing that the main fuzzy norm inequality can be reduced to a simpler condition. These results generalize known concepts in fuzzy algebra and provide a new analytical framework for studying BCK/BCI algebras.

math.GM↗

arXiv2023

Ordered homomorphisms and kernels of ordered BCI-algebras

Recently Yang-Roh-Jun introduced the notion of ordered BCI-algebras as a generalization of BCI-algebras. They also introduced the notions of homomorphisms and kernels of ordered BCI-algebras and investigated related properties. Here we extend their investigation to ordered homomorphisms, i.e., order-preserving homomorphisms. To this end, the notions of ordered homomorphism and kernel of ordered BCI-algebras are first defined. Next, properties associated with (ordered) subalgebras, (ordered) filters and direct products of ordered BCI-algebras are addressed.

math.RA↗

arXiv2015

Characterizations of Fuzzy Fated Filters of $R_0$-algebras Based on Fuzzy Points

The most general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of $R_0$-algebras is discussed. The notion of an $(ε, ε\vee q_k)$-fuzzy fated filter in an $R_0$-algebra is introduced, and several properties are investigated. Characterizations of an $(ε,ε\vee q_k)$-fuzzy fated filter in an $R_0$-algebra are discussed. Using a collection of fated filters, a $(ε,ε\vee q_k)$-fuzzy fated filter is established.

math.GM↗

arXiv2005

Intuitionistic fuzzy $H_v$-submodules

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to $H_v$-modules. The notion of an intuitionistic fuzzy $H_v$-submodule of an $H_v$-module is introduced, and some related properties are investigated. Characterizations of intuitionistic fuzzy $H_v$-submodules are given.

math.GM↗

arXiv2005

On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we consider the intuitionistic fuzzification of the concept of sub-hyperquasigroups in a hyperquasigroup and investigate some properties of such sub-hyperquasigroups. In particular, we investigate some natural equivalence relations on the set of all intuitionistic fuzzy sub-hyperquasigroups of a hyperquasigroup.

math.GM↗