• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.35-51
• /
• 2004

We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F(S) and F(C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.

• Korean Journal of Logic
• /
• v.17 no.1
• /
• pp.181-196
• /
• 2014

This paper deals with Kripke-style semantics for fuzzy logics. More exactly, I introduce algebraic Kripke-style semantics for some weakening-free extensions of the uninorm based fuzzy logic UL. For this, first, I introduce several weakening-free extensions of UL, define their corresponding algebraic structures, and give algebraic completeness. Next, I introduce several algebraic Kripke-style semantics for those systems, and connect these semantics with algebraic semantics.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.13 no.5
• /
• pp.614-620
• /
• 2003

The aim of this paper is to introduce good definitions of compactness, almost compactness, near compactness, weak compactness, and S-closedness in fuzzy topological spaces in Sostak s sense. These compactness related concepts are defined for arbitrary fuzzy sets and some of their properties studied.

• Korean Journal of Logic
• /
• v.12 no.1
• /
• pp.89-110
• /
• 2009

This paper investigates generalizations of weakening-free uninorm logics not assuming associativity of intensional conjunction (so called fusion) &, as non-associative fuzzy-relevance logics. First, the strong t-associative monoidal uninorm logic StAMUL and its schematic extensions are introduced as non-associative propositional fuzzy-relevance logics. (Non-associativity here means that, differently from classical logic, & is no longer associative.) Then the algebraic structures corresponding to the systems are defined, and algebraic completeness results for them are provided. Next, predicate calculi corresponding to the propositional systems introduced here are considered.

• Communications of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.265-277
• /
• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

• Korean Journal of Logic
• /
• v.19 no.3
• /
• pp.437-461
• /
• 2016

This paper investigates weakening-free fuzzy logics with three weak forms of associativity (of multiplicative conjunction &). First, the wta-uninorm (based) logic $WA_tMUL$ and its two axiomatic extensions are introduced as weakening-free weakly associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness is established for $WA_tMUL$ and the two axiomatic extensions with an additional axiom using construction in the style of Jenei-Montagna.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.14 no.2
• /
• pp.125-129
• /
• 2004

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic fuzzy sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.05a
• /
• pp.12-15
• /
• 2001

There are several kinds of fuzzy set extensions in the fuzzy set theory. Among them, this paper is concerned with interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets. In interval-valued fuzzy sets, membership degrees are represented by an interval value that reflects the uncertainty in assigning membership degrees. In intuitionistic sets, membership degrees are described with a pair of a membership degree and a nonmembership degree. In bipolar-valued fuzzy sets, membership degrees are specified by the satisfaction degrees to a constraint and its counter-constraint. This paper investigates the similarities and differences among these fuzzy set representations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.09a
• /
• pp.1-6
• /
• 2003

Associations, as specific forms of knowledge, reflect relationships among items in databases, and have been widely studied in the fields of knowledge discovery and data mining. Recent years have witnessed many efforts on discovering fuzzy associations, aimed at coping with fuzziness in knowledge representation and decision support processes. This paper focuses on associations of three kinds, namely, association rules, functional dependencies and pattern associations, and overviews major fuzzy logic extensions accordingly.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.2 no.1
• /
• pp.65-69
• /
• 2002

The main drawback of “classical”fuzzy systems is the inability to design and maintain their database. To overcome this disadvantage many types of extensions adding the adaptivity property to those systems were designed. This paper deals with one of them a new hybrid adaptation structure, called gradient-incremental adaptive fuzzy controller connecting gradient-descent methods with the so-called self-organizing fuzzy logic controller designed by Procyk and Mamdani. The aim is to incorporate the advantages of both Principles. This controller was implemented and tested on the system of LEGO robots. The results and comparison to a ‘classical’(non-adaptive) fuzzy controller designed by a human operator are also shown here.