• Honam Mathematical Journal
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• v.31 no.3
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• pp.351-368
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• 2009

Quick ideals and the fuzzification of quick ideals in d-algebras are considered, and some related properties are investigated. The intuitionistic fuzzification of quick ideals of a d-algebra is established, and related results are studied. The notion of equivalence relations on the family of all intuitionistic fuzzy quick ideals of a d-algebra is introduced, and then some properties are discussed.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.461-468
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• 2008

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.261-272
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• 2001

The intuitionistic fuzzification of a subalgebra in a BCK/BCI-algebra is considered, and related results are investigated. The notion of equivalence relations on the family of all intuitionistic fuzzy subalgebras of a BCK/BCI-algebra is introduced, and then some properties are discussed.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.215-225
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• 2017

In this paper, we study some equivalence relations between continuous frames in a Hilbert space ${\mathcal{H}}$. In particular, we seek two necessary and sufficient conditions under which two continuous frames are near. Moreover, we investigate a distance between continuous frames in order to acquire the closest and nearest tight continuous frame to a given continuous frame. Finally, we implement these results for shearlet and wavelet frames in two examples.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.9-30
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• 2005

The notion of intuitionistic fuzzy convex sublattices is introduced, and its characterization is given. Natural equivalence relations on the set of all intuitionistic fuzzy ideals/filters of a lattice are investigated. Operations on intuitionistic fuzzy sets of a lattice is introduced. Some results of intuitionistic fuzzy ideals/filters under these operations are provided. Using these operations, characterizations of intuitionistic fuzzy ideals/filters are given.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.91-98
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• 2007

We give definitions of hyperholomorphic functions of quaternionic functions of two quaternionic variables. We investigate properties of hyperholomorphic functions on quaternion analysis, and obtain equivalence relations for domains of hyperholomorphy and hyper Stein domains in a domain of $C^2{\times}C^2$.

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

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.373-378
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• 1994

This paper is concerned with assess the possibility of robust pole assignment of proportional integral(PI) state feedback control system. First, the equivalence relations between a PI control system and an argumented control system proposed by Kawaji and Kim(1994) are extended from the new points of views of invariant closed loop poles. Second, on the relations, a remarkable result that the integral gain of PI control system is directly related to the insensitivity of system is presented. And, it is shown that the design of robust PI pole assignment is possible under the certain conditions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.1
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• pp.26-32
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• 2002

The objectives of this paper are twofold. First is to introduce a model for representing documents with semantics relatedness using rough sets but with tolerance relations instead of equivalence relations (TRSM). Second is to introduce two document hierarchical and nonhierarchical clustering algorithms based on this model and TRSM cluster-based information retrieval using these two algorithms. The experimental results show that TRSM offers an alterative approach to text clustering and information retrieval.

• Journal of the Korean Institute of Telematics and Electronics
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• v.12 no.2
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• pp.11-17
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• 1975

The paper examined the character structure as a basic study for the recognition of Korean characters. In view of concave structure, line structure and node relationship of character graph, the algebraic structure of the basic Korean characters is are analized. Also, the degree of complexities in their character structure is discussed and classififed. Futhermore, by describing the fact that some equivalence relations are existed between the 10 vowels of rotational transformation group by Affine transformation of one element into another, it could be pointed out that the geometrical properting in addition to the topological properties are very important for the recognition of Korean characters.