• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.3
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• pp.377-379
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• 2003

In this paper, we define a strong fuzzy hyperK-subalgebra and investigate between a strong fuzzy hyperK-subalgebra and a fuzzy hyperK-subalgebra. And then we give some properties of a weak homomorphism and a strong fuzzy hyperK-subalgebra.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.1-8
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• 2003

In this paper, we further develop the weak polygroup theory, we define quotient weak polygroup and then the fundamental homomorphism theorem of group theory is derived in the context of weak polygroups. Also, we consider the fundamental relation $\beta$$^{*}$ defined on a weak polygroup and define a functor from the category of all weak polygroups into the category of all fundamental groups.s.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.315-325
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• 2006

The notion of intuitionistic fuzzy finite switchboard state machines and (strong) homomorphisms of intuitionistic fuzzy finite state machines are introduced, and related properties are investigated. After we give a congruence relation on the set of all words of elements of X of finite length, the quotient structure is discussed. We show that the family of equivalence classes is a finite semigroup with identity.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.233-245
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• 2019

Cyclic hypergroups are of great importance due to their applications to many field in mathematics. In this paper, we classify all polygroups of order less than six where each of its non-identity elements is a generator.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.2
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• pp.156-160
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• 2001

In this paper we define fuzzy subsystems of a fuzzy finite state machine by using maps $S^{\alpha}$ of each state subset to its all $\alpha$-successors, which is a natural generalization of crisp submachines as fuzzy. And the corresponding concepts are also examined. also examined.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.12
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• pp.4552-4567
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• 2014

A (n,t,n) secret sharing scheme is to share a secret among n group members, where each member also plays a role of a dealer,and any t shares can be used to recover the secret. In this paper, we propose a strong (k,t,n) verifiable multi-secret sharing scheme, where any k out of n participants operate as dealers. The scheme realizes both threshold structure and adversary structure simultaneously, and removes a trusted third party. The secret reconstruction phase is performed using an additive homomorphism for decreasing the storage cost. Meanwhile, the scheme achieves the pre-verification property in the sense that any participant doesn't need to reveal any information about real master shares in the verification phase. We compare our proposal with the previous (n,t,n) secret sharing schemes from the perspectives of what kinds of access structures they achieve, what kinds of functionalities they support and whether heavy storage cost for secret share is required. Then it shows that our scheme takes the following advantages: (a) realizing the adversary structure, (b) allowing any k out of n participants to operate as dealers, (c) small sized secret share. Moreover, our proposed scheme is a favorable candidate to be used in many applications, such as secure multi-party computation and privacy preserving data mining, etc.