• Korean Journal of Mathematics
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• v.17 no.2
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• pp.161-167
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• 2009

Category Fuz of fuzzy sets has a similar function to the Category Set. We study injective, absolute retract, enough injectives, injective hulls and essential extension in the Category Fuz of fuzzy sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.216-221
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• 2014

In this paper, we introduce the concept of generalized double fuzzy semi-basically disconnected space and related notions such as (r, s)-generalized fuzzy semiopen-$F_{\sigma}$ sets, (r, s)-generalized fuzzy semiclosed-$G_{\delta}$ sets, generalized double fuzzy $semi^*$-open function, generalized double fuzzy $semi^*$-continuous function and generalized double fuzzy $semi^*$-irresolute function. Some interesting properties and characterizations of the concepts introduced are studied.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.82-100
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• 2024

The main objective of the study is to introduce ideals of Sheffer stroke Hilbert algebras by means of fuzzy points, and investigate some properties. The process of making (fuzzy) ideals and fuzzy deductive systems through the fuzzy points of Sheffer stroke Hilbert algebras is illustrated, and the (fuzzy) ideals and the fuzzy deductive systems are characterized. Certain sets are defined by virtue of a fuzzy set, and the conditions under which these sets can be ideals are revealed. The union and intersection of two fuzzy ideals are analyzed, and the relationships between aforementioned structures of Sheffer stroke Hilbert algebras are built.

• Journal of Korea Multimedia Society
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• v.7 no.4
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• pp.559-566
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• 2004

In general, the certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions appearing in the rules are represented by real values between zero and one. If it can allow the certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions to be represented by interval -valued fuzzy sets, then it can allow the reasoning of rule-based systems to perform fuzzy reasoning in more flexible manner. This paper presents fuzzy Petri nets and proposes an interval-valued fuzzy backward reasoning algorithm for rule-based systems based on fuzzy Petri nets Fuzzy Petri nets model the fuzzy production rules in the knowledge base of a rule-based system, where the certainty factors of the fuzzy propositions appearing in the fuzzy production rules and the certainty factors of the rules are represented by interval-valued fuzzy sets. The algorithm we proposed generates the backward reasoning path from the goal node to the initial nodes and then evaluates the certainty factor of the goal node. The proposed interval-valued fuzzy backward reasoning algorithm can allow the rule-based systems to perform fuzzy backward reasoning in a more flexible and human-like manner.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.8
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• pp.1615-1623
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• 2009

In order to develop reliable on-site partial discharge (PD) pattern recognition algorithm, we introduce Type-2 Fuzzy Neural Networks (T2FNNs) optimized by means of Particle Swarm Optimization(PSO). T2FNNs exploit Type-2 fuzzy sets which have a characteristic of robustness in the diverse area of intelligence systems. Considering the on-site situation where it is not easy to obtain voltage phases to be used for PRPDA (Phase Resolved Partial Discharge Analysis), the PD data sets measured in the laboratory were artificially changed into data sets with shifted voltage phases and added noise in order to test the proposed algorithm. Also, the results obtained by the proposed algorithm were compared with that of conventional Neural Networks(NNs) as well as the existing Radial Basis Function Neural Networks (RBFNNs). The T2FNNs proposed in this study were appeared to have better performance when compared to conventional NNs and RBFNNs.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.897-914
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• 2022

Pythagorean fuzzy sets (PFSs) are capable of modelling information with more uncertainties in decision-making problems. The essential feature of PFSs is that they are described by three parameters: membership function, non-membership function and hesitant margin, with the total of the squares of each parameter equal to one. The purpose of this article is to suggest some new similarity measures and weighted similarity measures for PFSs. Numerical computations have been carried out to validate our proposed measures. Applications of these measures have been applied to some real-life decision-making problems of pattern detection and medicinal investigations. Moreover, a descriptive illustration is employed to compare the results of the proposed measures with the existing analogous similarity measures to show their effectiveness.

• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.625-631
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• 2004

In general, the certainty factors of the fuzzy production rules and the certainty factors of fuzzy Propositions appearing in the rules are represented by real values between zero and one. If it can allow the certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions to be represented by interval-valued fuzzy sets, then it can allow the reasoning of rule-based systems to perform fuzzy reasoning in more flexible manner(15). This paper presents a fuzzy Petri nets and proposes an interval-valued fuzzy reasoning algorithm for rule-based systems based on fuzzy Petri nets. Fuzzy Petri nets model the fuzzy production rules in the knowledge base of a rule-based system, where the certainty factors of the fuzzy Propositions appearing in the furry production rules and the certainty factors of the rules are represented by interval-valued fuzzy sets. The proposed interval-valued fuzzy set reasoning algorithm can allow the rule-based systems to perform fuzzy reasoning in a more flexible manner.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.4
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• pp.398-402
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• 2014

A generalized trigonometric fuzzy set is a generalization of a trigonometric fuzzy number. Zadeh([7]) defines the probability of the fuzzy event using the probability. We define the normal and exponential fuzzy probability on $\mathbb{R}$ using the normal and exponential distribution, respectively, and we calculate the normal and exponential fuzzy probability for generalized trigonometric fuzzy sets.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.73-84
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• 2008

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 Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to commutative ideals in BCK-algebras. The notion of an intuitionistic fuzzy commutative ideal of a BCK-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy commutative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy commutative ideal are given. Using a collection of commutative ideals, intuitionistic fuzzy commutative ideals are established.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.377-402
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• 2007

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 Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to implicative ideals in BCK-algebras. The notion of an intuitionistic fuzzy implicative ideal of a BCK-algebra is introduced, and some related properties are investigated. An extension property for intuitionistic fuzzy implicative ideals is established. Characterizations of an intuitionistic fuzzy implicative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy implicative ideal are given. Using a collection of implicative ideals, intuitionistic fuzzy implicative ideals are established.