• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.2
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• pp.212-217
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• 2012

A fuzzy set $A$ defined on a probability space ${\Omega}$, $\mathfrak{F}$, $P$ is called a fuzzy event. Zadeh defines the probability of the fuzzy event $A$ using the probability $P$. We define the generalized triangular fuzzy set and apply the extended algebraic operations to these fuzzy sets. A generalized triangular fuzzy set is symmetric and may not have value 1. For two generalized triangular fuzzy sets $A$ and $B$, $A(+)B$ and $A(-)B$ become generalized trapezoidal fuzzy sets, but $A({\cdot})B$ and $A(/)B$ need not to be a generalized triangular fuzzy set or a generalized trapezoidal fuzzy set. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized triangular fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.3
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• pp.389-394
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• 2011

The notion of generalized intuitionistic fuzzy soft set theory is proposed. Our generalized intuitionistic fuzzy soft set theory is a combination of the generalized intuitionistic fuzzy set theory and the soft set theory. In other words, our generalized intuitionistic fuzzy soft set theory is an extension of the intuitionistic fuzzy soft set theory. The complement, "and" and "or" operations are defined on the generalized intuitionistic fuzzy soft sets. Their basic properties for the generalized intuitionistic fuzzy soft sets are also presented and discussed.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.443-458
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• 2022

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.525-535
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• 2016

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.1
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• pp.79-86
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• 2015

This paper is devoted to finding relationship between intuitionistic fuzzy preorders and intuitionistic fuzzy topologies. For any intuitionistic fuzzy preordered space, an intuitionistic fuzzy topology will be constructed. Conversely, for any intuitionistic fuzzy topological space, we obtain an intuitionistic fuzzy preorder on the set. Moreover, we will show that the family of all intuitionistic fuzzy preorders on an underlying set has a very close link to the family of all intuitionistic fuzzy topologies on the set satisfying some extra condition.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.297-308
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• 2013

We define one-sided quadrangular fuzzy sets, a left quadrangular fuzzy set and a right quadrangular fuzzy set. And then we generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two one-sided quadrangular fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two one-sided quadrangular fuzzy sets becomes a triangular fuzzy number.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.2
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• pp.200-209
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• 2004

The fuzzy control based on $\alpha$-level fuzzy set decomposition. It is known to produce quick response and calculating time of fuzzy inference. This paper derived the embodiment computational algorithm for defuzzification by min-max fuzzy inference and the center of gravity method based on $\alpha$-level fuzzy set decomposition. It is easy to realize the fuzzy controller hardware. based on the calculation formula. In addition. this study proposed a circuit that generates PWM actual signals ranging from fuzzy inference to defuzzification. The fuzzy controller was implemented with mixed analog-digital logic circuit using the computational fuzzy inference algorithm by min-min-max and defuzzification by the center of gravity method. This study confirmed that the fuzzy controller worked satisfactorily when it was applied to the position control of a dc servo system.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.341-355
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• 2003

The fuzzification of ${\bigotimes}-closed$ set is considered, and its basic properties we investigated. Characterizations of fuazzy ${\bigotimes}-closed$ set we given. Using a collection of ${\bigotimes}-closed$ sets with additional conditions, a fuzzy ${\bigotimes}-closed$ set is stated. The theory of fuzzy topological ${\bigotimes}-closed$ sets is discussed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.353-356
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• 2001

In this paper, we study the existence of fuzzy solution for the following differential system with fuzzy coefficient using the different two methods: (equation omitted), where a, b is the fuzzy natural number generated by fuzzy number l . The a-level set of the fuzzy number (equation omitted). The -level set of a is (equation omitted) and -level set of b is (equation omitted).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.11a
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• pp.252-255
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• 1997

In this paper, we will propose the methodology of data analysis using the fuzzy property set model. In real world, the data can be represented with the object. $\theta$. and the property, $\pi$, and its has-property relation, P. Then, the conceptual space can be defined with the chosen properties. Each object has a unique location in the conceptual space. In Fuzzy mode, the fuzzy property, and fuzzy conceptual space can be redefined. To analyze data using the fuzzy property set model, the rough set need to be defined in the fuzzy conceptual space.