• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.85-98
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• 2022

The purpose of this paper is to introduce the notion of Fermatean fuzzy topological space by motivating from the notion of intuitionistic fuzzy topological space, and define Fermatean fuzzy continuity of a function defined between Fermatean fuzzy topological spaces. For this purpose, we define the notions of image and the pre-image of a Fermatean fuzzy subset with respect to a function and we investigate some basic properties of these notions. We also construct the coarsest Fermatean fuzzy topology on a non-empty set X which makes a given function f from X into Y a Fermatean fuzzy continuous where Y is a Fermatean fuzzy topological space. Finally, we introduce the concept of Fermatean fuzzy points and study some types of separation axioms in Fermatean fuzzy topological space.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Journal of Advanced Marine Engineering and Technology
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• 제28권8호
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• pp.1299-1312
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• 2004

This paper suggests the simple form of a fuzzy PID controller and describes the design principle, tracking performance, stability analysis and changes of parameters of a suggested fuzzy PID controller. A fuzzy PID controller is derived from the design procedure of fuzzy control. It is well known that a fuzzy PID controller has a simple structure of the conventional PID controller but posses its self-tuning control capability and the gains of a fuzzy PID controller become nonlinear functions of the inputs. Nonlinear calculation during fuzzification, defuzzification and the fuzzy inference require more time in computation. To increase the applicability of a fuzzy PID controller to digital computer, a simple form of a fuzzy PID controller is introduced by the backward difference mapping and the analysis of the fuzzy input space. To guarantee the BIBO stability of a suggested fuzzy PID controller, ‘small gain theorem’ which proves the BIBO stability of a fuzzy PI and a fuzzy PD controller is used. After a detailed stability analysis using ‘small gain theorem’, from which a simple and practical method to decide the parameters of a fuzzy PID controller is derived. Through the computer simulations for the linear and nonlinear plants, the performance of a suggested fuzzy PID controller will be assured and the variation of the gains of a fuzzy PID controller will be investigated.

• 한국지능시스템학회논문지
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• 제19권2호
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• pp.265-272
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• 2009

Fuzzy number intuitionistic fuzzy sets (FNIFSs), each of which is characterized by a membership function and a non-membership function whose values are trigonometric fuzzy number rather than exact numbers, are a very useful means to describe the decision information in the process of decision making. Wang [10] developed some arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator. In this paper, based on the FIFHA operator and the FIFWA operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as fuzzy number intuitionistic fuzzy decision matrices where each of the elements is characterized by fuzzy number intuitionistic fuzzy numbers, and the information about attribute weights is partially known. An example is used to illustrate the applicability of the proposed approach.

• 호남수학학술지
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• 제26권2호
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• pp.163-192
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• 2004

In this paper, we introduce the concepts of intuitionistic fuzzy subspaces, intuitionistic fuzzy topological groups and intuitionistic fuzzy quotient groups. And we investigate some of their properties.

• 충청수학회지
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• 제30권2호
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• pp.213-226
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• 2017

The concept of fuzzy transitive filters is introduced in BE-algebras. Some sufficient conditions are established for every fuzzy filter of a BE-algebra to become a fuzzy transitive filter. Some properties of fuzzy transitive filters are studied with respect to fuzzy relations and cartesian products.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권4호
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• pp.303-307
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• 2010

In this paper, we introduce the concept of fuzzy weakly r-minimal continuous function between a fuzzy r-minimal space and a fuzzy topological space. We investigate characterizations and some properties for the continuity.

• Korean Journal of Mathematics
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• 제10권2호
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• pp.131-140
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• 2002

This paper is devoted to the study of the role of fuzzy proximity spaces. We define a fuzzy K-proximity space, a fuzzy R-proximity space and prove some of its properties. Furthermore, we discuss the topological structure based on these fuzzy K-proximity and fuzzy R-proximity.

• Korean Journal of Mathematics
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• 제10권2호
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• pp.149-155
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• 2002

We develop some basic properties of $t$-fuzzy ideals in a monoid or a group and find the sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy subring and the necessary and sufficient conditions for a fuzzy set in a division ring to be a $t$-fuzzy ideal.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.77-82
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• 1996

We introduce the concepts of fuzzy $s$-continuous functions. And we investigate several properties of the fuzzy $s$-continuous function. In particular, we study the relation between fuzzy continuous functions and fuzzy $s$-continuous functions.