• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.4
• /
• pp.550-556
• /
• 2007

In this paper, we introduce the concepts of fuzzy (r, s)-semi-preopen sets and fuzzy (r, s)-semi-precontinuous mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense. The relations among fuzzy (r, s)-semicontinuous, fuzzy (r, s)-precontinuous, and fuzzy (r, s)-semi-precontinuous mappings we discussed. The concepts of fuzzy (r, s)-semi-preinterior, fuzzy (r, s)-semi-preclosure, fuzzy (r, s)-semi-preneighborhood, and fuzzy (r, s)-quasi-semi-preneighborhood are given. Using these concepts, the characterization for the fuzzy (r, s)-semi-precontinuous mapping is obtained. Also, we introduce the notions of fuzzy (r, s)-semi-preopen and fuzzy (r, s)-semi-preclosed mappings on intuitionistic fuzzy topological spaces in ${\check{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• Journal of applied mathematics & informatics
• /
• v.40 no.1_2
• /
• pp.85-98
• /
• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.129-130
• /
• 2008

In this paper, we introduce the concept of generalized fuzzy (r,s)-closed sets on intuitionistic fuzzy topological spaces in ${\v{S}ostak's$ sense. Using this concept, we introduce the notions of generalized fuzzy (r,s)-continuous mappings, and then we investigate some of their properties.

• Journal of Information Processing Systems
• /
• v.15 no.4
• /
• pp.986-1016
• /
• 2019

Mobile user interface pattern (MUIP) is a kind of structured representation of interaction design knowledge. Several studies have suggested that MUIPs are a proven solution for recurring mobile interface design problems. To facilitate MUIP selection, an effective clustering method is required to discover hidden knowledge of pattern data set. In this paper, we employ the semi-supervised kernel fuzzy c-means clustering (SSKFCM) method to cluster MUIP data. In order to improve the performance of clustering, clustering parameters are optimized by utilizing the global optimization capability of particle swarm optimization (PSO) algorithm. Since the PSO algorithm is easily trapped in local optima, a novel PSO algorithm is presented in this paper. It combines an improved intuitionistic fuzzy entropy measure and a new population search strategy to enhance the population search capability and accelerate the convergence speed. Experimental results show the effectiveness and superiority of the proposed clustering method.

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

• Communications for Statistical Applications and Methods
• /
• v.19 no.3
• /
• pp.359-365
• /
• 2012

The fuzzy set framework has a number of properties that make it suitable to formulize uncertain information in medical diagnosis. This study introduces a fuzzy diagnostic method based on the interval-valued interview chart and the interval-valued intuitionistic fuzzy weighted arithmetic average(IIFWAA) operator. An issue in the use of the IIFWAA operator is to determine the weights. In this study, we propose the occurrence information of symptoms as the weights. An illustrative example is provided to demonstrate its practicality and effectiveness.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.29-32
• /
• 2003

We introduce the subcategories IRe $l_{PR}$ (H), IRe $l_{PO}$ (H) and IRe $l_{E}$(H) of IRe $l_{R}$(H) and study their structures in a viewpoint of the topological universe introduced by L.D.Nel. In particular, the category IRe $l_{R}$(H)(resp. IRe $l_{P}$(H) and IRe $l_{E}$(H)) is a topological universe eve, Set. Moreover, we show that IRe $l_{E}$(H) has exponential objects.ial objects.