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Jang, Lee-Chae Korean Institute of Intelligent Systems 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.1
Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.
Lee-Chae Jang 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.1
Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.
장이채 한국지능시스템학회 2013 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.13 No.1
Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.
Uniform Hausdorff fuzzy metric on fuzzy sets
Baoqun Xie,Conghua Yan 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.21 No.2
In this paper, the uniform Hausdorff fuzzy metric is constructed in the sense of fuzzy metric spaces. Several topological properties as precompactness, completeness and compactness are investigated. Given a fuzzy metric space, we prove that a self mapping is continuous if and only if its Zadeh's extension is continuous which generated the result of Jardón (2020) [15] and establish a new fixed point theorem for fuzzy mapping. In this paper, the uniform Hausdorff fuzzy metric is constructed in the sense of fuzzy metric spaces. Several topological properties as precompactness, completeness and compactness are investigated. Given a fuzzy metric space, we prove that a self mapping is continuous if and only if its Zadeh's extension is continuous which generated the result of Jardón (2020) [15] and establish a new fixed point theorem for fuzzy mapping
HAUSDORFF TOPOLOGY INDUCED BY THE FUZZY METRIC AND THE FIXED POINT THEOREMS IN FUZZY METRIC SPACES
WU, HSIEN-CHUNG Korean Mathematical Society 2015 대한수학회지 Vol.52 No.6
The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.
HAUSDORFF TOPOLOGY INDUCED BY THE FUZZY METRIC AND THE FIXED POINT THEOREMS IN FUZZY
Hsien-Chung Wu 대한수학회 2015 대한수학회지 Vol.52 No.6
The Hausdorff topology induced by a fuzzy metric space un- der more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy met- ric space based on a natural concept of Cauchy sequence in fuzzy metric space.
CONVERGENCE IN METRIC DIFFERENTIAL GEOMETRY
Kim, Young-Wook,Lee, Hyoung-Yong Korean Mathematical Society 2003 대한수학회논문집 Vol.18 No.1
We use geometric properties of Gromov-Hausdorff-convergence to present a way to construct rough but natural invariants of metric geometry.
FIXED POINT OF α - ψ - CONTRACTIVE MULTIFUNCTION IN FUZZY METRIC SPACES
KUMAR, MOHIT,ARORA, RIITU The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.3
Recently Samet, Vetro and Vetro introduced the notion of ${\alpha}$-${\Psi}$-contractive type mappings and initiated some fixed point theorems in complete metric spaces. The notion of ${\alpha}_*$ - ${\Psi}$-contractive multifunctions and initiated some fixed point results by Hasanzade Asl et. al. [8]. In this paper, we introduced the notion of ${\alpha}_*$ - ${\Psi}$-contractive multifunctions in a fuzzy metric space and gave fixed point results for these multifunctions in complete fuzzy metric spaces. We also obtain a fixed point results for self-maps in complete fuzzy metric spaces satisfying contractive condition.
Some fixed fuzzy point results using Hausdorff metric in fuzzy metric spaces
Ferhan Sola Erduran,Cemil Yi Idiz 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.13 No.5
In this paper, we obtain coupled fixed fuzzy point theorem for a fuzzy mapping in Hausdorff fuzzy metric space and using it, we obtain a common fixed fuzzy point for a hybrid fuzzy pair. Also we give an auxiliary example to support our main theorem.