On fuzzy number lattice (R̃, ≤)

Kun Lun Zhang; Kaoru Hirota

doi:10.1016/S0165-0114(96)00164-9

On fuzzy number lattice (R̃, ≤)

Kun Lun Zhang
, Kaoru Hirota

Inner Mongolia University
Tokyo Institute of Technology

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

We give a systematic development of fuzzy number lattice theory. Many of our results generalize to number lattice over the lattice algebra. Our first main result is that the real number chain (R, ≤) is a homomorphic image of the fuzzy number lattice (R̃, ≤) (that is, R̃/Θ ≅ R), and the congruence class [á]Θ(∀ãεR̃) is a component of (R̃, ≤). Thus, we can be specialized to describe the structure of the fuzzy number lattice (R̃, ≤). Next we study the structure and representation of the congruence class [ã].

Original language	English
Pages (from-to)	113-122
Number of pages	10
Journal	Fuzzy Sets and Systems
Volume	92
Issue number	1
DOIs	https://doi.org/10.1016/S0165-0114(96)00164-9
Publication status	Published - 1997
Externally published	Yes

Keywords

Fuzzy number
Fuzzy number lattice
Lattice

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10.1016/S0165-0114(96)00164-9

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abstract = "We give a systematic development of fuzzy number lattice theory. Many of our results generalize to number lattice over the lattice algebra. Our first main result is that the real number chain (R, ≤) is a homomorphic image of the fuzzy number lattice ({\~R}, ≤) (that is, {\~R}/Θ ≅ R), and the congruence class [{\'a}]Θ(∀{\~a}ε{\~R}) is a component of ({\~R}, ≤). Thus, we can be specialized to describe the structure of the fuzzy number lattice ({\~R}, ≤). Next we study the structure and representation of the congruence class [{\~a}].",

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AU - Zhang, Kun Lun

AU - Hirota, Kaoru

PY - 1997

Y1 - 1997

N2 - We give a systematic development of fuzzy number lattice theory. Many of our results generalize to number lattice over the lattice algebra. Our first main result is that the real number chain (R, ≤) is a homomorphic image of the fuzzy number lattice (R̃, ≤) (that is, R̃/Θ ≅ R), and the congruence class [á]Θ(∀ãεR̃) is a component of (R̃, ≤). Thus, we can be specialized to describe the structure of the fuzzy number lattice (R̃, ≤). Next we study the structure and representation of the congruence class [ã].

AB - We give a systematic development of fuzzy number lattice theory. Many of our results generalize to number lattice over the lattice algebra. Our first main result is that the real number chain (R, ≤) is a homomorphic image of the fuzzy number lattice (R̃, ≤) (that is, R̃/Θ ≅ R), and the congruence class [á]Θ(∀ãεR̃) is a component of (R̃, ≤). Thus, we can be specialized to describe the structure of the fuzzy number lattice (R̃, ≤). Next we study the structure and representation of the congruence class [ã].

KW - Fuzzy number

KW - Fuzzy number lattice

KW - Lattice

UR - https://www.scopus.com/pages/publications/0000870953

U2 - 10.1016/S0165-0114(96)00164-9

DO - 10.1016/S0165-0114(96)00164-9

M3 - Article

AN - SCOPUS:0000870953

SN - 0165-0114

VL - 92

SP - 113

EP - 122

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

IS - 1

ER -

On fuzzy number lattice (R̃, ≤)

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Keywords

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