Near Fixed Point Theorems in the Space of Fuzzy Numbers

Wu, Chong

doi:10.3390/math6070108

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…For example, the space consisting of all subsets of R cannot satisfy all of the axioms in vector space (Wu [6]). Also, the space consisting of all fuzzy numbers in R cannot satisfy all of the axioms in vector space, where the addition and scalar multiplication of fuzzy sets are considered (Wu [7]). The main reason is that the additive inverse element does not exist.…”

Section: Introductionmentioning

confidence: 99%

Informal Complete Metric Space and Fixed Point Theorems

2019

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The concept of informal vector space is introduced in this paper. In informal vector space, the additive inverse element does not necessarily exist. The reason is that an element in informal vector space which subtracts itself cannot be a zero element. An informal vector space can also be endowed with a metric to define a so-called informal metric space. The completeness of informal metric space can be defined according to the similar concept of a Cauchy sequence. A new concept of fixed point and the related results are studied in informal complete metric space.

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Section: Introductionmentioning

confidence: 99%

Informal Complete Metric Space and Fixed Point Theorems

2019

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“…The properties of fuzzy numbers and the arithmetic of fuzzy quantities (or fuzzy numbers) have been studied for a long time. The interesting issue for studying the additive inverse of a fuzzy number may refer to Hong and Do [1], Vrba [2] and Wu [3,4]. Also, Anzilli and Facchinetti [5], Bodjanova [6], Dubois and Prade [7] investigated the median, mean and variance of fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Duality in Fuzzy Sets and Dual Arithmetics of Fuzzy Sets

2018

Mathematics

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The conventional concept of α-level sets of fuzzy sets will be treated as the upper α-level sets. In this paper, the concept of lower α-level sets of fuzzy sets will be introduced, which can also be regarded as a dual concept of upper α-level sets of fuzzy sets. We shall also introduce the concept of dual fuzzy sets. Under these settings, we can establish the so-called dual decomposition theorem. We shall also study the dual arithmetics of fuzzy sets in R and establish some interesting results based on the upper and lower α-level sets.

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Near fixed point theorems in near Banach spaces

2023

MATH

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<abstract><p>The near vector space in which the additive inverse element does not necessarily exist is introduced in this paper. The reason is that an element in a near vector space which subtracts itself may not be a zero element. Therefore, the concept of a null set is introduced in this paper to play the role of a zero element. A near vector space can also be endowed with a norm to define a so-called near normed space. Based on this norm, the concept of a Cauchy sequence can be similarly defined. A near Banach space can also be defined according to the concept of completeness using the Cauchy sequences. The main aim of this paper is to establish the so-called near fixed point theorems and Meir-Keeler type of near fixed point theorems in near Banach spaces.</p></abstract>

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Near Fixed Point Theorems in the Space of Fuzzy Numbers

Cited by 3 publications

References 18 publications

Informal Complete Metric Space and Fixed Point Theorems

Informal Complete Metric Space and Fixed Point Theorems

Duality in Fuzzy Sets and Dual Arithmetics of Fuzzy Sets

Near fixed point theorems in near Banach spaces

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