Fuzzy linear spaces

Gu, Wei; Tu, Lu

doi:10.1016/0165-0114(92)90288-f

Cited by 13 publications

(8 citation statements)

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“…Nanda [11] introduced the concept of fuzzy linear space. Later Gu Wexiang and Lu [18] redefined the concept of fuzzy field and fuzzy linear space and gave some fundamental properties. Vijaybalaji et al further advanced the theory to cubic linear space combining interval-valued fuzzy linear space and fuzzy linear space and their properties are presented in [17].…”

Section: Introductionmentioning

confidence: 99%

N-Cubic Sets Applied to Linear Spaces

Kavyasree¹,

Reddy²

2022

KgJMat

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The concept of N-fuzzy sets is a good mathematical tool to deal with uncertainties that use the co-domain [−1, 0] for the membership function. The notion of N-cubic sets is defined by combining interval-valued N-fuzzy sets and N-fuzzy sets. Using this N-cubic sets, we initiate a new theory called N-cubic linear spaces. Motivated by the notion of cubic linear spaces we define P-union (resp. R-union), P-intersection (resp. R-intersection) of N-cubic linear spaces. The notion of internal and external N-cubic linear spaces and their properties are investigated.

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Section: Introductionmentioning

confidence: 99%

N-Cubic Sets Applied to Linear Spaces

Kavyasree¹,

Reddy²

2022

KgJMat

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“…In this section the concept of fuzzy set field is introduced which is assumed to generalize a fuzzy field defined by [4]. Since we are dealing with a subset of original field, the axioms imposed on it are similar to that of the ordinary field.…”

Section: Fuzzy Set Fieldmentioning

confidence: 99%

“…This paper is an attempt to define a fuzzy set field in a field which is assumed to be the generalization of a fuzzy field introduced by [4]. We restate fuzzy set in more general form by allowing a particular fuzzy set to consist a family of membership functions.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy Set Field and Fuzzy Metric

Gebray

Reddy

2014

Advances in Fuzzy Systems

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“…Nanda [7] introduced the notion of fuzzy field and fuzzy linear space over a fuzzy field. Wenxiang and Lu [8] redefined the concepts of fuzzy field and fuzzy linear space. Vijayabalaji et al [9] introduced the notion of interval-valued fuzzy linear subspace and interval-valued fuzzy -normed linear space.…”

Section: Introductionmentioning

confidence: 99%

A Cubic Set Theoretical Approach to Linear Space

Vijayabalaji

Sivaramakrishnan²

2015

Abstract and Applied Analysis

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The main motivation of this paper is to introduce the notion of cubic linear space. This inspiration is received from the structure of cubic sets. The notions of R-intersection, R-union, P-intersection, and P-union of cubic linear spaces are defined and we provide some results on these. We further introduce the notion of internal cubic linear space and external cubic linear space and establish some results on them.

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Fuzzy linear spaces

Cited by 13 publications

References 1 publication

N-Cubic Sets Applied to Linear Spaces

N-Cubic Sets Applied to Linear Spaces

Fuzzy Set Field and Fuzzy Metric

A Cubic Set Theoretical Approach to Linear Space

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