Cut Sets on Trapezoidal Fuzzy Number and Intuitionistic Fuzzy Number: A New Perspective

Anand, M. Clement Joe; Bharatraj, Janani

doi:10.12732/ijpam.v112i4.7

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…Furthermore, the interval algebra in parametric form, as given by [1,11,13,20,56], is as follows: Definition 3 ([32,37,51]). For two parametric forms of fuzzy numbers…”

Section: Definition 1 ([1-6]) a Fuzzy Setmentioning

confidence: 99%

The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations

Mashadi,

Safitri,

Sukono

et al. 2024

Mathematics

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Trapezoidal positive/negative fuzzy numbers have no single definition; instead, various authors define them in relation to different concepts. This means that arithmetic operations for trapezoidal fuzzy numbers also differ. For the operations of addition, subtraction, and scalar multiplication, there are not many differences; for multiplication, however, there are many differences. In general, multiplication is divided into various cases. For the inverse operation, there is not much to define; in general, for any trapezoidal fuzzy number u~, u~⊗1u~=i~=(1,1,0,0) does not necessarily apply. As a result of the different arithmetic operations for multiplication and division employed by various authors, several researchers have tackled the same problem and reached different solutions, meaning that the application will also produce different results. To date, many authors have proposed various alternatives for the algebra of the trapezoidal fuzzy number. In this paper, using the parametric form approach to trapezoidal fuzzy numbers, an alternative to multiplication with only one formula is constructed for various cases. Furthermore, based on the definition of multiplication for any trapezoidal fuzzy number, u~ is constructed 1u~ so that u~⊗1u~=i~=(1,1,0,0). Based on these conditions, we show that various properties that apply to real numbers also apply to any trapezoidal fuzzy number. Furthermore, we modify the elementary row operational steps for the trapezoidal fuzzy number matrix, which can be used to determine the inverse of a trapezoidal fuzzy number matrix with the order m×m. We also give the steps and examples necessary to determine the general inverse for a trapezoidal fuzzy number matrix of the order m×n with m ≠n. This ability to easily determine the inverse and general inverse of a trapezoidal fuzzy number matrix has a number of applications, such as solving fully trapezoidal fuzzy number linear systems and fuzzy transportation problems, especially in applications in fields outside of mathematics; for example, the application of triangular fuzzy numbers in medical problems is a topic currently receiving a significant amount of attention.

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“…Furthermore, the interval algebra in parametric form, as given by [1,11,13,20,56], is as follows: Definition 3 ([32,37,51]). For two parametric forms of fuzzy numbers…”

Section: Definition 1 ([1-6]) a Fuzzy Setmentioning

confidence: 99%

The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations

Mashadi,

Safitri,

Sukono

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

“…In such cases, fuzzy numbers have been used to obtain better results in problems where decision making and analysis are involved. A fuzzy number, which is an extension of a real number, has its own properties that can be related to number theory [2]. The concept of the fuzzy derivative was introduced by many researchers (see, for example [3]), while in [4], the authors proposed a new concept of derivatives based on the Hukuhara difference.…”

Section: Introductionmentioning

confidence: 99%

Numerical Treatment of Hybrid Fuzzy Differential Equations Subject to Trapezoidal and Triangular Fuzzy Initial Conditions Using Picard’s and the General Linear Method

2022

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We study hybrid fuzzy differential equations (HFDEs) under the Hukuhara derivative numerically using Picard’s and the general linear method (GLM). We use trapezoidal and triangular fuzzy numbers as the initial conditions. To demonstrate the efficiency of the proposed methods, the exact as well as the numerical solutions are presented numerically and graphically. In addition, a comparison is made between the results from applying the GLM and those obtained when applying the fifth order Runge–Kutta method as reported in the literature.

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Sustainable Component and Supplier Selection: Application on Data Center Design

AlShamsi,

Aydin,

Cheaitou

2023

2023 9th International Conference on Optimization and Applications (ICOA)

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Cut Sets on Trapezoidal Fuzzy Number and Intuitionistic Fuzzy Number: A New Perspective

Cited by 3 publications

References 7 publications

The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations

The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations

Numerical Treatment of Hybrid Fuzzy Differential Equations Subject to Trapezoidal and Triangular Fuzzy Initial Conditions Using Picard’s and the General Linear Method

Sustainable Component and Supplier Selection: Application on Data Center Design

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