Fuzzy Numbers

Chakraverty, Snehashish; Sahoo, Deepti Moyi; Mahato, Nisha Rani

doi:10.1007/978-981-13-7430-2_3

Cited by 14 publications

(8 citation statements)

References 3 publications

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“…Representation of SGFN [47,48] In the case of SGFN ( ) [47,48] Implementing another parameter β on Equation ( 5), we may have the following expression Note. If σ 1 and σ 2 are the same (i.e., σ 1 = σ 2 = σ) for a Gaussian fuzzy number G, then it is said to be a symmetric Gaussian fuzzy number (SGFN) and is defined by G = sg f n (c, σ).…”

Section: Cut − αmentioning

confidence: 99%

“…2.5. α − Cut Representation of SGFN [47,48] In the case of SGFN G = sg f n (c, σ), the fuzzy interval form using α − cut is obtained as…”

Section: Double Parametric Form Of Sgfnmentioning

confidence: 99%

“…2.6. Double Parametric Form of SGFN [47,48] Implementing another parameter β on Equation ( 5), we may have the following expression…”

Section: Double Parametric Form Of Sgfnmentioning

confidence: 99%

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Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

Sahoo

Chakraverty

2022

Mathematics

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In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots.

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Section: Cut − αmentioning

confidence: 99%

“…2.5. α − Cut Representation of SGFN [47,48] In the case of SGFN G = sg f n (c, σ), the fuzzy interval form using α − cut is obtained as…”

Section: Double Parametric Form Of Sgfnmentioning

confidence: 99%

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Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

Sahoo

Chakraverty

2022

Mathematics

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“…There exist different types of fuzzy numbers that are used to describe vagueness and uncertainty such as triangular fuzzy numbers, trapezoidal fuzzy number, and gaussian fuzzy numbers. In this study, sentiments scores of customer concerns for all extracted review documents are converted into the triangular fuzzy numbers (Chakraverty et al 2019). A triangular fuzzy number can be described as (x, y, z) where x is the left value; y is the central value; and x is the right value.…”

Section: Fuzzification Of Sentiment Scoresmentioning

confidence: 99%

A multigene genetic programming-based fuzzy regression approach for modelling customer satisfaction based on online reviews

2021

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In previous studies, customer survey data were commonly adopted to perform the modelling of customer satisfaction (CS). However, it could be time-consuming to conduct surveys and obtain their data. On the other hand, respondents' responses are quite often confined by pre-set questions. Nowadays, a huge number of customer online reviews on products can be found on various websites. The reviews can be extracted easily in a very short time. Customers can freely express their concerns and views of products in their online reviews. Those reviews provide a valuable source of information for manufacturers to improve their existing products and develop their new products. Previous studies have attempted to develop CS models based on survey data by using various computational intelligence techniques. However, no attempt at developing explicit CS models based on online reviews was reported in literature. In this paper, a methodology for the modelling of CS based on customer online reviews and a multigene genetic programming based fuzzy regression (MGGP-FR) approach is proposed. In the proposed methodology, relevant textual reviews of products are extracted from e-commerce websites. Then, opinion mining is conducted on the reviews and sentiments scores of customer concerns are derived. A MGGP-FR approach is then introduced to develop CS models based on the derived sentiment scores. A case study on developing CS models for electronic hairdryers is conducted to illustrate the proposed methodology and validate the effectiveness of MGGP-FR in the modelling of CS. The validation results show MGGP-FR outperforms the other three modelling approaches, fuzzy regression, genetic programming, and genetic programming based fuzzy regression, in the CS modelling in terms of prediction accuracy.

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“…TFN), Trapezoidal Fuzzy Number (TrFN), and Gaussian Fuzzy Number (GFN), etc. In this study, TFNs are used for fuzzy numbers.The membership function f u of a TFN f  is defined as(Chakraverty et al, 2019): …”

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confidence: 99%

Readiness Assessment for Bim-Based Building Permit Processes Using Fuzzy-Copras

Ullah

Witt

Lill

et al. 2022

Journal of Civil Engineering and Management

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With the recent technological advancement in the Architecture, Engineering, and Construction (AEC) industry, building control authorities in a number of countries are trying to integrate BIM into their building permit processes. Nevertheless, considering the involvement of multiple stakeholders and contexts, adopting BIM in any organization is challenging. The aim of this research is to assess readiness for BIM-based building permit processes using Fuzzy-COPRAS, a multiple criteria decision making (MCDM) method. In this research, three municipalities were selected as alternatives and twenty-five criteria (categorized into technology, people, process, and policies) related to BIM-based building permit processes were identified from a literature review. Then, as part of the COPRAS method, the weights of the criteria were determined based on their importance level through expert evaluation. The results of the study revealed the most important criteria for BIM-based building permit processes, i.e., supporting open standards, compatibility with existing building regulations and codes, willingness of employees, support from top management, and comprehensiveness of code compliance checks. Finally, the readiness assessment results demonstrated the most prepared alternative in the selected municipalities for the BIM-based building permit process based on the status of the considered criteria. The findings of this research have practical implications for municipalities considering and/or developing their BIM-based building permit processes in terms of where to focus their efforts with respect to the criteria associated with BIM-based building permits.

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Fuzzy Numbers

Cited by 14 publications

References 3 publications

Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

A multigene genetic programming-based fuzzy regression approach for modelling customer satisfaction based on online reviews

Readiness Assessment for Bim-Based Building Permit Processes Using Fuzzy-Copras

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