Granular Differentiability of Fuzzy-Number-Valued Functions

Mazandarani, Mehran; Pariz, Naser; Kamyad, Ali Vahidian

doi:10.1109/tfuzz.2017.2659731

Cited by 158 publications

(51 citation statements)

References 33 publications

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“…In some latest publications, based on horizontal membership function approach and granular computing, Mazandarani et al [29][30][31] studied fuzzy differential systems and related problems, which can be considered as a particular scenario of neutrosophic dynamic systems. However, neutrosophic set theory in general and neutrosophic dynamic systems in particular are still in the first stage of development.…”

Section: Briefly Review the Calculus Of Uncertainty Functionsmentioning

confidence: 99%

“…The concept of arithmetic operations on the set of neutrosophic numbers is defined via horizontal membership functions. This idea original introduced Piegat et al (see [36][37][38]) and developed for granular differentiability of fuzzy-valued functions by Mazandarani et al [29][30][31]. Especially, we can define the granular difference between neutrosophic numbers -one important step to define further differentiability of neutrosophic-valued functions as well as neutrosophic differential equations and other applications.…”

Section: Contributions and Structure Of The Papermentioning

confidence: 99%

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Towards granular calculus of single-valued neutrosophic functions under granular computing

Son¹,

Dong

Sơn

et al. 2019

Multimed Tools Appl

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Neutrosophic theory studies objects whose values vary in the sets of elements and are not true or false, but in between, that can be called by neutral, indeterminate, unclear, vague, ambiguous, incomplete or contradictory quantities. In this paper, we firstly introduce preliminaries on granular calculus and analysis related to single-valued neutrosophic functions. Based on horizontal membership functions approach, we establish some basic arithmetic operations of single-valued neutrosophic numbers, that red allow us to directly introduce the terms of neutrosophic function in usual mathematical formulas. Additionally, we build metrics on the space of single-valued neutrosophic numbers induced from Hamming distance. Then, we define some backgrounds on the limit, derivative and integral of single-valued neutrosophic functions. Finally, in order to demonstrate the usable of our theoretical results, we present some applications to well-known problems arising in engineering such as logistic model, the inverted pendulum system, Mass-Spring-Damper model.

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Section: Briefly Review the Calculus Of Uncertainty Functionsmentioning

confidence: 99%

Section: Contributions and Structure Of The Papermentioning

confidence: 99%

Towards granular calculus of single-valued neutrosophic functions under granular computing

Son¹,

Dong

Sơn

et al. 2019

Multimed Tools Appl

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“…Fuzzy differential inclusion Baidosov [12], Hüllermeier [13] Zadeh's Extension principle Oberguggenberger and Pittschmann [14], Buckley Mazandarani et al [28] Approach using fuzzy bunch of real valued functions instead of fuzzy valued functions Gasilov et al [29][30][31][32], Amrahov et al [33] the initial value (or values) or boundary value (or values) is fuzzy valued number, (3) the forcing term is fuzzy valued function, and (4) all the conditions (1), (2), and (3) or their combination is present on the differential equation. There exist two types of strategies for solving the FDEs, which are as follows: Now we look on some different procedure and concepts of derivation in Table 1.…”

Section: Name Of the Theory Some Referencesmentioning

confidence: 99%

Different Solution Strategies for Solving Epidemic Model in Imprecise Environment

et al. 2018

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We study the different solution strategy for solving epidemic model in different imprecise environment, that is, a Susceptible-Infected-Susceptible (SIS) model in imprecise environment. The imprecise parameter is also taken as fuzzy and interval environment. Three different solution procedures for solving governing fuzzy differential equation, that is, fuzzy differential inclusion method, extension principle method, and fuzzy derivative approaches, are considered. The interval differential equation is also solved. The numerical results are discussed for all approaches in different imprecise environment.

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“…It also means that interval equation cannot be transformed into other form for calculating the result which can make solution determining impossible at all. This phenomenon characteristic for onedimensional interval arithmetic types was called the UBMphenomenon (unnatural behaviour phenomenon) in Mazandarani et al (2017). If principle of solution universality cannot be kept then interval equations to be solved cannot be transformed into other appropriate forms and calculating their results can be impossible.…”

Section: Summarizing Of Examples 1 Andmentioning

confidence: 99%

“…in Piegat and Landowski (2012, 2014 and Piegat and Tomaszewska (2013). It also has been applied in fuzzy arithmetic (RDM-FA) based on l-cuts, Plucinski (2015a, b, 2017), Landowski (2015, 2017a) and Mazandarani et al (2017). RDM-IA uses epistemic approach to interval calculations presented in Lodwick and Dubois (2015).…”

Section: Summarizing Of Examples 1 Andmentioning

confidence: 99%

Solving different practical granular problems under the same system of equations

Piegat

Landowski

2017

Granul. Comput.

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This paper contains discussion about the paper of Kreinovich (Granular Computing 1(3): [171][172][173][174][175][176][177][178][179] 2016) in which the author suggests the thesis that in conditions of uncertainty ''solving different practical problems we get different solutions of the same system of equations with the same granules''. Authors of the present paper are of the opinion that the above thesis is result of one-dimensional approach to interval analysis prevailing at present in scientific community and also used by Kreinovich. According to this approach the direct result of any arithmetic operation Ã 2 fþ; À; Â; =g on intervals is also an interval. The main scientific contribution of the paper is showing that a granular problem analysis in an incomplete, low-dimensional space can lead to untrue conclusions because picture of the problem in this space is too poor and part of valuable, important information is lost. What is seen in the fulldimensional space of the problem space cannot be seen in an incomplete, low-dimensional space. The paper also shortly describes a multidimensional approach to interval arithmetic that is free of the above-described deficiencies.

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Granular Differentiability of Fuzzy-Number-Valued Functions

Cited by 158 publications

References 33 publications

Towards granular calculus of single-valued neutrosophic functions under granular computing

Towards granular calculus of single-valued neutrosophic functions under granular computing

Different Solution Strategies for Solving Epidemic Model in Imprecise Environment

Solving different practical granular problems under the same system of equations

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