Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets

The paper presents a certain class of the mathematical models of diagnostic information granules describing the fuzzy symptoms-faults relationship. A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, an...
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Autor*in:	Anna Bryniarska [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	information granule database intuitionistic fuzzy set information granules diagnostic information n-scaling function granule language

Übergeordnetes Werk:	In: Applied Sciences - MDPI AG, 2012, 12(2022), 5, p 2597
Übergeordnetes Werk:	volume:12 ; year:2022 ; number:5, p 2597

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DOI / URN:	10.3390/app12052597

Katalog-ID:	DOAJ016529847

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spelling	10.3390/app12052597 doi (DE-627)DOAJ016529847 (DE-599)DOAJ0780bbf022514105adcaf4aa19222139 DE-627 ger DE-627 rakwb eng TA1-2040 QH301-705.5 QC1-999 QD1-999 Anna Bryniarska verfasserin aut Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The paper presents a certain class of the mathematical models of diagnostic information granules describing the fuzzy symptoms-faults relationship. A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, and with some scaling of the symptom-fault concept pair values. These value pairs can be considered as intuitionistic fuzzy sets for the space of diagnosed objects. In this article, for scaling intuitionistic fuzzy sets (n-ScIFS), the deductive theory is formulated. There the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs) are generalized to the n-ScIFS objects. The membership and non-membership values, as standard, can be described by the 1:1 scale or the quadratic function scale. However, any power scale <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<n</mi<<mo<<</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< can be used. In this paper, any n-Sc scaling functions retaining the IFSs properties are considered. The n-ScIFS theory introduces a conceptual apparatus analogous to the classical theory of Zadeh fuzzy sets and Yager PFSs, consistently striving, for the first time, to formulate the relational structure of n-ScIFSs as a model of a certain information granule system called here the diagnostic granule system. In addition, power- and linear-repeatable diagnostic granules are defined in the n-ScIFSs structure for serial or parallel diagnosis processes. The information granule base is determined and a diagnostic granule system model produced by this information granule base is shown. Certain algorithms have been given to establish the semantic language of diagnosis describing the system of diagnostic information granules. information granule database intuitionistic fuzzy set information granules diagnostic information n-scaling function granule language Technology T Engineering (General). Civil engineering (General) Biology (General) Physics Chemistry In Applied Sciences MDPI AG, 2012 12(2022), 5, p 2597 (DE-627)737287640 (DE-600)2704225-X 20763417 nnns volume:12 year:2022 number:5, p 2597 https://doi.org/10.3390/app12052597 kostenfrei https://doaj.org/article/0780bbf022514105adcaf4aa19222139 kostenfrei https://www.mdpi.com/2076-3417/12/5/2597 kostenfrei https://doaj.org/toc/2076-3417 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2022 5, p 2597
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callnumber-first	T - Technology
author	Anna Bryniarska
spellingShingle	Anna Bryniarska misc TA1-2040 misc QH301-705.5 misc QC1-999 misc QD1-999 misc information granule database misc intuitionistic fuzzy set misc information granules misc diagnostic information misc n-scaling function misc granule language misc Technology misc T misc Engineering (General). Civil engineering (General) misc Biology (General) misc Physics misc Chemistry Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets
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topic_title	TA1-2040 QH301-705.5 QC1-999 QD1-999 Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets information granule database intuitionistic fuzzy set information granules diagnostic information n-scaling function granule language
topic	misc TA1-2040 misc QH301-705.5 misc QC1-999 misc QD1-999 misc information granule database misc intuitionistic fuzzy set misc information granules misc diagnostic information misc n-scaling function misc granule language misc Technology misc T misc Engineering (General). Civil engineering (General) misc Biology (General) misc Physics misc Chemistry
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title	Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets
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title_sort	mathematical models of diagnostic information granules generated by scaling intuitionistic fuzzy sets
callnumber	TA1-2040
title_auth	Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets
abstract	The paper presents a certain class of the mathematical models of diagnostic information granules describing the fuzzy symptoms-faults relationship. A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, and with some scaling of the symptom-fault concept pair values. These value pairs can be considered as intuitionistic fuzzy sets for the space of diagnosed objects. In this article, for scaling intuitionistic fuzzy sets (n-ScIFS), the deductive theory is formulated. There the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs) are generalized to the n-ScIFS objects. The membership and non-membership values, as standard, can be described by the 1:1 scale or the quadratic function scale. However, any power scale <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<n</mi<<mo<<</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< can be used. In this paper, any n-Sc scaling functions retaining the IFSs properties are considered. The n-ScIFS theory introduces a conceptual apparatus analogous to the classical theory of Zadeh fuzzy sets and Yager PFSs, consistently striving, for the first time, to formulate the relational structure of n-ScIFSs as a model of a certain information granule system called here the diagnostic granule system. In addition, power- and linear-repeatable diagnostic granules are defined in the n-ScIFSs structure for serial or parallel diagnosis processes. The information granule base is determined and a diagnostic granule system model produced by this information granule base is shown. Certain algorithms have been given to establish the semantic language of diagnosis describing the system of diagnostic information granules.
abstractGer	The paper presents a certain class of the mathematical models of diagnostic information granules describing the fuzzy symptoms-faults relationship. A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, and with some scaling of the symptom-fault concept pair values. These value pairs can be considered as intuitionistic fuzzy sets for the space of diagnosed objects. In this article, for scaling intuitionistic fuzzy sets (n-ScIFS), the deductive theory is formulated. There the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs) are generalized to the n-ScIFS objects. The membership and non-membership values, as standard, can be described by the 1:1 scale or the quadratic function scale. However, any power scale <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<n</mi<<mo<<</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< can be used. In this paper, any n-Sc scaling functions retaining the IFSs properties are considered. The n-ScIFS theory introduces a conceptual apparatus analogous to the classical theory of Zadeh fuzzy sets and Yager PFSs, consistently striving, for the first time, to formulate the relational structure of n-ScIFSs as a model of a certain information granule system called here the diagnostic granule system. In addition, power- and linear-repeatable diagnostic granules are defined in the n-ScIFSs structure for serial or parallel diagnosis processes. The information granule base is determined and a diagnostic granule system model produced by this information granule base is shown. Certain algorithms have been given to establish the semantic language of diagnosis describing the system of diagnostic information granules.
abstract_unstemmed	The paper presents a certain class of the mathematical models of diagnostic information granules describing the fuzzy symptoms-faults relationship. A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, and with some scaling of the symptom-fault concept pair values. These value pairs can be considered as intuitionistic fuzzy sets for the space of diagnosed objects. In this article, for scaling intuitionistic fuzzy sets (n-ScIFS), the deductive theory is formulated. There the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs) are generalized to the n-ScIFS objects. The membership and non-membership values, as standard, can be described by the 1:1 scale or the quadratic function scale. However, any power scale <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<n</mi<<mo<<</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< can be used. In this paper, any n-Sc scaling functions retaining the IFSs properties are considered. The n-ScIFS theory introduces a conceptual apparatus analogous to the classical theory of Zadeh fuzzy sets and Yager PFSs, consistently striving, for the first time, to formulate the relational structure of n-ScIFSs as a model of a certain information granule system called here the diagnostic granule system. In addition, power- and linear-repeatable diagnostic granules are defined in the n-ScIFSs structure for serial or parallel diagnosis processes. The information granule base is determined and a diagnostic granule system model produced by this information granule base is shown. Certain algorithms have been given to establish the semantic language of diagnosis describing the system of diagnostic information granules.
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title_short	Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets
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A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, and with some scaling of the symptom-fault concept pair values. These value pairs can be considered as intuitionistic fuzzy sets for the space of diagnosed objects. In this article, for scaling intuitionistic fuzzy sets (n-ScIFS), the deductive theory is formulated. There the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs) are generalized to the n-ScIFS objects. The membership and non-membership values, as standard, can be described by the 1:1 scale or the quadratic function scale. However, any power scale <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<n</mi<<mo<<</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula< can be used. In this paper, any n-Sc scaling functions retaining the IFSs properties are considered. The n-ScIFS theory introduces a conceptual apparatus analogous to the classical theory of Zadeh fuzzy sets and Yager PFSs, consistently striving, for the first time, to formulate the relational structure of n-ScIFSs as a model of a certain information granule system called here the diagnostic granule system. In addition, power- and linear-repeatable diagnostic granules are defined in the n-ScIFSs structure for serial or parallel diagnosis processes. The information granule base is determined and a diagnostic granule system model produced by this information granule base is shown. 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Mathematical Models of Diagnostic Information Granules Generated by Scaling Intuitionistic Fuzzy Sets

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