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Ifigenia Administrator uploaded File:NIFS-32-2-163-175.pdf == Summary == {{upload | description = Issue:Effects of fuzzy and advanced fuzzy sets in mammogram image clustering | author = Tamalika Chaira and Rita Chhikara | source = Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 163-175 | date = 2026 | license = Creative Commons Attribution (CC BY 4.0) | other-version = }} Category:PDF files

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== Summary ==
{{upload
| description = [[Issue:Effects of fuzzy and advanced fuzzy sets in mammogram image clustering|Effects of fuzzy and advanced fuzzy sets in mammogram image clustering]]
| author = [[Tamalika Chaira]] and [[Rita Chhikara]]
| source = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 163-175
| date = 2026
| license = Creative Commons Attribution (CC BY 4.0)
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Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = Effects of fuzzy and advanced fuzzy sets in mammogram image clustering | shortcut = nifs/32/2/163-175 }} {{issue/author | author = Tamalika Chaira | institution = Department of Computer Science and Engineering, South Asian University | addre..."

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{{issue/title
| title = Effects of fuzzy and advanced fuzzy sets in mammogram image clustering
| shortcut = nifs/32/2/163-175
}}
{{issue/author
| author = Tamalika Chaira
| institution = Department of Computer Science and Engineering, South Asian University
| address = Maidan Garhi, New Delhi, India
| email-before-at = tchaira
| email-after-at = yahoo.com
| orcid = 0000-0002-8839-0423
}}
{{issue/author
| author = Rita Chhikara
| institution = Department of Computer Science and Engineering, South Asian University
| address = Maidan Garhi, New Delhi, India
| email-before-at = ritachhikara
| email-after-at = ncuindia.edu
| orcid = 0000-0001-9537-3907
}}

{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 163–175
| doi = https://doi.org/10.7546/nifs.2026.32.2.163-175
| file = NIFS-32-2-163-175.pdf
| format = PDF
| size = 881
| abstract = Breast cancer is one of the leading causes of death in the world among women. Early detection of breast masses may increase the survival rate and so automated techniques are suggested by researchers across the globe. Mammogram images are vague and many of the patterns are not visible clearly, thereby making it difficult to distinguish them using traditional crisp classification methods. So, segmentation of mammogram images remains a complex task and is necessary before moving for classification. Fuzzy/advanced fuzzy methods consider uncertainty in an image and so these sets can deal with uncertainty in medical images in an efficient manner. This paper presents the effect of using fuzzy, intuitionistic fuzzy set, Interval-type2 fuzzy set and intuitionistic fuzzy set of second type on segmenting lesions in mammogram images. Quantitative and qualitative analysis reveals that segmentation error is more on using fuzzy sets where only one uncertainty, which is membership function, is considered. Experimental results show that though intuitionistic fuzzy set, Interval-type2 fuzzy set performs well, intuitionistic fuzzy set of second type performs better than the other sets.
| keywords = Intuitionistic fuzzy set, Intuitionistic fuzzy set of second type, Interval valued type-2 fuzzy set, Intuitionistic fuzzy entropy, Clustering.
| ams = 03E72, 03B20, 68U10, 62H30.
| references =
# Aruna Kumar, S. V., & Harish, B. S. (2018). A modified intuitionistic fuzzy clustering algorithm for medical image segmentation. Journal of Intelligent Systems, 27(4), 593–607.
# Atanassov, K. (1989). Geometrical interpretation of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia, 1989. Reprinted: International Journal Bioautomation, 2016, 20(S1), S27–S42.
# Atanassov, K. (1993). A second type of intuitionistic fuzzy sets. BUSEFAL, 56, 66–70.
# Atanassov, K. (1993). Relations between both types of intuitionistic fuzzy sets. BUSEFAL, 56, 71–72.
# Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Series in Fuzziness and Soft Computing, Vol. 35, Springer Physica-Verlag, Heidelberg.
# Bezdek, J. C., Hall, L. O., & Clark, L. P. (1993). Review of MR segmentation techniques using pattern recognition. Medical Physics, 20(4), 1033–1048.
# Chaira, T. (2011). A novel intuitionistic fuzzy C means clustering algorithm and its application to medical images. Applied Soft Computing, 11(2), 1711–1717.
# Chaira, T. (2012). Intuitionistic fuzzy color clustering of human cell images on different color models. Journal of Intelligent & Fuzzy Systems, 23 (2–3), 43–51.
# Chaira, T. (2021). An intuitionistic fuzzy clustering approach for detection of abnormal regions in mammogram images. Journal of Digital Imaging, 34(2), 428–439.
# Chaira, T., & Sarkar, A. (2024). Pythagorean fuzzy set for enhancement of low contrast mammogram images. International Journal of Imaging Systems and Technology, 34(4), Article ID e23137.
# Cherif, S., Baklouti, N., Hagras, H., & Alimi, A. M. (2022). Novel intuitionistic-based interval type-2 fuzzy similarity measures with application to clustering. IEEE Transactions on Fuzzy Systems, 30 (5), 1260–1271.
# Das, A., & Sabut, S. K. (2016). Kernelized fuzzy C-means clustering with adaptive thresholding for segmenting liver tumors. Procedia Computer Science, 92, 389–395.
# Ejegwa, P. A., & Adamu, I. M. (2019). [[Issue:Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine|Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine]]. Notes on Intuitionistic Fuzzy Sets, 25(3), 53–70.
# Kannan, S. R., Ramathilagam, S., Sathya, A., & Pandiyaraja, R. (2010). Effective fuzzy c-means based kernel function in segmenting medical images. Computers in Biology and Medicine, 40(6), 572–579.
# Mendel, J. M. (2014). General type-2 fuzzy logic systems made simple: A tutorial. IEEE Transactions on Fuzzy Systems, 22(5), 1162–1182.
# Own, C.-M. (2009). Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: An application in medical diagnosis. Applied Intelligence, 31, 283–291.
# Premalatha, R., & Dhanalakshmi, P. (2022). Enhancement and segmentation of medical images through pythagorean fuzzy sets–An innovative approach. Neural Computing and Application, 34(14), 11553–11569.
# Rangasamy, P. (2006). Theory of Operators over Intuitionistic Fuzzy Sets of Second Type and Their Applications to Image Processing. PhD Thesis, Alagappa University, Karaikudi, India.
# Rangasamy, P., & Palaniappan, N. (2004). [[Issue:Some operations on intuitionistic fuzzy sets of second type|Some operations on intuitionistic fuzzy sets of second type]]. Notes on Intuitionistic Fuzzy Sets, 10(2), 1–19.
# Verma, H., Gupta, A., & Dhirendra, K. (2019). Modified intuitionistic fuzzy c-means algorithm incorporating hesitation degree. Pattern Recognition Letters, 122, 45–52.
# Zadeh, L. A. (1965). Fuzzy sets. Information & Control, 8, 338–353.

| citations =
| see-also =
}}

Notes on Intuitionistic Fuzzy Sets/32/2

Ifigenia Administrator — Mon, 31 Aug 2026 09:36:31 GMT

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	Bulgarian National Science Fund bears no liability for the content of the published materials.		Bulgarian National Science Fund bears no liability for the content of the published materials.

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Issue:An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis

Ifigenia Administrator — Fri, 28 Aug 2026 19:30:17 GMT

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	\| format = PDF		\| format = PDF
	\| size = 272		\| size = 272
	\| abstract = Human health risk assessment of environmental contamination is commonly based on deterministic or semi-probabilistic indices such as the hazard quotient (HQ) and hazard index (HI). Although widely used, these indicators have limited capacity to explicitly represent uncertainty and variability in exposure and toxicological parameters. Monte Carlo simulation is often		\| abstract = Human health risk assessment of environmental contamination is commonly based on deterministic or semi-probabilistic indices such as the hazard quotient (HQ) and hazard index (HI). Although widely used, these indicators have limited capacity to explicitly represent uncertainty and variability in exposure and toxicological parameters. Monte Carlo simulation is often employed to address this limitation by propagating uncertainty; however, probabilistic outputs alone do not fully support decision-making when multiple contaminants must be aggregated into a single interpretable metric.
	employed to address this limitation by propagating uncertainty; however, probabilistic outputs alone do not fully support decision-making when multiple contaminants must be aggregated into a single interpretable metric.

	In this study, we propose a Monte Carlo-based intuitionistic fuzzy health risk assessment framework that integrates probabilistic exposure modeling with intuitionistic fuzzy set (IFS) theory. Hazard quotients obtained from Monte Carlo simulations are mapped to intuitionistic fuzzy membership, non-membership, and hesitation degrees using transparent threshold-based functions. Aggregation across multiple contaminants is performed using a component-wise weighted averaging scheme for the intuitionistic fuzzy components, yielding a site-level risk representation that preserves both risk magnitude and associated uncertainty. An entropy-based measure is further introduced to quantify uncertainty in the aggregated intuitionistic fuzzy assessment.		In this study, we propose a Monte Carlo-based intuitionistic fuzzy health risk assessment framework that integrates probabilistic exposure modeling with intuitionistic fuzzy set (IFS) theory. Hazard quotients obtained from Monte Carlo simulations are mapped to intuitionistic fuzzy membership, non-membership, and hesitation degrees using transparent threshold-based functions. Aggregation across multiple contaminants is performed using a component-wise weighted averaging scheme for the intuitionistic fuzzy components, yielding a site-level risk representation that preserves both risk magnitude and associated uncertainty. An entropy-based measure is further introduced to quantify uncertainty in the aggregated intuitionistic fuzzy assessment.

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| date = 2026

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	\| author = [[Nora Angelova]], [[Janusz Kacprzyk]], [[Krassimir Atanassov]] and [[Vassia Atanassova]]		\| author = [[Nora Angelova]], [[Janusz Kacprzyk]], [[Krassimir Atanassov]] and [[Vassia Atanassova]]
	\| source = [[Notes on Intuitionistic Fuzzy Sets/32/2\|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 133-143		\| source = [[Notes on Intuitionistic Fuzzy Sets/32/2\|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 133-143
	\| date = ~~2024~~		\| date = 2026
	\| license = Creative Commons Attribution (CC BY 4.0)		\| license = Creative Commons Attribution (CC BY 4.0)
	\| other-version =		\| other-version =

File:NIFS-32-2-144-162.pdf

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Ifigenia Administrator uploaded File:NIFS-32-2-144-162.pdf == Summary == {{upload | description = An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis | author = Toncho Ivanov Boyukov, Stefka Fidanova | source = Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 144-162 | date = 2026 | license...

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== Summary ==
{{upload
| description = [[Issue:An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis|An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis]]
| author = [[Toncho Ivanov Boyukov]], [[Stefka Fidanova]]
| source = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 144-162
| date = 2026
| license = Creative Commons Attribution (CC BY 4.0)
| other-version =
}}

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Issue:An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis

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Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis | shortcut = nifs/32/2/144-162 }} {{issue/author | author = Toncho Ivanov Boyukov | institution = Faculty of Technical Sciences,..."

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2026 year|{{PAGENAME}}]]
{{issue/title
| title = An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis
| shortcut = nifs/32/2/144-162
}}
{{issue/author
| author = Toncho Ivanov Boyukov
| institution = Faculty of Technical Sciences, Burgas State University "Prof. Dr. Asen Zlatarov"
| address = 1 Prof. Yakimov Str., 8010 Burgas, Bulgaria
| email-before-at = toncho_b
| email-after-at = abv.bg
| orcid = 0000-0002-1349-4893
}}
{{issue/author
| author = Stefka Fidanova
| institution = Institute of Information and Communication Technologies, Bulgarian Academy of Sciences
| address = Sofia, Bulgaria
| institution-2 = Centre of Excellence in Informatics and Information and Communication Technologies
| address-2 = Sofia, Bulgaria
| email-before-at = stefka.fidanova
| email-after-at = iict.bas.bg
| orcid = 0000-0002-8484-5849
}}

{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 144–162
| doi = https://doi.org/10.7546/nifs.2026.32.2.144-162
| file = NIFS-32-2-144-162.pdf
| format = PDF
| size = 272
| abstract = Human health risk assessment of environmental contamination is commonly based on deterministic or semi-probabilistic indices such as the hazard quotient (HQ) and hazard index (HI). Although widely used, these indicators have limited capacity to explicitly represent uncertainty and variability in exposure and toxicological parameters. Monte Carlo simulation is often
employed to address this limitation by propagating uncertainty; however, probabilistic outputs alone do not fully support decision-making when multiple contaminants must be aggregated into a single interpretable metric.

In this study, we propose a Monte Carlo-based intuitionistic fuzzy health risk assessment framework that integrates probabilistic exposure modeling with intuitionistic fuzzy set (IFS) theory. Hazard quotients obtained from Monte Carlo simulations are mapped to intuitionistic fuzzy membership, non-membership, and hesitation degrees using transparent threshold-based functions. Aggregation across multiple contaminants is performed using a component-wise weighted averaging scheme for the intuitionistic fuzzy components, yielding a site-level risk representation that preserves both risk magnitude and associated uncertainty. An entropy-based measure is further introduced to quantify uncertainty in the aggregated intuitionistic fuzzy assessment.

The proposed framework enables enhanced interpretability and robust decision support under uncertainty, as demonstrated through a numerical example. By explicitly combining probabilistic uncertainty propagation with intuitionistic fuzzy modeling, this approach advances classical health risk assessment methodologies and provides a structured basis for risk-informed environmental decision-making.
| keywords = Health risk assessment, Monte Carlo simulation, Intuitionistic fuzzy sets, Uncertainty analysis, Multi-contaminant exposure, Hazard quotient.
| ams = 03E72.
| references =
# Atanassov, K. (1983). Intuitionistic fuzzy sets. VII ITKR Session, Sofia, 20–23 June 1983. Reprinted in International Journal Bioautomation, 20(S1) (2016), S1–S6.
# Atanassov, K. (1997). Generalized Nets and Systems Theory. Prof. M. Drinov Academic Publishing House, Sofia.
# Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
# Atanassov, K. T. (2014). Index Matrices: Towards an Augmented Matrix Calculus. Studies in Computational Intelligence 573, Springer, Cham.
# Atanassov, K., Szmidt, E., Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
# Atanassov, K., Vassilev, P. (2020). Intuitionistic fuzzy sets and other fuzzy sets extensions representable by them. Journal of Intelligent & Fuzzy Systems, 38(1), 525–530.
# Atanassova, L., & Dworniczak, P. (2021). Operation as the tool for the de-i-fuzzification procedure and for the correction of the unconscientious experts’ evaluations. Notes on Intuitionistic Fuzzy Sets, 27(4), 9–19.
# Atanassova, V., & Sotirov, S. (2012). A new formula for de-i-fuzzification of intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 18(3), 49–51.
# Ban, A., Kacprzyk, J., & Atanassov, K. (2008). On de-I-fuzzification of intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, 61(12), 1535–1540.
# Briffa, J., Sinagra, E., & Blundell, R. (2020). Heavy metal pollution in the environment and their toxicological effects on humans. Heliyon, 6, Article ID e04691.
# Bulgarian State Standard (2005). Water quality. Application of inductively coupled plasma mass spectrometry (ICP-MS). BSS EN ISO 17294-2/2005.
# Ivanova, D., Nikolaeva, Z., & Dimitrov, A. (2022). Study of the concentration of heavy metals in silt loading from transport arteries in the city of Burgas, Bulgaria. Oxidation Communications, 45(2), 390–397.
# Ivanova, D., Tasheva, Y., Sotirova, E., Dimitrov, A., & Sotirov, S. (2023). Prediction of the granulometric composition of the silt loading on transport arteries in the city of Bourgas based on artificial neural networks. Lecture Notes in Networks and Systems (Vol. 658, pp. 21–31). Springer, Cham.
# Jayarathne, A., Egodawatta, P., Ayoko, G. A., & Goonetilleke, A. (2018). Assessment of ecological and human health risks of metals in urban road dust based on geochemical fractionation and potential bioavailability. Science of the Total Environment, 635, 1609–1619.
# Kroese, D. P, Brereton, T., Taimre, T., & Botev, Z. I. (2014). Why the Monte Carlo method is so important today. WIREs Comput Stat., 6(6), 386–392.
# Li, J., Cui, D., Yang, Z., Ma, J., Liu, J., Yu, Y., Huang, X., & Xiang, P. (2024). Health risk assessment of heavy metal(loid)s in road dust via dermal exposure pathway from a low latitude plateau provincial capital city: The importance of toxicological verification. Environmental Research, 252, Article ID 118890.
# Mendel, J. M. (2001). Uncertain Rule-based Fuzzy Logic Systems. Prentice Hall, Upper Saddle River.
# Novak, V., Perfilieva, I., Mockor, J. (1999). Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht.
# Patrascu, V. (2024). Two de-I-fuzzification procedures for intuitionistic fuzzy information. Notes on Intuitionistic Fuzzy Sets, 30 (1), 18–25.
# Pedrycz, W., Gomide, F. (2021). Fuzzy Systems Engineering: Toward Human-Centric Computing. Wiley-IEEE Press, Hoboken.
# Potocki, S., Rowinska-Zyrek, M., Witkowska, D., Pyrkosz, M., Szebesczyk, A., Krzywoszynska, K., & Kozlowski, H. (2012). Metal transport and homeostasis within the human body: Toxicity associated with transport abnormalities. Current Medicinal Chemistry, 19(17), 2738–2759.
# Ross, T. J. (2010). Fuzzy Logic with Engineering Applications. 3rd ed., Wiley, Chichester.
# Sotirov, S., Sotirova, E., Werner, M., Simeonov, S., Hardt, W., & Simeonova, N. (2016). Intuitionistic fuzzy estimation of the generalized nets model of spatial-temporal group scheduling problems. In: Imprecision and Uncertainty in Information Representation and Processing, Studies in Fuzziness and Soft Computing 332, Springer, Cham, 401–414.
# Todorov, V., Georgiev, S., Lazarova, M., Todorov, M., Sapundzhi, M., Traneva, V., & Petrov, M. (2026). An enhanced lattice rule with an optimized generating vector for high-dimensional sensitivity analysis. Lecture Notes in Networks and Systems (Vol. 1799, pp. 163–175), Springer, Cham.
# Todorov, V., & Zhivkov, P. (2025). Efficient Evaluation of Sobol’ sensitivity indices via polynomial lattice rules and modified sobol’ sequences. Mathematics, 13(21), Article ID 3402.
# Yager, R. R., & Zadeh, L. A. (Eds.) (1992). An Introduction to Fuzzy Logic Applications in Intelligent Systems. Springer, Boston.
# Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
# Zimmermann, H. J. (2001). Fuzzy Set Theory and Its Applications. 4th ed., Springer, Boston.

| citations =
| see-also =
}}

Issue:Research on intuitionistic fuzzy implications. Part 5

Ifigenia Administrator — Fri, 28 Aug 2026 14:41:07 GMT

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Notes on Intuitionistic Fuzzy Sets/32/2

Ifigenia Administrator — Thu, 27 Aug 2026 14:25:54 GMT

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			\|title = [[Issue:An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis\|An intuitionistic fuzzy framework for human health risk assessment incorporating Monte Carlo uncertainty analysis]]
			\|authors = [[Toncho Ivanov Boyukov]], [[Stefka Fidanova]]
			\|pages = 144–162
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Issue:Research on intuitionistic fuzzy implications. Part 5

Ifigenia Administrator — Thu, 27 Aug 2026 05:45:22 GMT

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	\| email-before-at = noraa		\| email-before-at = noraa
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	\| email-before-at = janusz.kacprzyk		\| email-before-at = janusz.kacprzyk
	\| email-after-at = ibspan.waw.pl		\| email-after-at = ibspan.waw.pl
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	\| sec-email-before-at = k.t.atanassov		\| sec-email-before-at = k.t.atanassov
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	\| email-before-at = vassia.atanassova		\| email-before-at = vassia.atanassova
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Issue:Nifs/32/2/133-143

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Summary

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	\| description = [[Issue:Research on intuitionistic fuzzy implications. Part 5\|Research on intuitionistic fuzzy implications. Part 5]]		\| description = [[Issue:Research on intuitionistic fuzzy implications. Part 5\|Research on intuitionistic fuzzy implications. Part 5]]
	\| author = [[Nora Angelova]], [[Janusz ~~Kacorzyk~~]], [[Krassimir Atanassov]] and [[Vassia Atanassova]]		\| author = [[Nora Angelova]], [[Janusz Kacprzyk]], [[Krassimir Atanassov]] and [[Vassia Atanassova]]
	\| source = [[Notes on Intuitionistic Fuzzy Sets/32/2\|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 133-143		\| source = [[Notes on Intuitionistic Fuzzy Sets/32/2\|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 133-143
	\| date = 2024		\| date = 2024

File:NIFS-32-2-133-143.pdf

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Ifigenia Administrator uploaded File:NIFS-32-2-133-143.pdf == Summary == {{upload | description = Research on intuitionistic fuzzy implications. Part 5 | author = Nora Angelova, Janusz Kacorzyk, Krassimir Atanassov and Vassia Atanassova | source = Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 133-143 | date = 2024 | license = Creative Commons Attribution (CC BY 4.0) | other-version = }} [[Category...

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== Summary ==
{{upload
| description = [[Issue:Research on intuitionistic fuzzy implications. Part 5|Research on intuitionistic fuzzy implications. Part 5]]
| author = [[Nora Angelova]], [[Janusz Kacorzyk]], [[Krassimir Atanassov]] and [[Vassia Atanassova]]
| source = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 133-143
| date = 2024
| license = Creative Commons Attribution (CC BY 4.0)
| other-version =
}}

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Issue:Research on intuitionistic fuzzy implications. Part 5

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Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = Research on intuitionistic fuzzy implications. Part 5 | shortcut = nifs/32/2/133-143 }} {{issue/author | author = Nora Angelova | institution = Faculty of Mathematics and Informatics, Sofia University | address = 5 James Bourchier..."

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2024 year|{{PAGENAME}}]]
{{issue/title
| title = Research on intuitionistic fuzzy implications. Part 5
| shortcut = nifs/32/2/133-143
}}
{{issue/author
| author = Nora Angelova
| institution = Faculty of Mathematics and Informatics, Sofia University
| address = 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
| email-before-at = noraa
| email-after-at = fmi.uni-sofia.bg
}}
{{issue/author
| author = Janusz Kacprzyk
| institution = System Research Institute, Polish Academy of Sciences
| address = Newelska, 6, 01-447, Warsaw, Poland
| email-before-at = janusz.kacprzyk
| email-after-at = ibspan.waw.pl
}}
{{issue/author
| author = Krassimir Atanassov
| institution = Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
| address = 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
| email-before-at = krat
| email-after-at = bas.bg
| sec-email-before-at = k.t.atanassov
| sec-email-after-at = gmail.com
}}
{{issue/author
| author = Vassia Atanassova
| institution = Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
| address = 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
| email-before-at = vassia.atanassova
| email-after-at = gmail.com
}}
{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 133–143
| doi = https://doi.org/10.7546/nifs.32.2.133-143
| file = NIFS-32-2-133-143.pdf
| format = PDF
| size = 157
| abstract = Continuing the research from four previous papers of the authors, here we check the validity of the two tautologies from the two tautologies of propositional logic

((A → B) & (A → C)) → (A → (B & C)),

((B ∨ C) → A) → ((B → A) ∨ (C → A))

and give the list of the intuitionistic fuzzy implications that satisfy these two formulas.
| keywords = Intuitionistic fuzzy implication, Intuitionistic fuzzy pair.
| ams = 03E72.
| references =
# Angelova, N., & Atanassov, K. (2021). [[Issue:Research on intuitionistic fuzzy implications|Research on intuitionistic fuzzy implications]]. Notes on Intuitionistic Fuzzy Sets, 27(2), 20–93.
# Angelova, N., Atanassov, K., & Atanassova, V. (2022). [[Issue:Research on intuitionistic fuzzy implications. Part 2|Research on intuitionistic fuzzy implications. Part 2]]. Notes on Intuitionistic Fuzzy Sets, 28(2), 172–192.
# Angelova, N., Atanassova, V., & Atanassov, K. (2023). [[Issue:Research on intuitionistic fuzzy implications. Part 3|Research on intuitionistic fuzzy implications. Part 3]]. Notes on Intuitionistic Fuzzy Sets, 29(4), 365–370.
# Angelova, N., Atanassov, K., & Atanassova, V. (2024). [[Issue:Research on intuitionistic fuzzy implications. Part 4|Research on intuitionistic fuzzy implications. Part 4]]. Notes on Intuitionistic Fuzzy Sets, 30(1), 1–8.
# Angelova, N., & Stoenchev, M. (2015/2016). Intuitionistic fuzzy conjunctions and disjunctions from first type. Annual of “Informatics” Section, Union of Scientists, 8, 1–17 (in Bulgarian).
# Angelova, N., & Stoenchev, M. (2017). [[Issue:Intuitionistic fuzzy conjunctions and disjunctions from third type|Intuitionistic fuzzy conjunctions and disjunctions from third type]]. Notes on Intuitionistic Fuzzy Sets, 23(5), 29–41.
# Angelova, N., Stoenchev, M., & Todorov, V. (2017). Intuitionistic fuzzy conjunctions and disjunctions from second type. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 13, 143–170.
# Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham.
# Hodas, J. (1994). Logic programming with multiple context management schemes. In: Lecture Notes in Artificial Intelligence (Vol. 798, pp. 171–182). Springer.

| citations =
| see-also =
}}

Notes on Intuitionistic Fuzzy Sets/32/2

Ifigenia Administrator — Wed, 26 Aug 2026 14:08:13 GMT

133-143

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			\|title = [[Issue:Research on intuitionistic fuzzy implications. Part 5\|Research on intuitionistic fuzzy implications. Part 5]]
			\|authors = [[Nora Angelova]], [[Janusz Kacprzyk]], [[Krassimir Atanassov]], [[Vassia Atanassova]]
			\|pages = 133–143
			}}
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