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Issue:New implication deviation and entropy measures in intuitionistic fuzzy sets

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	# [[Lilija Atanassova\|Atanassova, L.]] (2009). [[Issue:On some properties of intuitionistic fuzzy negation ¬@\|On some properties of intuitionistic fuzzy negation ¬@]]. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.		# [[Lilija Atanassova\|Atanassova, L.]] (2009). [[Issue:On some properties of intuitionistic fuzzy negation ¬@\|On some properties of intuitionistic fuzzy negation ¬@]]. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.
	# Atanassova, L. (2012). [[Issue:On two modifications of the intuitionistic fuzzy implication →@\|On two modifications of the intuitionistic fuzzy implication →@]]. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.		# Atanassova, L. (2012). [[Issue:On two modifications of the intuitionistic fuzzy implication →@\|On two modifications of the intuitionistic fuzzy implication →@]]. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.
	# Atanassova, L., & Dworniczak, P. (2021). On the weak intuitionistic fuzzy implication based on ∆ operation. Notes on Intuitionistic Fuzzy Sets, 27(2), 11–19.		# Atanassova, L., & [[Piotr Dworniczak\|Dworniczak, P.]] (2021). On the weak intuitionistic fuzzy implication based on ∆ operation. Notes on Intuitionistic Fuzzy Sets, 27(2), 11–19.
	# Ban, A. (2017). Intuitionistic fuzzy measures and intuitionistic entropies. Granular Computation, 3, 111–122.		# [[Adrian Ban\|Ban, A.]] (2017). Intuitionistic fuzzy measures and intuitionistic entropies. Granular Computation, 3, 111–122.
	# Burillo, P., & Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78(3), 305–316.		# [[Pedro Burillo\|Burillo, P.]], & [[Humberto Bustince\|Bustince, H.]] (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78(3), 305–316.
	# Bustince, H., Barrenechea, E., & Mohedano, V. (2004). Intuitionistic fuzzy implication operators-An expression and main properties. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03), 387–406.		# Bustince, H., Barrenechea, E., & Mohedano, V. (2004). Intuitionistic fuzzy implication operators-An expression and main properties. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03), 387–406.
	# Cornelis, C., Deschrijver, G., & Kerre, E. E. (2004). Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: Construction, classification, application. International Journal of Approximate Reasoning, 35(1), 55–95.		# [[Chris Cornelis\|Cornelis, C.]], [[Glad Deschrijver\|Deschrijver, G.]], & [[Etienne Kerre\|Kerre, E. E]]. (2004). Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: Construction, classification, application. International Journal of Approximate Reasoning, 35(1), 55–95.
	# De Luca, A., & Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, 20(4), 301–312.		# De Luca, A., & Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, 20(4), 301–312.
	# Dengfeng, L., & Chuntian, C. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1–3), 221–225.		# Dengfeng, L., & Chuntian, C. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1–3), 221–225.

Category:Publications of Mihir Kumar Chakraborty

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Category:Publications of Ria Rejal Sharma

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File:NIFS-32-3-105-132.pdf

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== Summary ==
{{upload
| description = [[Issue:New implication deviation and entropy measures in intuitionistic fuzzy sets|New implication deviation and entropy measures in intuitionistic fuzzy sets]]
| author = [[Ria Rejal Sharma]], [[Santanu Acharjee]], [[Mihir Kumar Chakraborty]]
| source = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 105-132
| date = 2026
| license = Creative Commons Attribution (CC BY 4.0)
| other-version =
}}

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File:NIFS-32-3-105-132.pdf

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Ifigenia Administrator uploaded File:NIFS-32-3-105-132.pdf == Summary == {{upload | description = Issue:New implication deviation and entropy measures in intuitionistic fuzzy sets | author = Ria Rejal Sharma, Santanu Acharjee, Mihir Kumar Chakraborty | source = Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 105-132 | date = 2026 | license = Creative Commons Attribution (CC BY 4.0) | other-version = }} Category:PDF files

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Issue:New implication deviation and entropy measures in intuitionistic fuzzy sets

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Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = New implication deviation and entropy measures in intuitionistic fuzzy sets | shortcut = nifs/32/2/105-132 }} {{issue/author | author = Ria Rejal Sharma | institution = Department of Mathematics, Gauhati University | address = Guwa..."

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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 = New implication deviation and entropy measures in intuitionistic fuzzy sets
| shortcut = nifs/32/2/105-132
}}
{{issue/author
| author = Ria Rejal Sharma
| institution = Department of Mathematics, Gauhati University
| address = Guwahati-781014, Assam, India
| email-before-at = sharmariarejal
| email-after-at = gmail.com
| orcid = 0009-0008-4032-4014
}}
{{issue/author
| author = Santanu Acharjee
| institution = Department of Mathematics, Gauhati University
| address = Guwahati-781014, Assam, India
| email-before-at = sacharjee326
| email-after-at = gmail.com
| orcid = 0000-0003-4932-3305
}}
{{issue/author
| author = Mihir Kumar Chakraborty
| institution = Department of Mathematics, University of Calcutta
| address = Kolkata-780073, West Bengal, India
| email-before-at = mihirc4
| email-after-at = gmail.com
| orcid = 0009-0003-7669-3720
}}

{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/32/2|Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2]], pages 105–132
| doi = https://doi.org/10.7546/nifs.2026.32.2.105-132
| file = NIFS-32-2-105-132.pdf
| format = PDF
| size = 319
| abstract = This paper presents two new concepts within the framework of intuitionistic fuzzy set (IFS). An implication deviation is introduced, formulated using the implication operator together with a universal quantifier in the framework of intuitionistic fuzzy set. In addition to being a crucial analytical tool, this measure emphasizes its theoretical significance in the study of intuitionistic fuzzy sets by making it easier to define basic notions like inclusion and similarity. In addition, the paper introduces two new entropy measures, referred to as the α-intuitionistic fuzzy entropy and the β-intuitionistic fuzzy entropy, to quantify uncertainty of intuitionistic fuzzy sets. The α-intuitionistic fuzzy entropy evaluates uncertainty in terms of the deviation from the extreme situations of complete inclusion and complete exclusion. In contrast, the β-intuitionistic fuzzy entropy reflects maximum uncertainty when degrees of membership and non-membership are balanced or when the degree of hesitancy is maximal, while minimum entropy corresponds to the case, when complete inclusion or exclusion is there. Both entropy measures are constructed using the Hamming distance to ensure a consistent and intuitive representation of uncertainty.
| keywords = Intuitionistic fuzzy set, Implication deviation, Entropy.
| ams = 03B52, 03B50, 94D05.
| references =
# [[Krassimir Atanassov|Atanassov, K.]] (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Heidelberg: Physica-Verlag.
# Atanassov, K. (2011). Second Zadeh’s intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 17(3), 11–14.
# Atanassov, K., Angelova, N., & Atanassova, V. (2021). On an intuitionistic fuzzy form of the Goguen’s implication. Mathematics, 9(6), Article ID 676.
# Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Cham: Springer.
# Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, 9(2), 21–25.
# [[Lilija Atanassova|Atanassova, L.]] (2009). [[Issue:On some properties of intuitionistic fuzzy negation ¬@|On some properties of intuitionistic fuzzy negation ¬@]]. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.
# Atanassova, L. (2012). [[Issue:On two modifications of the intuitionistic fuzzy implication →@|On two modifications of the intuitionistic fuzzy implication →@]]. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.
# Atanassova, L., & Dworniczak, P. (2021). On the weak intuitionistic fuzzy implication based on ∆ operation. Notes on Intuitionistic Fuzzy Sets, 27(2), 11–19.
# Ban, A. (2017). Intuitionistic fuzzy measures and intuitionistic entropies. Granular Computation, 3, 111–122.
# Burillo, P., & Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78(3), 305–316.
# Bustince, H., Barrenechea, E., & Mohedano, V. (2004). Intuitionistic fuzzy implication operators-An expression and main properties. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12(03), 387–406.
# Cornelis, C., Deschrijver, G., & Kerre, E. E. (2004). Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: Construction, classification, application. International Journal of Approximate Reasoning, 35(1), 55–95.
# De Luca, A., & Termini, S. (1972). A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, 20(4), 301–312.
# Dengfeng, L., & Chuntian, C. (2002). New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters, 23(1–3), 221–225.
# Fan, J., & Xie, W. (1999). Distance measure and induced fuzzy entropy. Fuzzy Sets and Systems, 104(2), 305–314.
# [[Tadeusz Gerstenkorn|Gerstenkorn, T.]], & [[Jacek Mańko|Manko, J.]] (2001). [[Issue:Intuitionistic fuzzy set energies|Intuitionistic fuzzy set energies]]. Notes on Intuitionistic Fuzzy Sets, 9(1), 41–48.
# Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. New Jersey: Prentice Hall.
# Kosko, B. (1986). Fuzzy entropy and conditioning. Information Sciences, 40(2), 165–174.
# [[Alžbeta Michalíková|Michalíková, A.]] (2022). [[Issue:Some notes on intuitionistic fuzzy equivalence relations and their use on real data|Some notes on intuitionistic fuzzy equivalence relations and their use on real data]]. Notes on Intuitionistic Fuzzy Sets, 28(3), 306–318.
# Montes, I., Pal, N. R., & Montes, S. (2018). Entropy measures for Atanassov intuitionistic fuzzy sets based on divergence. Soft Computing, 22(15), 5051–5071.
# [[Eulalia Szmidt|Szmidt, E.]] (1997). [[Issue:A concept of entropy for intuitionistic fuzzy sets|A concept of entropy for intuitionistic fuzzy sets]]. Notes on Intuitionistic Fuzzy Sets, 3(2), 41–52.
# [[Eulalia Szmidt|Szmidt, E.]], & [[Jim Baldwin|Baldwin, J.]] (2004). [[Issue:Entropy for intuitionistic fuzzy set theory and mass assignment theory|Entropy for intuitionistic fuzzy set theory and mass assignment theory]]. Notes on Intuitionistic Fuzzy Sets, 10(3), 15–28.
# [[Eulalia Szmidt|Szmidt, E.]], & [[Janusz Kacprzyk|Kacprzyk, J.]] (2005). [[Issue:New measures of entropy for intuitionistic fuzzy sets|New measures of entropy for intuitionistic fuzzy sets]]. Notes on Intuitionistic Fuzzy Sets, 11(2), 12–20.
# Vlachos, I. K., & Sergiadis, G. D. (2006). Inner product based entropy in the intuitionistic fuzzy setting. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14(03), 351–366.
# Xuecheng, L. (1992). Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems, 52(3), 305–318.
# Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
# Zhang, Q., Xing, H., & Wu, L. (2012). Entropy, similarity measure, inclusion measure of intuitionistic fuzzy sets and their relationships. International Journal of Computational Intelligence Systems, 5(3), 519–529.
# Zhu, Y.-J., & Li, D.-F. (2016). A new definition and formula of entropy for intuitionistic fuzzy sets. Journal of Intelligent & Fuzzy Systems, 30(6), 3057–3066.

| citations =
| see-also =
}}

Notes on Intuitionistic Fuzzy Sets/32/2

Ifigenia Administrator — Sat, 18 Jul 2026 05:33:50 GMT

105-132

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	{{journal-contents/row		{{journal-contents/row
	\|number = <font color="red">2</font>		\|number = 2
			\|title = [[Issue:New implication deviation and entropy measures in intuitionistic fuzzy sets\|New implication deviation and entropy measures in intuitionistic fuzzy sets]]
			\|authors = [[Ria Rejal Sharma]], [[Santanu Acharjee]], [[Mihir Kumar Chakraborty]]
			\|pages = 105–132
			}}
			{{journal-contents/row
			\|number = <font color="red">3</font>
	\|title = <font color="red">TBA</font>		\|title = <font color="red">TBA</font>
	\|authors =		\|authors =

ICIFS-2026

Ifigenia Administrator — Fri, 17 Jul 2026 07:22:16 GMT

Registration: NEW EXTENDED DEADLINES

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	<div style="text-align:center; font-size:125%; font-weight:bold;">Important dates</div>		<div style="text-align:center; font-size:125%; font-weight:bold;">Important dates</div>
	-------		-------
	; <font color="red">'''Extended: 15 ~~June~~ 2026'''</font>		; <font color="red">'''NEW Extended: 15 AUGUST 2026'''</font>
	: Submission of manuscripts<br/>		: Submission of manuscripts<br/>
	; <font color="red">'''Extended: ~~30 July~~ 2026''' </font>		; <font color="red">'''NEW Extended: 15 SEPTEMBER 2026''' </font>
	: Peer review process complete, <br/>notification of acceptance		: Peer review process complete, <br/>notification of acceptance
	; <font color="red">'''Extended: ~~31 August~~ 2026''' </font>		; <font color="red">'''NEW Extended: 1 OCTOBER 2026''' </font>
	: Submission of revised versions. Payment of early conference fees		: Submission of revised versions. Payment of early conference fees
	; '''1 October 2026'''		; '''15 October 2026'''
	: Payment of late conference fees		: Payment of late conference fees
	; '''6–7 November 2026'''		; '''6–7 November 2026'''
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	! !! Regular participants !! PhD students and EUSFLAT members		! !! Regular participants !! PhD students and EUSFLAT members
	\|-		\|-
	\| <font color="red">'''Extended: ~~31 August~~ 2026''' </font>		\| <font color="red">'''NEW Extended: 1 OCTOBER 2026''' </font>
	\| EUR 150.00 \|\| EUR 90.00		\| EUR 150.00 \|\| EUR 90.00
	\|-		\|-
	\| '''Late payment:''' 1 October 2026		\| '''Late payment:''' 15 October 2026
	\| EUR 250.00 \|\| EUR 150.00		\| EUR 250.00 \|\| EUR 150.00
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MediaWiki:Sitenotice

Ifigenia Administrator — Fri, 17 Jul 2026 07:20:07 GMT

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	[[Notes on Intuitionistic Fuzzy Sets\|Read here the full announcement.]]</center></div>		[[Notes on Intuitionistic Fuzzy Sets\|Read here the full announcement.]]</center></div>
	-----------		-----------
	<div style="padding:1em; background-color:#F0F8FF;"><center><span style="font-size:125%;">'''Open Call for Papers:''' [[ICIFS-2026\|29<sup>th</sup> International Conference on Intuitionistic Fuzzy Sets]] • 6–7 November 2026 • Sofia, Bulgaria / Online </span><br><font color="red">'''EXTENDED deadline for submissions: 15 ~~June~~ 2026.'''</font><div>		<div style="padding:1em; background-color:#F0F8FF;"><center><span style="font-size:125%;">'''Open Call for Papers:''' [[ICIFS-2026\|29<sup>th</sup> International Conference on Intuitionistic Fuzzy Sets]] • 6–7 November 2026 • Sofia, Bulgaria / Online </span><br><font color="red">'''NEW EXTENDED deadline for submissions: 15 AUGUST 2026.'''</font><div>