Issue:From 0,1-based logic to interval logic - Revision history

Vassia Atanassova at 11:00, 13 August 2024

2024-08-13T11:00:09Z

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	{{issue/data		{{issue/data
	\| conference = 6<sup>th</sup> [[ICIFS]], Varna, 13—14 Sept 2002		\| conference = 6<sup>th</sup> [[ICIFS]], Varna, 13—14 Sept 2002
	\| issue = ~~Conference proceedings,~~ [[Notes on Intuitionistic Fuzzy Sets/08/3\|"Notes on Intuitionistic Fuzzy Sets", Volume 8 (2002) Number 3]], pages 75—94		\| issue = [[Notes on Intuitionistic Fuzzy Sets/08/3\|"Notes on Intuitionistic Fuzzy Sets", Volume 8 (2002) Number 3]], pages 75—94
	\| file = NIFS-08-3-075-094.pdf		\| file = NIFS-08-3-075-094.pdf
	\| format = PDF		\| format = PDF

Vassia Atanassova at 13:46, 12 August 2024

2024-08-12T13:46:42Z

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	{{issue/data		{{issue/data
	\| conference = 6<sup>th</sup> [[ICIFS]], Varna, 13—14 Sept 2002		\| conference = 6<sup>th</sup> [[ICIFS]], Varna, 13—14 Sept 2002
	\| issue = Conference proceedings, [[Notes on Intuitionistic Fuzzy Sets/08/3\|"Notes on ~~IFS~~", Volume 8 (2002) Number 3]], pages 75—94		\| issue = Conference proceedings, [[Notes on Intuitionistic Fuzzy Sets/08/3\|"Notes on Intuitionistic Fuzzy Sets", Volume 8 (2002) Number 3]], pages 75—94
	\| file = NIFS-08-3-075-094.pdf		\| file = NIFS-08-3-075-094.pdf
	\| format = PDF		\| format = PDF

Vassia Atanassova at 09:50, 6 November 2009

2009-11-06T09:50:28Z

← Older revision		Revision as of 12:50, 6 November 2009
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	\| file = NIFS-08-3-075-094.pdf		\| file = NIFS-08-3-075-094.pdf
	\| format = PDF		\| format = PDF
	\| size =		\| size = 199
	\| abstract =		\| abstract =
	Since early 1960s, we have a complete description of all possible [0,1]-based logical operations, namely of "and"-operations (t-norms) and of "or"-operations (t-conorms). In some real-life situations, intervals provide a more adequate way of describing uncertainty, so we need to describe interval-based logical operations ([[intuitionistic fuzzy logic]] can be viewed as an equivalent form of [[interval-valued fuzzy logic]]). Usually, researchers followed a pragmatic path and simply derived these operations from the [0,1]-based ones. From the foundational viewpoint, it is desirable not to a priori restrict ourselves to such derivative operations but, instead, to get a description of all interval-based operations which satisfy reasonable properties.		Since early 1960s, we have a complete description of all possible [0,1]-based logical operations, namely of "and"-operations (t-norms) and of "or"-operations (t-conorms). In some real-life situations, intervals provide a more adequate way of describing uncertainty, so we need to describe interval-based logical operations ([[intuitionistic fuzzy logic]] can be viewed as an equivalent form of [[interval-valued fuzzy logic]]). Usually, researchers followed a pragmatic path and simply derived these operations from the [0,1]-based ones. From the foundational viewpoint, it is desirable not to a priori restrict ourselves to such derivative operations but, instead, to get a description of all interval-based operations which satisfy reasonable properties.

Vassia Atanassova at 10:25, 4 November 2009

2009-11-04T10:25:15Z

Vassia Atanassova at 10:23, 4 November 2009

2009-11-04T10:23:21Z

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	{{issue/author		{{issue/author
	\| author = Hung Nguyen		\| author = Hung Nguyen
	\| institution =		\| institution = Department of Mathematical Sciences, New Mexico State University
	\| address =		\| address = Las Cruces, NM 88003, USA
	\| email-before-at =		\| email-before-at = hunguyen
	\| email-after-at =		\| email-after-at = nmsu.edu
	}}		}}
	{{issue/author		{{issue/author
	\| author = Vladik Kreinovich		\| author = Vladik Kreinovich
	\| institution =		\| institution = Department of Computer Science, University of Texas at El Paso
	\| address =		\| address = El Paso, TX
	\| email-before-at =		\| email-before-at = vladik
	\| email-after-at =		\| email-after-at = cs.utep.edu
	}}		}}
	{{issue/data		{{issue/data

Vassia Atanassova: New page: {{PAGENAME}} {{PAGENAME}} {{PAGENAME}} [[Category:IC...

2009-11-04T09:06:52Z

New page: {{PAGENAME}} {{PAGENAME}} {{PAGENAME}} [[Category:IC...

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2002 year|{{PAGENAME}}]]
[[Category:ICIFS conference publications|{{PAGENAME}}]]
{{issue/title
| title = From [0,1]-based logic to interval logic
| shortcut = nifs/8/3/75-94
}}
{{issue/author
| author = Hung Nguyen
| institution =
| address =
| email-before-at =
| email-after-at =
}}
{{issue/author
| author = Vladik Kreinovich
| institution =
| address =
| email-before-at =
| email-after-at =
}}
{{issue/data
| conference = 6<sup>th</sup> [[ICIFS]], Varna, 13—14 Sept 2002
| issue = Conference proceedings, [[Notes on Intuitionistic Fuzzy Sets/08/3|"Notes on IFS", Volume 8 (2002) Number 3]], pages 75—94
| file = NIFS-08-3-075-094.pdf
| format = PDF
| size =
| abstract =
Since early 1960s, we have a complete description of all possible [0,1]-based logical operations, namely of "and"-operations (t-norms) and of "or"-operations (t-conorms). In some real-life situations, intervals provide a more adequate way of describing uncertainty, so we need to describe interval-based logical operations ([[intuitionistic fuzzy logic]] can be viewed as an equivalent form of [[interval-valued fuzzy logic]]). Usually, researchers followed a pragmatic path and simply derived these operations from the [0,1]-based ones. From the foundational viewpoint, it is desirable not to a priori restrict ourselves to such derivative operations but, instead, to get a description of all interval-based operations which satisfy reasonable properties.

Such description is presented in this paper. It turns out that all such operations can be described as the result of applying interval computations to the corresponding [0,1]-based ones.
| keywords =
| references =
# Atanassov K. [[Intuitionistic Fuzzy Sets: Theory and Applications]], Physica-Verlag, Heidelberg, 1999.
# W. Bandler and L. J. Kohout, "Unified theory of multi-valued logical operations in the light of the checklist paradigm", Proc. of IEEE Conference on Systems, Man, and Cybernetics, Halifax, Nova Scotia, Oct. 1984.
# D. Berleant and H. Cheng, "A Software Tool for Automatically Verified Operations on Intervals and Probability Distributions", Reliable Computing, 1998, Vol. 4, No. 1, pp. 71-82.
# D. Berleant and C. Goodman-Strauss, "Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency using Intervals", Reliable Computing, 1998, Vol. 4, No. 2, pp. 147-165.
# S. Ferson, "Probability bounds analysis software," Computing in Environmental Resource Management: Proceedings of a Special Conference, Research Triangle Park, NC, December 2-4, 1996, Air and Waste Management Association, Pittsburgh, Pennsylvania, 1996, pp. 669-678.
# S. Ferson and L. Ginzburg, "Hybrid arithmetic", In: B. M. Ayyub (ed.), Proceedings of the ISUMA-NAFIPS'95, IEEE Computer Society Press, Los Alamitos, California, 1995, pp. 619-623.
# S. Ferson, L. Ginzburg, V. Kreinovich, and H. Schulte, "Interval Computations as a Particular Case of a General Scheme Involving Classes of Probability Distributions", In: J. Wolff von Gudenberg and Walter Kräamer (eds.), Proceedings of the SCAN'2000/INTERVAL'2000, Kluwer Academic/Plenum Publishers, Dordrecht, 2001 (to appear).
# M. Gehrke, C. Walker, and E. Walker, "Some comments on interval-valued fuzzy sets", Internat. J. Intelligent Systems, 1996, Vol. 11, pp. 751-759.
# R. Giles, "Lukasiewicz logic and fuzzy set theory", Internat. J. Man-Machine Stud.,1976, Vol. 8, pp. 313-327.
# R. Hammer, M. Hocks, U. Kulisch, and D. Ratz, Numerical toolbox for verified computing. I. Basic numerical problems, Springer-Verlag, Heidelberg, 1993.
# R. B. Kearfott, Rigorous global search: continuous problems, Kluwer, Dordrecht, 1996.
# R. B. Kearfott and V. Kreinovich (eds.), Applications of Interval Computations, Kluwer, Dordrecht, 1996.
# G. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, New Jersey, 1995.
# V. Kreinovich, G. C. Mouzouris, and H. T. Nguyen, "Fuzzy rule based modeling as a universal control tool", In: H. T. Nguyen and M. Sugeno (eds.), Fuzzy Systems: Modeling and Control, Kluwer, Boston, Massachusetts, 1998, pp. 135-195.
# C. H. Ling, "Representation of associative functions", Publ. Math. Debrecen, 1965, Vol. 12, pp. 189-212.
# K. Marriott and P. J. Stuckey, Programming with Constraints: An Introduction, MIT Press, Cambridge, Massachusetts, 1998.
# P. S. Mostert and A. L. Shields, "On the structure of semigroups on a compact manifold with boundary", Ann, of Math., 1957, Vol. 65, pp. 117-143.
# H. T. Nguyen and V. Kreinovich, "Methodology of fuzzy control: an introduction", In: H. T. Nguyen and M. Sugeno (eds.), Fuzzy Systems: Modeling and Control, Kluwer, Boston, Massachusetts, 1998, pp. 19-62.
# H. T. Nguyen, V. Kreinovich, and Q. Zuo, "Interval-valued degrees of belief: applications of interval computations to expert systems and intelligent control", International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems (IJUFKS), 1997, Vol. 5, No. 3, pp. 317-358.
# H. T. Nguyen and E. A. Walker, First Course in Fuzzy Logic, CRC Press, Boca Raton, Florida, 1999.
# H. Ratschek and J. Rokne, New computer methods for global optimization, Ellis Horwood, Chichester, 1988.
# B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.
# M. H. Smith and V. Kreinovich, "Optimal strategy of switching reasoning methods in fuzzy control", In: H. T. Nguyen, M. Sugeno, R. Tong, and R. Yager (eds.), Theoretical aspects of fuzzy control, J. Wiley, New York, 1995, pp. 117-146.
# E. Tsang, Foundations of Constraint Satisfaction, Academic Press, N.Y., 1993.
# I. B. Türkşen, "Interval valued fuzzy sets based on normal forms", Fuzzy Sets and Systems, 1986, Vol. 20, pp. 191-210.
# P. Van Hentenryck, Constraint Satisfaction in Logic Programming, MIT Press, Cambridge, Massachusetts, 1989.
# P. Van Hentenryck, L. Michel, and Y. Deville, Numerica: A Modeling Language for Global Optimization, MIT Press, Cambridge, Massachusetts, 1997.
# C. Walker and E. A. Walker, private communication, 1995.
# L. A. Zadeh, "Fuzzy Sets", Information and Control, 1965, Vol. 8, pp. 338-353.
# Q. Zuo, "Description of strictly monotonic interval AND/OR operations", Reliable Computing, 1995, Supplement (Extended Abstracts of APIC'95: International Workshop on Applications of Interval Computations, El Paso, TX, Febr. 23{25, 1995), pp. 232-235.

| citations =
| see-also =
}}

← Older revision		Revision as of 13:25, 4 November 2009
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	# R. B. Kearfott, Rigorous global search: continuous problems, Kluwer, Dordrecht, 1996.		# R. B. Kearfott, Rigorous global search: continuous problems, Kluwer, Dordrecht, 1996.
	# R. B. Kearfott and V. Kreinovich (eds.), Applications of Interval Computations, Kluwer, Dordrecht, 1996.		# R. B. Kearfott and V. Kreinovich (eds.), Applications of Interval Computations, Kluwer, Dordrecht, 1996.
	# G. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, New Jersey, 1995.		# [[George Klir\|G. Klir]] and [[Bo Yuan\|B. Yuan]], Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, New Jersey, 1995.
	# V. Kreinovich, G. C. Mouzouris, and H. T. Nguyen, "Fuzzy rule based modeling as a universal control tool", In: H. T. Nguyen and M. Sugeno (eds.), Fuzzy Systems: Modeling and Control, Kluwer, Boston, Massachusetts, 1998, pp. 135-195.		# V. Kreinovich, G. C. Mouzouris, and H. T. Nguyen, "Fuzzy rule based modeling as a universal control tool", In: H. T. Nguyen and M. Sugeno (eds.), Fuzzy Systems: Modeling and Control, Kluwer, Boston, Massachusetts, 1998, pp. 135-195.
	# C. H. Ling, "Representation of associative functions", Publ. Math. Debrecen, 1965, Vol. 12, pp. 189-212.		# C. H. Ling, "Representation of associative functions", Publ. Math. Debrecen, 1965, Vol. 12, pp. 189-212.
Line 55:		Line 55:
	# H. Ratschek and J. Rokne, New computer methods for global optimization, Ellis Horwood, Chichester, 1988.		# H. Ratschek and J. Rokne, New computer methods for global optimization, Ellis Horwood, Chichester, 1988.
	# B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.		# B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.
	# M. H. Smith and V. Kreinovich, "Optimal strategy of switching reasoning methods in fuzzy control", In: H. T. Nguyen, M. Sugeno, R. Tong, and R. Yager (eds.), Theoretical aspects of fuzzy control, J. Wiley, New York, 1995, pp. 117-146.		# M. H. Smith and V. Kreinovich, "Optimal strategy of switching reasoning methods in fuzzy control", In: H. T. Nguyen, M. Sugeno, R. Tong, and [[Ronald Yager\|R. Yager]] (eds.), Theoretical aspects of fuzzy control, J. Wiley, New York, 1995, pp. 117-146.
	# E. Tsang, Foundations of Constraint Satisfaction, Academic Press, N.Y., 1993.		# E. Tsang, Foundations of Constraint Satisfaction, Academic Press, N.Y., 1993.
	# I. B. Türkşen, "Interval valued fuzzy sets based on normal forms", Fuzzy Sets and Systems, 1986, Vol. 20, pp. 191-210.		# I. B. Türkşen, "Interval valued fuzzy sets based on normal forms", Fuzzy Sets and Systems, 1986, Vol. 20, pp. 191-210.
Line 61:		Line 61:
	# P. Van Hentenryck, L. Michel, and Y. Deville, Numerica: A Modeling Language for Global Optimization, MIT Press, Cambridge, Massachusetts, 1997.		# P. Van Hentenryck, L. Michel, and Y. Deville, Numerica: A Modeling Language for Global Optimization, MIT Press, Cambridge, Massachusetts, 1997.
	# C. Walker and E. A. Walker, private communication, 1995.		# C. Walker and E. A. Walker, private communication, 1995.
	# L. A. Zadeh, "Fuzzy Sets", Information and Control, 1965, Vol. 8, pp. 338-353.		# [[Lotfi Zadeh\|L. A. Zadeh]], "Fuzzy Sets", Information and Control, 1965, Vol. 8, pp. 338-353.
	# Q. Zuo, "Description of strictly monotonic interval AND/OR operations", Reliable Computing, 1995, Supplement (Extended Abstracts of APIC'95: International Workshop on Applications of Interval Computations, El Paso, TX, Febr. 23{25, 1995), pp. 232-235.		# Q. Zuo, "Description of strictly monotonic interval AND/OR operations", Reliable Computing, 1995, Supplement (Extended Abstracts of APIC'95: International Workshop on Applications of Interval Computations, El Paso, TX, Febr. 23{25, 1995), pp. 232-235.