Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages
Although the usefulness of fuzzy databases has been
pointed out in several works, they are not fully developed in numerous
domains. A task that is mostly disregarded and which is the topic
of this paper is the determination of suitable inequalities for fuzzy
sets in fuzzy query languages. This paper examines which kinds
of fuzzy inequalities exist at all. Afterwards, different procedures
are presented that appear theoretically appropriate. By being applied
to various examples, their strengths and weaknesses are revealed.
Furthermore, an algorithm for an efficient computation of the selected
fuzzy inequality is shown.
[1] S. Abbasbandy and B. Asasy, Ranking of Fuzzy Numbers by Sign
Distance. Information Sciences, vol. 176(16), 2006, pp. 2405-2416.
[2] J. M. Adamo, Fuzzy Decision Trees. Fuzzy Sets and Systems, vol. 4(3),
1980, pp. 207-219.
[3] S. M. Baas and H. Kwakernaak, Rating and Ranking of Multiple-Aspect
Alternatives Using Fuzzy Sets. Automatica, vol. 13(1), 1977, pp. 47-58.
[4] J. F. Baldwin and N. C. F. Guild, Comparison of Fuzzy Sets on the Same
Decision Space. Fuzzy Sets and Systems, vol. 2(3), 1979, pp. 213-231.
[5] G. Bortolan and R. Degani, A Review of Some Methods for Ranking
Fuzzy Subsets. Fuzzy Sets and Systems, vol. 15(1), 1985, pp. 1-19.
[6] P. Bosc and O. Pivert, About Projection-Selection-Join-Queries Addressed
to Possibilistic Relational Databases. IEEE Transactions on Fuzzy Systems,
vol. 13(1), 2005, pp. 124-139.
[7] B. P. Buckles and F. E. Petry, Query Languages for Fuzzy Databases.
Management Decision Support Systems Using Fuzzy Sets and Possibility
Theory, Edited by J. Kacprzyk and R. R. Yager, Cologne, 1985, pp. 241-
252.
[8] J. J. Buckley, A Fuzzy Ranking of Fuzzy Numbers. Fuzzy Sets and
Systems, vol. 33(1), 1989, pp. 119-121.
[9] J. J. Buckley and S. Chanas, A Fast Method of Ranking Alternatives
Using Fuzzy Numbers. Fuzzy Sets and Systems, vol. 30(3), 1989, pp.
337-338.
[10] R. De Caluwe, R. Vandenberghe, N. Van Gyseghem and A. Van
Schooten, Integrating Fuzziness in Database Models. Fuzziness in Database
Management Systems, Edited by P. Bosc and J. Kacprzyk, Heidelberg,
1995, pp. 71-113.
[11] L. M. De Campos-Ibanez and A. Gonzales-Munoz, A Subjective Approach
for Ranking Fuzzy Numbers. Fuzzy Sets and Systems, vol. 29(2),
1989, pp. 145-153.
[12] G. Canfora and L. Troiano, Fuzzy Ordering of Fuzzy Numbers. Proceedings
of the IEEE International Conference on Fuzzy Systems, vol. 2,
Budapest, 2004, pp. 669-674.
[13] J. R. Chang, C. H. Cheng and C. Y. Kuo, Conceptual Procedure of Ranking
Fuzzy Numbers Based on Adaptive Two-Dimensions Dominance. Soft
Computing - A Fusion of Foundations, Methodologies and Applications,
vol. 10(2), 2006, pp. 94-103.
[14] G. Chen, Fuzzy Data Modeling: Perspectives, Problems and Solutions.
Introduction to the Basic Principles of Fuzzy Set Theory and Some of its
Applications, Edited by E. E. Kerre, Gent, 1991, pp. 294-343.
[15] L. H. Chen and H. W. Lu, An Approximate Approach for Ranking
Fuzzy Numbers Based on Left and Right Dominance. Computers and
Mathematics with Applications, vol. 41(12), 2001, pp. 1589-1602.
[16] S. H. Chen, Ranking Fuzzy Numbers with Maximizing Set and Minimizing
Set. Fuzzy Sets and Systems, vol. 17(2), 1985, pp. 113-129.
[17] S. J. Chen and C. L. Hwang, Fuzzy Multiple Attribute Decision Making
- Methods and Applications, Berlin, 1992.
[18] C. H. Cheng, A New Approach for Ranking Fuzzy Numbers by Distance
Method. Fuzzy Sets and Systems, vol. 95(3), 1998, pp. 307-317.
[19] F. Choobineh and H. Li, An Index for Ordering Fuzzy Numbers. Fuzzy
Sets and Systems, vol. 54(3), 1993, pp. 287-294.
[20] T. C. Chu and C. T. Tsao, Ranking Fuzzy Numbers with an Area between
the Centroid Point and Original Point. Computers and Mathematics with
Applications, vol. 43(1-2), 2002, pp. 111-117.
[21] M. Delgado, J. L. Verdegay and M. A. Vila, A Procedure for Ranking
Fuzzy Numbers Using Fuzzy Relations. Fuzzy Sets and Systems, vol.
26(1), 1988, pp. 49-62.
[22] D. Dubois and H. Prade, Ranking Fuzzy Numbers in the Setting of
Possibility Theory. Information Sciences, vol. 30(3), 1983, pp. 183-224.
[23] D. Dubois and H. Prade, A Unified View of Ranking Techniques for
Fuzzy Numbers. Proceedings of the IEEE International Conference on
Fuzzy Systems, vol. 3, Seoul, 1999, pp. 1328-1333.
[24] J. Efstathiou and R. M. Tong, Ranking Fuzzy Sets Using Linguistic
Preference Relations. Proceedings of the International Symposium on
Multiple-Valued Logic, Evanston, 1980, pp. 137-142.
[25] P. Fortemps and M. Roubens, Ranking and Defuzzification Methods
Based on Area Compensation. Fuzzy Sets and Systems, vol. 82(3), 1996,
pp. 319-330.
[26] J. Galindo, A. Urrutia and M. Piattini, Fuzzy Databases: Modeling,
Design and Implementation, Hershey, 2006.
[27] R. Jain, A Procedure for Multiple-Aspect Decision-Making Using Fuzzy
Sets. International Journal of Systems Science, vol. 8(1), 1977, pp. 1-7.
[28] E. E. Kerre, The Use of Fuzzy Set Theory in Electrocardiological
Diagnostics. Approximate Reasoning in Decision Analysis, Edited by M.
M. Gupta and E. Sanchez, Amsterdam, 1982, pp. 277-282.
[29] K. Kim and K. S. Park, Ranking Fuzzy Numbers with Index of
Optimism. Fuzzy Sets and Systems, vol. 35(2), 1990, pp. 143-150.
[30] W. Kolodziejczyk, Orlovsky-s Concept of Decision-Making with Fuzzy
Preference Relation-Further Results. Fuzzy Sets and Systems, vol. 19(1),
1986, pp. 11-20.
[31] E. S. Lee and R. J. Li, Comparison of Fuzzy Numbers Based on the
Propability Measure of Fuzzy Events. Computers and Mathematics with
Applications, vol. 15(10), 1988, pp. 887-896.
[32] Z. Lian, B. Jiao and X. Gu, A Novel Method of Ranking Fuzzy Numbers
for Decision-Making Problems. International Conference on Intelligent
Systems Design and Applications, vol. 1, Jinan, 2006, pp. 354-360.
[33] T. S. Liou and M. J. J. Wang, Ranking Fuzzy Numbers with Integral
Value. Fuzzy Sets and Systems, vol. 50(3), 1992, pp. 247-255.
[34] Z. M. Ma and L. Yan, Updating Extended Possibility-Based Fuzzy
Relational Databases. International Journal of Inteligent Systems, vol.
22(3), 2007, pp. 237-258.
[35] S. Mabuchi, An Approach to the Comparison of Fuzzy Subsets with
an a-Cut Dependent Index. IEEE Transactions on Systems, Man and
Cybernetics, vol. 18(2), 1988, pp. 264-272.
[36] C. S. McCahon, Fuzzy Set Theory Applied to Production and Inventory
Control, Ph.D. Thesis, University of Kansas State, 1987.
[37] J. M. Medina, O. Pons and M. A. Vila, GEFRED. A Generalized Model
of Fuzzy Relational Databases. Ver. 1.1. Information Sciences, vol. 76(1-
2), 1994, pp. 87-109.
[38] S. Murakami, S. Maeda and S. Imamura, Fuzzy Decision Analysis
on the Development of Centralized Regional Energy Control System.
Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge
Representation and Decision Analysis, Marseille, 1983, pp. 363-368.
[39] K. Nakamura, Preference Relations on a Set of Fuzzy Utilities as a
Basis for Decision Making. Fuzzy Sets and Systems, vol. 20(2), 1986,
pp. 147-162.
[40] H. Prade and C. Testemale, Generalizing Database Relational Algebra
for the Treatment of Incomplete or Uncertain Information and Vague
Queries. Information Sciences, vol. 34(4), 1984, pp. 115-143.
[41] J. Ramik and J. Rimanek, Inequality Relation between Fuzzy Numbers
and its Use in Fuzzy Optimization. Fuzzy Sets and Systems, vol. 16(2),
1985, pp. 123-138.
[42] H. Rommelfanger, Rangordnungsverfahren fuer unscharfe Mengen - Ein
kritischer Vergleich mit empirisch ermittelten Praeferenzaussagen. ORSpectrum,
vol. 8(4), 1986, pp. 219-228.
[43] J. J. Saade and H. Schwarzlander, Ordering Fuzzy Sets over the Real
Line: An Approach Based on Decision Making under Uncertainty. Fuzzy
Sets and Systems, vol. 50(3), 1992, pp. 237-246.
[44] M. Setnes and V. Cross, Compatibility-Based Ranking of Fuzzy-
Numbers. Proceedings of the International Conference of the North
American Fuzzy Information Processing Society, Syracuse, 1997, pp.
305-310.
[45] S. Shenoi and A. Melton, An Extended Version of the Fuzzy Relational
Database Model. Information Sciences, vol. 52(1), 1990, pp. 35-52.
[46] X. Tang and G. Chen, A Complete Set of Fuzzy Relational Algebraic
Operators in Fuzzy Relational Databases. Proceedings of the IEEE
International Conference on Fuzzy Systems, vol. 1, Budapest, 2004, pp.
565-569.
[47] R. M. Tong and P. P. Bonissone, Linguistic Solutions to Fuzzy Decision
Problems. Studies in the Management Science, Edited by H. J. Zimmermann,
L. A. Zadeh and B. R. Gaines, vol. 20, North-Holland, 1984, pp.
323-334.
[48] L. Tran and L. Duckstein, Comparison of Fuzzy Numbers Using a Fuzzy
Distance Measure. Fuzzy Sets and Systems, vol. 130(3), 2002, pp. 331-
341.
[49] T. Y. Tseng and C. M. Klein, New Algorithm for the Ranking Procedure
in Fuzzy Decision-Making. IEEE Transactions on Systems, Man and
Cybernetics, vol. 19(5), 1989, pp. 1289-1296.
[50] Y. Tsukamoto, P. N. Nikiforuk and M. M. Gupta, On the Comparison of
Fuzzy Sets Using Fuzzy Chopping. Proceedings of the Triennial World
Congress of the International Federation of Automatic Control (Control
Science and Technology for the Progress of Society), vol. 5 (Process
Control), Kyoto, 1981, pp. 46-51.
[51] M. Umano, Freedom-0: A Fuzzy Database System. Fuzzy Information
and Decision Processes, Edited by M. M. Gupta and E. Sanchez,
Amsterdam, 1982, pp. 339-347.
[52] M. Umano and S. Fukami, Fuzzy Relational Algebra for Possibility-
Distribution-Fuzzy-Relational Model of Fuzzy Data. Journal of Intelligent
Information Systems, vol. 3(1), 1994, pp. 7-27.
[53] X. Wang and E. E. Kerre, On the Classification and the Dependencies
of the Ordering Methods. Fuzzy Logic Foundations and Industrial Applications,
Edited by D. Ruan, Dordrecht, 1996, pp. 73-90.
[54] X. Wang and E. E. Kerre, Reasonable Properties for the Ordering of
Fuzzy Quantities (I). Fuzzy Sets and Systems, vol. 118(3), 2001, pp. 375-
385.
[55] X. Wang and E. E. Kerre, Reasonable Properties for the Ordering of
Fuzzy Quantities (II). Fuzzy Sets and Systems, vol. 118(3), 2001, pp.
387-405.
[56] S. R. Watson, J. J. Weiss and M. L. Donnell, Fuzzy Decision Analysis.
IEEE Transactions on Systems, Man and Cybernetics, vol. 9(1), 1979,
pp. 1-9.
[57] R. R. Yager, Ranking Fuzzy Subsets over the Unit Interval. Proceedings
of the International Conference on Decision and Control, San Diego,
1978, pp. 1435-1437.
[58] R. R. Yager, On Choosing between Fuzzy Subsets. Kybernetes, vol. 9(2),
1980, pp. 151-154.
[59] R. R. Yager, A Procedure for Ordering Fuzzy Subsets of the Unit
Interval. Information Sciences, vol. 24(2), 1981, pp. 143-161.
[60] Y. Yuan, Criteria for Evaluating Fuzzy Ranking Methods. Fuzzy Sets
and Systems, vol. 43(2), 1991, pp. 139-157.
[61] M. Zemankova-Leech and A. Kandel, Fuzzy Relational Data Bases - A
Key to Expert Systems, Cologne, 1984.
[62] Q. Zhu and E. S. Lee, Comparison and Ranking of Fuzzy Numbers.
Fuzzy Regression Analysis, Edited by J. Kacprzyk and M. Fedrizzi,
Warsaw, 1992, pp. 21-44.
[1] S. Abbasbandy and B. Asasy, Ranking of Fuzzy Numbers by Sign
Distance. Information Sciences, vol. 176(16), 2006, pp. 2405-2416.
[2] J. M. Adamo, Fuzzy Decision Trees. Fuzzy Sets and Systems, vol. 4(3),
1980, pp. 207-219.
[3] S. M. Baas and H. Kwakernaak, Rating and Ranking of Multiple-Aspect
Alternatives Using Fuzzy Sets. Automatica, vol. 13(1), 1977, pp. 47-58.
[4] J. F. Baldwin and N. C. F. Guild, Comparison of Fuzzy Sets on the Same
Decision Space. Fuzzy Sets and Systems, vol. 2(3), 1979, pp. 213-231.
[5] G. Bortolan and R. Degani, A Review of Some Methods for Ranking
Fuzzy Subsets. Fuzzy Sets and Systems, vol. 15(1), 1985, pp. 1-19.
[6] P. Bosc and O. Pivert, About Projection-Selection-Join-Queries Addressed
to Possibilistic Relational Databases. IEEE Transactions on Fuzzy Systems,
vol. 13(1), 2005, pp. 124-139.
[7] B. P. Buckles and F. E. Petry, Query Languages for Fuzzy Databases.
Management Decision Support Systems Using Fuzzy Sets and Possibility
Theory, Edited by J. Kacprzyk and R. R. Yager, Cologne, 1985, pp. 241-
252.
[8] J. J. Buckley, A Fuzzy Ranking of Fuzzy Numbers. Fuzzy Sets and
Systems, vol. 33(1), 1989, pp. 119-121.
[9] J. J. Buckley and S. Chanas, A Fast Method of Ranking Alternatives
Using Fuzzy Numbers. Fuzzy Sets and Systems, vol. 30(3), 1989, pp.
337-338.
[10] R. De Caluwe, R. Vandenberghe, N. Van Gyseghem and A. Van
Schooten, Integrating Fuzziness in Database Models. Fuzziness in Database
Management Systems, Edited by P. Bosc and J. Kacprzyk, Heidelberg,
1995, pp. 71-113.
[11] L. M. De Campos-Ibanez and A. Gonzales-Munoz, A Subjective Approach
for Ranking Fuzzy Numbers. Fuzzy Sets and Systems, vol. 29(2),
1989, pp. 145-153.
[12] G. Canfora and L. Troiano, Fuzzy Ordering of Fuzzy Numbers. Proceedings
of the IEEE International Conference on Fuzzy Systems, vol. 2,
Budapest, 2004, pp. 669-674.
[13] J. R. Chang, C. H. Cheng and C. Y. Kuo, Conceptual Procedure of Ranking
Fuzzy Numbers Based on Adaptive Two-Dimensions Dominance. Soft
Computing - A Fusion of Foundations, Methodologies and Applications,
vol. 10(2), 2006, pp. 94-103.
[14] G. Chen, Fuzzy Data Modeling: Perspectives, Problems and Solutions.
Introduction to the Basic Principles of Fuzzy Set Theory and Some of its
Applications, Edited by E. E. Kerre, Gent, 1991, pp. 294-343.
[15] L. H. Chen and H. W. Lu, An Approximate Approach for Ranking
Fuzzy Numbers Based on Left and Right Dominance. Computers and
Mathematics with Applications, vol. 41(12), 2001, pp. 1589-1602.
[16] S. H. Chen, Ranking Fuzzy Numbers with Maximizing Set and Minimizing
Set. Fuzzy Sets and Systems, vol. 17(2), 1985, pp. 113-129.
[17] S. J. Chen and C. L. Hwang, Fuzzy Multiple Attribute Decision Making
- Methods and Applications, Berlin, 1992.
[18] C. H. Cheng, A New Approach for Ranking Fuzzy Numbers by Distance
Method. Fuzzy Sets and Systems, vol. 95(3), 1998, pp. 307-317.
[19] F. Choobineh and H. Li, An Index for Ordering Fuzzy Numbers. Fuzzy
Sets and Systems, vol. 54(3), 1993, pp. 287-294.
[20] T. C. Chu and C. T. Tsao, Ranking Fuzzy Numbers with an Area between
the Centroid Point and Original Point. Computers and Mathematics with
Applications, vol. 43(1-2), 2002, pp. 111-117.
[21] M. Delgado, J. L. Verdegay and M. A. Vila, A Procedure for Ranking
Fuzzy Numbers Using Fuzzy Relations. Fuzzy Sets and Systems, vol.
26(1), 1988, pp. 49-62.
[22] D. Dubois and H. Prade, Ranking Fuzzy Numbers in the Setting of
Possibility Theory. Information Sciences, vol. 30(3), 1983, pp. 183-224.
[23] D. Dubois and H. Prade, A Unified View of Ranking Techniques for
Fuzzy Numbers. Proceedings of the IEEE International Conference on
Fuzzy Systems, vol. 3, Seoul, 1999, pp. 1328-1333.
[24] J. Efstathiou and R. M. Tong, Ranking Fuzzy Sets Using Linguistic
Preference Relations. Proceedings of the International Symposium on
Multiple-Valued Logic, Evanston, 1980, pp. 137-142.
[25] P. Fortemps and M. Roubens, Ranking and Defuzzification Methods
Based on Area Compensation. Fuzzy Sets and Systems, vol. 82(3), 1996,
pp. 319-330.
[26] J. Galindo, A. Urrutia and M. Piattini, Fuzzy Databases: Modeling,
Design and Implementation, Hershey, 2006.
[27] R. Jain, A Procedure for Multiple-Aspect Decision-Making Using Fuzzy
Sets. International Journal of Systems Science, vol. 8(1), 1977, pp. 1-7.
[28] E. E. Kerre, The Use of Fuzzy Set Theory in Electrocardiological
Diagnostics. Approximate Reasoning in Decision Analysis, Edited by M.
M. Gupta and E. Sanchez, Amsterdam, 1982, pp. 277-282.
[29] K. Kim and K. S. Park, Ranking Fuzzy Numbers with Index of
Optimism. Fuzzy Sets and Systems, vol. 35(2), 1990, pp. 143-150.
[30] W. Kolodziejczyk, Orlovsky-s Concept of Decision-Making with Fuzzy
Preference Relation-Further Results. Fuzzy Sets and Systems, vol. 19(1),
1986, pp. 11-20.
[31] E. S. Lee and R. J. Li, Comparison of Fuzzy Numbers Based on the
Propability Measure of Fuzzy Events. Computers and Mathematics with
Applications, vol. 15(10), 1988, pp. 887-896.
[32] Z. Lian, B. Jiao and X. Gu, A Novel Method of Ranking Fuzzy Numbers
for Decision-Making Problems. International Conference on Intelligent
Systems Design and Applications, vol. 1, Jinan, 2006, pp. 354-360.
[33] T. S. Liou and M. J. J. Wang, Ranking Fuzzy Numbers with Integral
Value. Fuzzy Sets and Systems, vol. 50(3), 1992, pp. 247-255.
[34] Z. M. Ma and L. Yan, Updating Extended Possibility-Based Fuzzy
Relational Databases. International Journal of Inteligent Systems, vol.
22(3), 2007, pp. 237-258.
[35] S. Mabuchi, An Approach to the Comparison of Fuzzy Subsets with
an a-Cut Dependent Index. IEEE Transactions on Systems, Man and
Cybernetics, vol. 18(2), 1988, pp. 264-272.
[36] C. S. McCahon, Fuzzy Set Theory Applied to Production and Inventory
Control, Ph.D. Thesis, University of Kansas State, 1987.
[37] J. M. Medina, O. Pons and M. A. Vila, GEFRED. A Generalized Model
of Fuzzy Relational Databases. Ver. 1.1. Information Sciences, vol. 76(1-
2), 1994, pp. 87-109.
[38] S. Murakami, S. Maeda and S. Imamura, Fuzzy Decision Analysis
on the Development of Centralized Regional Energy Control System.
Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge
Representation and Decision Analysis, Marseille, 1983, pp. 363-368.
[39] K. Nakamura, Preference Relations on a Set of Fuzzy Utilities as a
Basis for Decision Making. Fuzzy Sets and Systems, vol. 20(2), 1986,
pp. 147-162.
[40] H. Prade and C. Testemale, Generalizing Database Relational Algebra
for the Treatment of Incomplete or Uncertain Information and Vague
Queries. Information Sciences, vol. 34(4), 1984, pp. 115-143.
[41] J. Ramik and J. Rimanek, Inequality Relation between Fuzzy Numbers
and its Use in Fuzzy Optimization. Fuzzy Sets and Systems, vol. 16(2),
1985, pp. 123-138.
[42] H. Rommelfanger, Rangordnungsverfahren fuer unscharfe Mengen - Ein
kritischer Vergleich mit empirisch ermittelten Praeferenzaussagen. ORSpectrum,
vol. 8(4), 1986, pp. 219-228.
[43] J. J. Saade and H. Schwarzlander, Ordering Fuzzy Sets over the Real
Line: An Approach Based on Decision Making under Uncertainty. Fuzzy
Sets and Systems, vol. 50(3), 1992, pp. 237-246.
[44] M. Setnes and V. Cross, Compatibility-Based Ranking of Fuzzy-
Numbers. Proceedings of the International Conference of the North
American Fuzzy Information Processing Society, Syracuse, 1997, pp.
305-310.
[45] S. Shenoi and A. Melton, An Extended Version of the Fuzzy Relational
Database Model. Information Sciences, vol. 52(1), 1990, pp. 35-52.
[46] X. Tang and G. Chen, A Complete Set of Fuzzy Relational Algebraic
Operators in Fuzzy Relational Databases. Proceedings of the IEEE
International Conference on Fuzzy Systems, vol. 1, Budapest, 2004, pp.
565-569.
[47] R. M. Tong and P. P. Bonissone, Linguistic Solutions to Fuzzy Decision
Problems. Studies in the Management Science, Edited by H. J. Zimmermann,
L. A. Zadeh and B. R. Gaines, vol. 20, North-Holland, 1984, pp.
323-334.
[48] L. Tran and L. Duckstein, Comparison of Fuzzy Numbers Using a Fuzzy
Distance Measure. Fuzzy Sets and Systems, vol. 130(3), 2002, pp. 331-
341.
[49] T. Y. Tseng and C. M. Klein, New Algorithm for the Ranking Procedure
in Fuzzy Decision-Making. IEEE Transactions on Systems, Man and
Cybernetics, vol. 19(5), 1989, pp. 1289-1296.
[50] Y. Tsukamoto, P. N. Nikiforuk and M. M. Gupta, On the Comparison of
Fuzzy Sets Using Fuzzy Chopping. Proceedings of the Triennial World
Congress of the International Federation of Automatic Control (Control
Science and Technology for the Progress of Society), vol. 5 (Process
Control), Kyoto, 1981, pp. 46-51.
[51] M. Umano, Freedom-0: A Fuzzy Database System. Fuzzy Information
and Decision Processes, Edited by M. M. Gupta and E. Sanchez,
Amsterdam, 1982, pp. 339-347.
[52] M. Umano and S. Fukami, Fuzzy Relational Algebra for Possibility-
Distribution-Fuzzy-Relational Model of Fuzzy Data. Journal of Intelligent
Information Systems, vol. 3(1), 1994, pp. 7-27.
[53] X. Wang and E. E. Kerre, On the Classification and the Dependencies
of the Ordering Methods. Fuzzy Logic Foundations and Industrial Applications,
Edited by D. Ruan, Dordrecht, 1996, pp. 73-90.
[54] X. Wang and E. E. Kerre, Reasonable Properties for the Ordering of
Fuzzy Quantities (I). Fuzzy Sets and Systems, vol. 118(3), 2001, pp. 375-
385.
[55] X. Wang and E. E. Kerre, Reasonable Properties for the Ordering of
Fuzzy Quantities (II). Fuzzy Sets and Systems, vol. 118(3), 2001, pp.
387-405.
[56] S. R. Watson, J. J. Weiss and M. L. Donnell, Fuzzy Decision Analysis.
IEEE Transactions on Systems, Man and Cybernetics, vol. 9(1), 1979,
pp. 1-9.
[57] R. R. Yager, Ranking Fuzzy Subsets over the Unit Interval. Proceedings
of the International Conference on Decision and Control, San Diego,
1978, pp. 1435-1437.
[58] R. R. Yager, On Choosing between Fuzzy Subsets. Kybernetes, vol. 9(2),
1980, pp. 151-154.
[59] R. R. Yager, A Procedure for Ordering Fuzzy Subsets of the Unit
Interval. Information Sciences, vol. 24(2), 1981, pp. 143-161.
[60] Y. Yuan, Criteria for Evaluating Fuzzy Ranking Methods. Fuzzy Sets
and Systems, vol. 43(2), 1991, pp. 139-157.
[61] M. Zemankova-Leech and A. Kandel, Fuzzy Relational Data Bases - A
Key to Expert Systems, Cologne, 1984.
[62] Q. Zhu and E. S. Lee, Comparison and Ranking of Fuzzy Numbers.
Fuzzy Regression Analysis, Edited by J. Kacprzyk and M. Fedrizzi,
Warsaw, 1992, pp. 21-44.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57094", author = "Marcel Shirvanian and Wolfram Lippe", title = "Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages", abstract = "Although the usefulness of fuzzy databases has been
pointed out in several works, they are not fully developed in numerous
domains. A task that is mostly disregarded and which is the topic
of this paper is the determination of suitable inequalities for fuzzy
sets in fuzzy query languages. This paper examines which kinds
of fuzzy inequalities exist at all. Afterwards, different procedures
are presented that appear theoretically appropriate. By being applied
to various examples, their strengths and weaknesses are revealed.
Furthermore, an algorithm for an efficient computation of the selected
fuzzy inequality is shown.", keywords = "Fuzzy Databases, Fuzzy Inequalities, Fuzzy QueryLanguages, Fuzzy Ranking.", volume = "2", number = "10", pages = "724-7", }
