A Comparative study of different order relations of intervals

Reliable Computing

Volumn 16, Issue , 2012, Pages 38-72

  Karmakar, Samiran ^a   Bhunia, A K ^b  

^a ST XAVIER S COLLEGE   (India)

^b UNIVERSITY OF BURDWAN   (India)

Author keywords

90 02; Interval numbers; Interval order relations; Optimization AMS subject classifications

Indexed keywords

90-02; COMPARATIVE STUDIES; DECISION-MAKING PROBLEM; DIFFERENT ORDER; INTERVAL NUMBER; INTERVAL ORDERS; ORDER RELATION;

EID: 84856998407     PISSN: 13853139     EISSN: 15731340     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. S. Chanas and D. Kuchta. Multiobjective programming in optimization of interval objective functions - A generalized approach. European Journal of Operational Research, 94(3):594-598, 1996. (Pubitemid 126391964)
2. B. Q. Hu and S. Wang. A novel approach in uncertain programming part i: New arithmetic and order relation for interval numbers. Journal of Industrial and Management Optimization, 2(4):351-371, 2006.
3. H. Ishibuchi and H. Tanaka. Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48:219-225, 1990.
4. L. Jaulin, M. Kiefier, O. Didrit, and E. Walter. Applied Interval Analysis with Examples in Parameter and State Estimation, Robust Control and Robotics. Springer-Verlag, London, 2001.
5. R. B. Kearfott. Rigorous Global Search: Continuous Problems. Kluwer, Dor- drecht, 1996.
6. Z. Kulpa. Diagrammatic representation for a space of intervals. Machine Graphics and Vision, 6(1):5-24, 1997.
7. Z. Kulpa. Diagrammatic representation for interval arithmetic. Linear Algebra and its Applications, 324:55-80, 2001.
8. Z. Kulpa. A diagrammatic approach to investigate interval relations. Journal of Visual Languages and Computing, 17:466-502, 2006. (Pubitemid 44296404)
9. S. Kundu. Min-transitivity of fuzzy leftness relationship and its application to decision making. Fuzzy Sets and Systems, 86:357-367, 1997. (Pubitemid 127683590)
10. V. I. Levin. Ordering of intervals and optimization problems with interval pa- rameters. Cybernetics and Systems Analysis, 40(3):316-323, 2004.
11. S. K. Mahato and A. K. Bhunia. Interval-arithmetic-oriented interval computing technique for global optimization. Applied Mathematics Research Express, 2006:1- 19, 2006.
12. R. E. Moore. Methods and Applications of Interval Analysis. SIAM, Philadelphia, 1979.
13. R. E. Moore, R. B. Kearfott, and M. J. Cloud. Introduction to Interval Analysis. SIAM, Philadelphia, 2009.
14. A. Sengupta and T. K Pal. On comparing interval numbers. European Journal of Operational Research, 127:28-43, 2000.
15. P. Sevastjanov and P. Róg. Two-objective method for crisp and fuzzy interval comparison in optimization. Computers and Operations Research, 33:115-131, 2006. (Pubitemid 40920612)
16. R. R. Yager. An introduction to applications of possibility theory. Human Systems Management, 3:246-269, 1983.
17. L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1:3-28, 1978.
18. Q. Zhang, Z. P. Fan, and D. H. Pan. A ranking approach for interval numbers in uncertain multiple attribute decision making problems. Systems Engineering - Theory and Practice, 5:129-133, 1999.