The concept of Hukuhara Derivative and Aumann Integrals for Intuitionistic fuzzy number valued functions
Abstract
In this paper we have frstly defned a metric in intuitionistic fuzzy environment and studied its properties. Then we have proved that the metric space of fuzzy number valued functions is complete under this metric. We have studied the concept of Aumann integration for intuitionistic fuzzy number valued functions in terms of α and β cuts. We have given the relation between Hukuhara derivative and Aumann integral for intuitionistic fuzzy valued functions by using the fundamental theorem of calculus.
Keywords
References
- [1] Lotf A. Z., ”Fuzzy Sets,” Information and Control, 8, (1965), pp. 338-353.
- [2] Krassimir T. A., ”Intuitionistic Fuzzy Sets,” Fuzzy Sets and Systems, 20, 1, (1986), pp. 87–96.
- [3] Joseph A. G. ”L-Fuzzy Sets,” Journal of Mathematical Analysis and Applications, 18, 1,(1967), 145-174.
- [4] Jerry M. M. ”Advances in Type-2 Fuzzy Sets and Systems,” Information Sciences, 177, 1, (2007), pp. 84-110.
- [5] Krassimir T. A., Intuitionistic Fuzzy Sets: Theory and Applications, Physica, Heidelberg, 1999.
- [6] Laecio C. B., Rodney C. B, Pedro A. T., ”Fuzzy Modelling in Population Dynamics,” Ecol. Model, 128, (2000), pp. 27-33.
- [7] Deng-Feng L., ”Multiattribute Decision Making Models and Methods Using Intuitionistic Fuzzy Sets,” Journal of Computer and System Sciences, 70, 1 (2005), pp. 73-85.
- [8] Jun Y., ”Multicriteria Fuzzy Decision-Making Method Based on a Novel Accuracy Function under Interval-Valued Intuitionistic Fuzzy Environment,” Expert Systems with Applications, 36, 3, (2009), pp. 6899-6902.
- [9] Li D., Cheng C., ”New Similarity Measures of Intuitionistic Fuzzy Sets and Application to Pattern Recognitions,” Pattern Recognition Letters, 23, 1-3, (2002), pp. 221-225.
- [10] Supriya K. D., Ranjit B., Akhil R. R., ”An Application of Intuitionistic Fuzzy Sets in Medical Diagnosis,” Fuzzy Sets and Systems, 117, 2, (2001), pp. 209-213.