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A New Condition for Conflicting Bifuzzy Sets Based On Intuitionistic Evaluation

Authors: Imran C.T., Syibrah M.N., Mohd Lazim A.

Abstract:

Fuzzy sets theory affirmed that the linguistic value for every contraries relation is complementary. It was stressed in the intuitionistic fuzzy sets (IFS) that the conditions for contraries relations, which are the fuzzy values, cannot be greater than one. However, complementary in two contradict phenomena are not always true. This paper proposes a new idea condition for conflicting bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets. Here, we will critically forward examples using triangular fuzzy number in formulating a new condition for conflicting bifuzzy sets (CBFS). Evaluation of positive and negative in conflicting phenomena were calculated concurrently by relaxing the condition in IFS. The hypothetical illustration showed the applicability of the new condition in CBFS for solving non-complement contraries intuitionistic evaluation. This approach can be applied to any decision making where conflicting is very much exist.

Keywords: Conflicting bifuzzy set, conflicting degree, fuzzy sets, fuzzy numbers.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070231

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References:


[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 11087 - 96, 1986.
[2] K. Atanassov, Remarks on the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 75, 401- 402, 1995.
[3] K. Atanassov, Intuitionistics fuzzy sets, Physica-Verlag, (Heidelberg/New York, 1999).
[4] K. Atanassov, Two theorems for intuitionistics fuzzy sets, Fuzzy Sets and System, 110(2000) 267 - 269.
[5] M. T. Abu Osman, Conflicting bifuzzy evaluation, Proceeding and Mathematics Symposium (CSMS06). Kolej Universiti Sains dan Teknologi Malaysia, Kuala Terengganu, Malaysia (8 - 9 Nov 2006) In Malay.
[6] K. Basu, R. Deb and P. K. Pattanaik, Soft sets: an ordinal formulation of vagueness with some applications to the theory of choice, Fuzzy Sets and Systems, 45(1992) 45- 58.
[7] P. Burillo and H. Bustinces, Construction theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 84(1996) 271 - 281.
[8] W. L. Gau and D. J. Buehrer, Vague sets, IEEE Trans. Systems Man. Cybernet, 23(2)(1993) 610 - 614.
[9] J. K. George and Y. Bo, Fuzzy sets and fuzzy logic theory and applications, (Prentice- Hall of India Private limited, 2000).
[10] C. Gianpiero and C. David, Basic intuitionistic principle in fuzzy set theories and its extension (A terminological debate on Atanassov IFS), Fuzzy Sets and System, 157(2006) 3198 - 3219.
[11] J. Goguen, L -fuzzy sets, Journals of Mathematical Analysis and Applications, 18(1967) 145 - 174.
[12] D. Kahneman, & S. Frederick, A model of heuristic judgment. In K. J. Holyoak & R. G. Morrison (Eds.), Cambridge MA: Cambridge University Press. The cambridge Handbook of thinking and reasoning (pp. 267 - 293, 2005.)
[13] D. F. Li, F. Shan and C. T. Cheng, on properties of four IFS operators, Fuzzy Sets and Systems, 154(2005) 151 - 155.
[14] G. Przemyslaw and M. Edyta, Some notes on (Atanassov-s) intuitionistic fuzzy sets, Fuzzy Sets and System, 156(2005) 492 - 495.
[15] R. Sambuc, Fonctions O -floues. Application a-l-aide au diagnostic en pathologie thyrodienne, Ph.D. Thesis, Universite- de Marseille, France.
[16] K. D. Supriya, B. Ranjit and R. R. Akhil, Some operations on intuitionistic fuzzy sets, Fuzzy Sets and System, 114(2000) 477 - 484.
[17] G. Tadeusz and M. Jacek, Bifuzzy probabilistic sets, Fuzzy Sets and Systems, 71(1995) 207 - 214.
[18] C. Tamalika and A.K. Raya, A new measure using intuitionistic fuzzy set theory and its application to edge detection, Applied Soft Computing, xxx(2007) xxx-xxx.
[19] L. A. Zadeh, Fuzzy Sets, Information and Control, 8(1965) 338 - 353.
[20] T. Zamali, A. Mohd Lazim, M. T. Abu Osman, An Introduction to Conflicting Bifuzzy Sets Theory, International Journal of Mathematics and Statistics, (2008) 86 - 101.
[21] W. R. Zhang and L. Zhang, YinYang bipolar logic and bipolar fuzzy logic, Information Sciences, 165(2004) 265 - 287.
[22] A. Kauffman, and M.M Gupta, (1985) . Introduction to Fuzzy Arithmetic: Theory and application., Van Nostrand-Reinhold.