A New Condition for Conflicting Bifuzzy Sets Based On Intuitionistic Evaluation

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.

Authors:

• Imran C.T.
• Syibrah M.N.
• Mohd Lazim A.

Keywords:

• Conflicting bifuzzy set
• conflicting degree
• fuzzy sets
• fuzzy numbers.

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.