CLC number: TP273
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2014-06-16
Cited: 2
Clicked: 8229
Farnaz Sabahi, M.-R. Akbarzadeh-T. A framework for analysis of extended fuzzy logic[J]. Journal of Zhejiang University Science C, 2014, 15(7): 584-591.
@article{title="A framework for analysis of extended fuzzy logic",
author="Farnaz Sabahi, M.-R. Akbarzadeh-T",
journal="Journal of Zhejiang University Science C",
volume="15",
number="7",
pages="584-591",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.C1300217"
}
%0 Journal Article
%T A framework for analysis of extended fuzzy logic
%A Farnaz Sabahi
%A M.-R. Akbarzadeh-T
%J Journal of Zhejiang University SCIENCE C
%V 15
%N 7
%P 584-591
%@ 1869-1951
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C1300217
TY - JOUR
T1 - A framework for analysis of extended fuzzy logic
A1 - Farnaz Sabahi
A1 - M.-R. Akbarzadeh-T
J0 - Journal of Zhejiang University Science C
VL - 15
IS - 7
SP - 584
EP - 591
%@ 1869-1951
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C1300217
Abstract: We address a framework for the analysis of fuzzy logic%29&ck%5B%5D=abstract&ck%5B%5D=keyword'>extended fuzzy logic (FLe) and elaborate mainly the key characteristics of FLe by proving several qualification theorems and proposing a new mathematical tool named the A-granule. Specifically, we reveal that within FLe a solution in the presence of incomplete information approaches the one gained by complete information. It is also proved that the answers and their validities have a structural isomorphism within the same context. This relationship is then used to prove the representation theorem that addresses the rationality of FLe-based reasoning. As a consequence of the developed theoretical description of FLe, we assert that in order to solve a problem, having complete information is not a critical need; however, with more information, the answers achieved become more specific. Furthermore, reasoning based on FLe has the advantage of being computationally less expensive in the analysis of a given problem and is faster.
[1]Aliev, R.A., Alizadeh, A.V., Guirimov, B.G., 2010. Unpre-cisiated information-based approach to decision making with imperfect information. Proc. 9th Int. Conf. on Application of Fuzzy Systems and Soft Computing, p.387-397.
[2]Dubois, D., Prade, H., 1996. What are fuzzy rules and how to use them. Fuzzy Sets Syst., 84(2):169-185.
[3]Dubois, D., Prade, H., 2012. Gradualness, uncertainty and bipolarity: making sense of fuzzy sets. Fuzzy Sets Syst., 192:3-24.
[4]Hájek, P., 2006. What is mathematical fuzzy logic. Fuzzy Sets Syst., 157(5):597-603.
[5]Imran, B.M., Beg, M.M.S., 2011. Elements of sketching with words. Int. J. Gran. Comput. Rough Sets Intell. Syst., 2(2):166-178.
[6]Imran, B.M., Beg, M.M.S., 2012. Fuzzy identification of geometric shapes. In: Meghanathan, N., Chaki, N., Nagamalai, D. (Eds.), Advances in Computer Science and Information Technology. Springer Berlin Heidelberg, p.269-279.
[7]Niskanen, V.A., 2009. Application of Zadeh’s impossibility principle to approximate explanation. IFSA/EUSFLAT Conf., p.561-567.
[8]Niskanen, V.A., 2010. A meta-level approach to approximate probability. In: Setchi, R., Jordanov, I., Howlett, R.J., et al. (Eds.), Knowledge-based and Intelligent Information and Engineering Systems. Springer Berlin Heidelberg, p.116-123.
[9]Niskanen, V.A., 2012. Prospects for applying fuzzy extended logic to scientific reasoning. In: Kantola, J., Karwowski, W. (Eds.), Knowledge Service Engineering Handbook. CRC Press, p.279-306.
[10]Niskanen, V.A., 2013. On examination of medical data with approximate reasoning. In: Seising, R., Tabacchi, M.E. (Eds.), Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care. Springer Berlin Heidelberg, p.269-290.
[11]Perfilieva, I., 2006. Fuzzy transforms: theory and applications. Fuzzy Sets Syst., 157(8):993-1023.
[12]Raha, S., Ray, K.S., 1999. Reasoning with vague truth. Fuzzy Sets Syst., 105(3):385-399.
[13]Sabahi, F., Akbarzadeh-T, M.R., 2013. A qualified descrip-tion of extended fuzzy logic. Inform. Sci., 244:60-74.
[14]Sabahi, F., Akbarzadeh-T, M.R., 2014a. Comparative evaluation of risk factors in coronary heart disease based on fuzzy probability-validity modeling. ZUMS J., 22(91):73-83.
[15]Sabahi, F., Akbarzadeh-T, M.R., 2014b. Introducing validity in fuzzy probability for judicial decision-making. Int. J. Approx. Reason., 55(6):1383-1403.
[16]Tolosa, J.B., Guadarrama, S., 2010. Collecting fuzzy percep-tions from non-expert users. IEEE Int. Conf. on Fuzzy Systems, p.1-8.
[17]Wilke, G., 2009. Approximate geometric reasoning with extended geographic objects. Proc. Workshop on Quality, Scale and Analysis Aspects of City Models, p.102-106.
[18]Zadeh, L.A., 1965. Fuzzy sets. Inform. Contr., 8(3):338-353.
[19]Zadeh, L.A., 1997. Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst., 90(2):111-127.
[20]Zadeh, L.A., 2009. Toward extended fuzzy logic—a first step. Fuzzy Sets Syst., 160(21):3175-3181.
[21]Zadeh, L.A., 2010. Precisiation of Meaning—Toward Computation with Natural Language. Key Note on IRI, Las Vegas, Nevada.
Open peer comments: Debate/Discuss/Question/Opinion
<1>