How to measure the amount of knowledge conveyed by Atanassov's intuitionistic fuzzy sets

We address the problem of how to measure the amount of knowledge conveyed by the Atanassov's intuitionistic fuzzy set (A-IFS for short). The problem is relevant from the point of view of many application areas, notably decision making. An amount of knowledge considered is strongly linked to its related amount of information. Our analysis is concerned with an intrinsic relationship between the positive and negative information and a lack of information expressed by the hesitation margin. Illustrative examples are shown.

[1]  Janusz Kacprzyk,et al.  A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work , 2007, 2007 IEEE International Fuzzy Systems Conference.

[2]  J. Baldwin,et al.  Entropy for Intuitionistic Fuzzy, Set Theory and Mass Assignment Theory , 2004 .

[3]  V. Kreinovich,et al.  Symmetry Between True, False, and Uncertain: An Explanation , 2009 .

[4]  Janusz Kacprzyk,et al.  Entropy for intuitionistic fuzzy sets , 2001, Fuzzy Sets Syst..

[5]  Eulalia Szmidt,et al.  Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[6]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[7]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[8]  J. Kacprzyk,et al.  An intuitionistic fuzzy set based approach to intelligent data analysis: an application to medical diagnosis , 2003 .

[9]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[10]  E. Szmidt,et al.  Classification of Imbalanced and Overlapping Classes using Intuitionistic Fuzzy Sets , 2006, 2006 3rd International IEEE Conference Intelligent Systems.

[11]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[12]  S. Ahamed.  Wealth of Knowledge , 2006 .

[13]  Renata M. C. R. de Souza,et al.  Statistical proximity functions of Boolean symbolic objects based on histograms , 1998 .

[14]  Janusz Kacprzyk,et al.  Analysis of consensus under intuitionistic fuzzy preferences , 2001, EUSFLAT Conf..

[15]  Francisco de A. T. de Carvalho,et al.  Proximity Coefficients between Boolean symbolic objects , 1994 .

[16]  Janusz Kacprzyk,et al.  Intuitionistic fuzzy sets - two and three term representations in the context of a Hausdor distance , 2011 .

[17]  Eulalia Szmidt,et al.  Amount of Information and Its Reliability in the Ranking of Atanassov’s Intuitionistic Fuzzy Alternatives , 2009 .

[18]  Janusz Kacprzyk,et al.  Some Problems with Entropy Measures for the Atanassov Intuitionistic Fuzzy Sets , 2007, WILF.

[19]  Eulalia Szmidt,et al.  A NEW APPROACH TO RANKING ALTERNATIVES EXPRESSED VIA INTUITIONISTIC FUZZY SETS , 2008 .

[20]  Janusz Kacprzyk,et al.  Measuring the Amount of Knowledge for Atanassov's Intuitionistic Fuzzy Sets , 2011, WILF.

[21]  Eulalia Szmidt,et al.  Atanassov's Intuitionistic Fuzzy Sets in Classification of Imbalanced and Overlapping Classes , 2008, Intelligent Techniques and Tools for Novel System Architectures.

[22]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[23]  Janusz Kacprzyk,et al.  Dealing with typical values via Atanassov's intuitionistic fuzzy sets , 2010, Int. J. Gen. Syst..

[24]  Krassimir T. Atanassov,et al.  On Intuitionistic Fuzzy Sets Theory , 2012, Studies in Fuzziness and Soft Computing.

[25]  J. Kacprzyk,et al.  Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work , 2006, 2006 3rd International IEEE Conference Intelligent Systems.

[26]  Eulalia Szmidt,et al.  A New Approach to Classification of Imbalanced Classes via Atanassov's Intuitionistic Fuzzy Sets , 2009 .

[27]  Janusz Kacprzyk,et al.  An Application of Intuitionistic Fuzzy Set Similarity Measures to a Multi-criteria Decision Making Problem , 2006, ICAISC.