Diversity of Opinion Evaluated by Ordered Fuzzy Numbers

Diversity of opinion is an empirical fact often appearing in social networks. In the paper known statistical methods of evaluation is substituted by fuzzy concepts, namely Step Ordered Fuzzy Numbers (SOFN). SOFN are extentions of Ordered Fuzzy Numbers (OFN) introduced by Kosinski, Prokopowicz and Ślezak in 2002. In 2011 Kacprzak and Kosinski observed that SOFN may be equipped with a lattice structure. In consequence, Boolean operations like conjunction, disjunction and, what is more important, diverse types of implications can be defined on SOFN. In this paper we show how SOFN can be applied for modelling diversity of beliefs even in fuzzy expressions.

[1]  Guanrong Chen,et al.  Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems , 2000 .

[2]  Janusz Kacprzyk,et al.  Views on Fuzzy Sets and Systems from Different Perspectives , 2009 .

[3]  Dominik Ślęzak,et al.  Ordered fuzzy numbers , 2003 .

[4]  D. Swanson.  Medical literature as a potential source of new knowledge. , 1990, Bulletin of the Medical Library Association.

[5]  Magdalena Kacprzak,et al.  On lattice structure and implications on ordered fuzzy numbers , 2011, EUSFLAT Conf..

[6]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[7]  M. K. Luhandjula.  Studies in Fuzziness and Soft Computing , 2013 .

[8]  L. Goble.  The Blackwell guide to philosophical logic , 2001 .

[9]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[10]  Richard S. Bird,et al.  An introduction to the theory of lists , 1987 .

[11]  K. Tanaka.  The Blackwell Guide to Philosophical Logic , 2002 .

[12]  Witold Kosiński,et al.  On fuzzy number calculus , 2006 .

[13]  George J. Klir,et al.  Fuzzy arithmetic with requisite constraints , 1997, Fuzzy Sets Syst..

[14]  Dominik Slezak,et al.  Fuzzy Reals with Algebraic Operations: Algorithmic Approach , 2002, Intelligent Information Systems.

[15]  Joseph Y. Halpern.  Reasoning about uncertainty , 2003 .

[16]  Michal Baczynski,et al.  Fuzzy Implications , 2008, Studies in Fuzziness and Soft Computing.

[17]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[18]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[19]  Anand Kumar,et al.  Text mining and ontologies in biomedicine: Making sense of raw text , 2005, Briefings Bioinform..

[20]  L. Zadeh.  The role of fuzzy logic in the management of uncertainty in expert systems , 1983 .

[21]  Magdalena Kacprzak,et al.  Perseus. Software for Analyzing Persuasion Process , 2009, Fundam. Informaticae.

[22]  Witold Kosiński,et al.  Meta Sets – Another Approach to Fuzziness , 2009 .

[23]  Dominik Slezak,et al.  Algebraic Operations on Fuzzy Numbers , 2003, IIS.

[24]  Joel D. Martin,et al.  Getting to the (c)ore of knowledge: mining biomedical literature , 2002, Int. J. Medical Informatics.

[25]  D. Dubois,et al.  Operations on fuzzy numbers , 1978 .

[26]  Grzegorz Malinowski,et al.  Many-Valued Logics , 1994 .