Extension to fuzzy logic representation: Moving towards neutrosophic logic - A new laboratory rat

Real world problems have been effectively modeled using fuzzy logic that gives suitable representation of real-world data/information and enables reasoning that is approximate in nature. It is quite uncommon that the inputs captured by the fuzzy models are 100% complete and determinate. Though, humans can take intelligent decisions in such situations but fuzzy models require complete information. Incompleteness and indeterminacy in the data can arise from inherent non-linearity, time-varying nature of the process to be controlled, large unpredictable environmental disturbances, degrading sensors or other difficulties in obtaining precise and reliable measurements. Neutrosophic logic is an extended and general framework for measuring the truth, indeterminacy and falsehood-ness of the information. It is effective in representing different attributes of information like inaccuracy, incompleteness and ambiguous, thus giving fair estimate about the reliability of information. This paper suggests extending the capabilities of fuzzy representation and reasoning system by introducing Neutrosophic representation of the data and Neutrosophic reasoning system.

[1]  J. Harris Fuzzy Logic Applications in Engineering Science , 2005 .

[2]  Ivor Grattan-Guinness,et al.  Fuzzy Membership Mapped onto Intervals and Many-Valued Quantities , 1976, Math. Log. Q..

[3]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[4]  Ronald R. Yager,et al.  Decision making with fuzzy probability assessments , 1999, IEEE Trans. Fuzzy Syst..

[5]  Jerry M. Mendel,et al.  Advances in type-2 fuzzy sets and systems , 2007, Inf. Sci..

[6]  Z. Pawlak Rough set approach to knowledge-based decision support , 1997 .

[7]  Etienne E. Kerre,et al.  On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision , 2007, Inf. Sci..

[8]  Rohit Parikh,et al.  An Inconsistency Tolerant Model for Belief Representation and Belief Revision , 1999, IJCAI.

[9]  Lotfi A. Zadeh,et al.  Computing with Words and Perceptions - A Paradigm Shift , 2009, PDPTA.

[10]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[11]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[12]  Z. Pawlak,et al.  Rough sets perspective on data and knowledge , 2002 .

[13]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[14]  F. Smarandache A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[15]  Florentin Smarandache Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic , 2003, EUSFLAT Conf..

[16]  J. Buckley Fuzzy Probability and Statistics , 2006 .

[17]  Marzena Kryszkiewicz,et al.  Rough Set Approach to Incomplete Information Systems , 1998, Inf. Sci..

[18]  Jun Ye,et al.  Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment , 2009, Expert Syst. Appl..

[19]  Ronald R. Yager A General Approach to Uncertainty Representation Using Fuzzy Measures , 2001, FLAIRS Conference.

[20]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[21]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[22]  K. Jahn Intervall‐wertige Mengen , 1975 .

[23]  Alexej P. Pynko Functional completeness, axiomatizability within Belnap's four valued logic and its expansions , 1999, J. Appl. Non Class. Logics.

[24]  Emil L. Post Introduction to a General Theory of Elementary Propositions , 1921 .

[25]  Florentin Smarandache,et al.  Neutrosophy, A New Branch of Philosophy , 2014 .

[26]  Zhou-Jing Wang,et al.  An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights , 2009, Inf. Sci..

[27]  Huawen Liu,et al.  Multi-criteria decision-making methods based on intuitionistic fuzzy sets , 2007, Eur. J. Oper. Res..

[28]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[29]  R. A. ALIEV,et al.  Decision Theory with Imprecise Probabilities , 2012, Int. J. Inf. Technol. Decis. Mak..

[30]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[31]  Robert Ivor John,et al.  Type 2 Fuzzy Sets: An Appraisal of Theory and Applications , 1998, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[32]  Deng-Feng Li,et al.  Multiattribute decision making models and methods using intuitionistic fuzzy sets , 2005, J. Comput. Syst. Sci..

[33]  Lotfi A. Zadeh,et al.  Computation with imprecise probabilities , 2008, IRI.

[34]  Alexei Yu. Muravitsky,et al.  A knowledge representation based on the Belnap's four-valued logic , 1995, J. Appl. Non Class. Logics.

[35]  N. K. Sinha,et al.  Fuzzy Logic Applications in Engineering Science , 2006 .

[36]  Zdzislaw Pawlak,et al.  Rough Set Theory and its Applications to Data Analysis , 1998, Cybern. Syst..

[37]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[38]  RONALD R. YAGER,et al.  Fuzzy Subsets of Type Ii in Decisions , 1980, Cybern. Syst..

[39]  Ioannis K. Vlachos,et al.  Intuitionistic fuzzy information - Applications to pattern recognition , 2007, Pattern Recognit. Lett..

[40]  Ranjit Biswas,et al.  An application of intuitionistic fuzzy sets in medical diagnosis , 2001, Fuzzy Sets Syst..

[41]  Lotfi A. Zadeh,et al.  Generalized theory of uncertainty (GTU) - principal concepts and ideas , 2006, Comput. Stat. Data Anal..