Computing with words with the use of inverse RDM models of membership functions

Abstract Computing with words is a way to artificial, human-like thinking. The paper shows some new possibilities of solving difficult problems of computing with words which are offered by relative-distance-measure RDM models of fuzzy membership functions. Such models are based on RDM interval arithmetic. The way of calculation with words was shown using a specific problem of flight delay formulated by Lotfi Zadeh. The problem seems easy at first sight, but according to the authors’ knowledge it has not been solved yet. Results produced with the achieved solution were tested. The investigations also showed that computing with words sometimes offers possibilities of achieving better problem solutions than with the human mind.

[1]  E. R. Hansen,et al.  A Generalized Interval Arithmetic , 1975, Interval Mathematics.

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

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

[4]  Andrzej Piegat,et al.  Fuzzy Modeling and Control , 2001 .

[5]  L. Zadeh.  Linguistic characterization of preference relations as a basis for choice in social systems , 1996 .

[6]  Andrzej Piegat,et al.  Is the conventional interval arithmetic correct , 2012 .

[7]  Michael Hanss,et al.  Applied Fuzzy Arithmetic , 2005 .

[8]  Jonathan Lawry.  Modelling and Reasoning with Vague Concepts (Studies in Computational Intelligence) , 2006 .

[9]  Ulrich Amsel.  Soft Computing In Economics And Finance , 2016 .

[10]  L. Zadeh,et al.  Outline of a theory of usuality based on fuzzy logic , 1996 .

[11]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU)--an outline , 2005, Inf. Sci..

[12]  M. D. Cock,et al.  A Context Based Approach to Linguistic Hedges. , 2002 .

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

[14]  Jerry M. Mendel,et al.  AN ARCHITECTURE FOR MAKING JUDGMENTS USING COMPUTING WITH WORDS , 2002 .

[15]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[16]  Equivalent method for accurate solution to linear interval equations , 2013 .

[17]  I. Batyrshin.  On granular derivatives and the solution of a granular initial value problem , 2002 .

[18]  Changjiu Zhou,et al.  Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach , 2002 .

[19]  Witold Pedrycz,et al.  Fuzzy logic-based generalized decision theory with imperfect information , 2012, Inf. Sci..

[20]  Lotfi A. Zadeh,et al.  A New Frontier in Computation-Computation with Information Described in Natural Language , 2007, 2007 IEEE International Symposium on Intelligent Signal Processing.

[21]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

[22]  Andrzej Piegat,et al.  Application of the Horizontal Membership Function to the Uncertain Displacement Calculation of a Composite Massless Rod Under a Tensile Load , 2014, ACS.

[23]  Andrzej Piegat,et al.  Decision-Making under uncertainty using Info-Gap Theory and a new multi-dimensional RDM interval arithmetic , 2013 .

[24]  Marek Landowski,et al.  Differences between Moore and RDM Interval Arithmetic , 2014, IEEE Conf. on Intelligent Systems.

[25]  A. Tversky,et al.  Choices, Values, and Frames , 2000 .

[26]  Lotfi A. Zadeh,et al.  A New Direction in AI: Toward a Computational Theory of Perceptions , 2001, AI Mag..

[27]  Pavel V. Sevastjanov,et al.  A new method for solving interval and fuzzy equations: Linear case , 2009, Inf. Sci..

[28]  I. Burhan Türksen,et al.  Meta-linguistic axioms as a foundation for computing with words , 2007, Inf. Sci..

[29]  Ildar Batyrshin,et al.  Towards a linguistic description of dependencies in data , 2002 .

[30]  Lotfi A. Zadeh,et al.  A note on web intelligence, world knowledge and fuzzy logic , 2004, Data Knowl. Eng..

[31]  Tru H. Cao,et al.  Conceptual Graphs for Modelling and Computing with Generally Quantified Statements , 2003, Modelling with Words.

[32]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[33]  Jerry M. Mendel,et al.  Lower and upper probability calculations using compatibility measures for solving Zadeh's challenge problems , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[34]  高木 友博,et al.  Computing with Words(用語解説) , 2003 .

[35]  Caroline M. Eastman,et al.  Response: Introduction to fuzzy arithmetic: Theory and applications : Arnold Kaufmann and Madan M. Gupta, Van Nostrand Reinhold, New York, 1985 , 1987, Int. J. Approx. Reason..

[36]  Andrzej Piegat,et al.  Two Interpretations of Multidimensional RDM Interval Arithmetic-Multiplication and Division , 2013 .

[37]  Jonathan Lawry.  Modelling and Reasoning with Vague Concepts , 2006, Studies in Computational Intelligence.

[38]  Witold Pedrycz,et al.  Fuzzy Systems Engineering - Toward Human-Centric Computing , 2007 .

[39]  Przemysław Grzegorzewski,et al.  COMPUTING WITH WORDS AND LIFE DATA , 2002 .

[40]  Jerry M. Mendel,et al.  Solving Zadeh's Magnus challenge problem on linguistic probabilities via Linguistic Weighted Averages , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).

[41]  Slawomir Zadrozny,et al.  Computing With Words Is an Implementable Paradigm: Fuzzy Queries, Linguistic Data Summaries, and Natural-Language Generation , 2010, IEEE Transactions on Fuzzy Systems.

[42]  Janusz Kacprzyk,et al.  The Paradigm of Computing with Words in Intelligent Database Querying , 1999 .

[43]  Ludmila Dymowa.  Soft Computing in Economics and Finance , 2011, Intelligent Systems Reference Library.

[44]  Karina Tomaszewska,et al.  The application of horizontal membership functions to fuzzy arithmetic operations , 2014 .

[45]  F. Herrera,et al.  A Linguistic Decision Model to Suppliers Selection in International Purchasing , 1999 .

[46]  Marina Lyashko,et al.  The Optimal Solution of an Interval System of Linear Algebraic Equations , 2005, Reliab. Comput..

[47]  M. Gemeinder.  Imposing restrictions on density functions utilised in computing with words , 2002 .