The Use of Intuitionistic Fuzzy Values in Rule-Base Evidential Reasoning

A new approach to the rule-base evidential reasoning based on the synthesis of fuzzy logic, Atannasov’s intuitionistic fuzzy sets theory and the Dempster-Shafer theory of evidence is proposed. It is shown that the use of intuitionistic fuzzy values and the classical operations on them directly may provide counter-intuitive results. Therefore, an interpretation of intuitionistic fuzzy values in the framework of Dempster-Shafer theory is proposed and used in the evidential reasoning. Using the real-world example, it is shown that such an approach provides reasonable and intuitively obvious results when the classical method of rule-base evidential reasoning cannot produce any reasonable results.

[1]  John Yen,et al.  Generalizing the Dempster-Schafer theory to fuzzy sets , 1990, IEEE Trans. Syst. Man Cybern..

[2]  Jian-Bo Yang,et al.  Belief rule-base inference methodology using the evidential reasoning Approach-RIMER , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[4]  Mitsuru Ishizuka,et al.  Inference procedures under uncertainty for the problem-reduction method , 1982, Inf. Sci..

[5]  Ignazio Gallo,et al.  A neural model for fuzzy Dempster-Shafer classifiers , 2000, Int. J. Approx. Reason..

[6]  Ranjit Biswas,et al.  Some operations on intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[7]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[8]  Lotfi A. Zadeh,et al.  A Simple View of the Dempster-Shafer Theory of Evidence and Its Implication for the Rule of Combination , 1985, AI Mag..

[9]  Pavel V. Sevastjanov,et al.  A new approach to the rule-base evidential reasoning: Stock trading expert system application , 2010, Expert Syst. Appl..

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

[11]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[12]  Jian-Bo Yang,et al.  Optimization Models for Training Belief-Rule-Based Systems , 2007, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[13]  Pavel V. Sevastjanov,et al.  A stock trading expert system based on the rule-base evidential reasoning using Level 2 Quotes , 2012, Expert Syst. Appl..

[14]  Pavel V. Sevastjanov,et al.  A framework for rule-base evidential reasoning in the interval setting applied to diagnosing type 2 diabetes , 2012, Expert Syst. Appl..

[15]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[16]  K. Atanassov.  New operations defined over the intuitionistic fuzzy sets , 1994 .

[17]  Didier Dubois,et al.  Terminological difficulties in fuzzy set theory - The case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

[18]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[19]  Pavel V. Sevastjanov,et al.  The operations on intuitionistic fuzzy values in the framework of Dempster-Shafer theory , 2012, Knowl. Based Syst..

[20]  Jian-Bo Yang,et al.  Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties , 2001, Eur. J. Oper. Res..

[21]  Ian Jenkinson,et al.  Inference and learning methodology of belief-rule-based expert system for pipeline leak detection , 2007, Expert Syst. Appl..

[22]  E. Binaghi,et al.  Fuzzy Dempster–Shafer reasoning for rule‐based classifiers , 1999 .

[23]  Ronald R. Yager,et al.  Generalized probabilities of fuzzy events from fuzzy belief structures , 1982, Inf. Sci..

[24]  Gholam Ali Montazer,et al.  A fuzzy-evidential hybrid inference engine for coronary heart disease risk assessment , 2010, Expert Syst. Appl..

[25]  Ewa Straszecka,et al.  Combining uncertainty and imprecision in models of medical diagnosis , 2006, Inf. Sci..

[26]  Pavel V. Sevastjanov,et al.  An interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect , 2010, Knowl. Based Syst..