### THE REAL-WORLD-SEMANTICS INTERPRETABILITY OF LINGUISTIC RULE BASES AND THE APPROXIMATE REASONING METHOD OF FUZZY SYSTEMS

#### Abstract

The real-world-semantics interpretability concept of fuzzy systems introduced in [1] is new for the both methodology and application and is necessary to meet the demand of establishing a mathematical basis to construct computational semantics of linguistic words so that a method developed based on handling the computational semantics of linguistic terms to simulate a human method immediately handling words can produce outputs similar to the one produced by the human method. As the real world of each application problem having its own structure which is described by certain linguistic expressions, this requirement can be ensured by imposing constraints on the interpretation assigning computational objects in the appropriate computational structure to the words so that the relationships between the computational semantics in the computational structure is the image of relationships between the real-world objects described by the word-expressions. This study will discuss more clearly the concept of real-world-semantics interpretability and point out that such requirement is a challenge to the study of the interpretability of fuzzy systems, especially for approaches within the fuzzy set framework. A methodological challenge is that it requires both the computational expression representing a given linguistic fuzzy rule base and an approximate reasoning method working on this computation expression must also preserve the real-world semantics of the application problem. Fortunately, the hedge algebra (HA) based approach demonstrates the expectation that the graphical representation of the rule of fuzzy systems and the interpolation reasoning method on them are able to preserve the real-world semantics of the real-world counterpart of the given application problem.

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Cat Ho Nguyen, Jose M. Alonso - Looking for a real-world-semantics-based approach to the interpretability of fuzzy systems. FUZZ-IEEE 2017 Technical Program Committee and Technical Chairs, Italy, (2017) July 9-12.

C.H. Nguyen, V.Th. Hoang, V.L. Nguyen - A discussion on interpretability of linguistic rule base systems and its application to solve regression problems, Knowledge-Based Syst., 88 (2015) 107-133.

C.H. Nguyen and W. Wechler - Hedge algebras: an algebraic approach to structures of sets of linguistic domains of linguistic truth variables, Fuzzy Sets and Systems, 35(3) (1990), 281-293.

Cat-Ho Nguyen and W. Wechler - Extended hedge algebras and their application to Fuzzy logic, Fuzzy Sets and Systems, 52 (1992) 259-281.

C. H. Nguyen and N.V. Huynh - An algebraic approach to linguistic hedges in Zadeh's fuzzy logic, Fuzzy Sets and Syst., 129 (2002) 229-254.

C. H. Nguyen and V. L. Nguyen - Fuzziness measure on complete hedges algebras and quantifying semantics of terms in linear hedge algebras, Fuzzy Sets and Syst., 158 (2007) 452-471.

Thu Anh Nguyen, Cat Ho Nguyen - On the real-world-semantics interpretability of fuzzy rule based systems under fuzzy set approach and hedge algebra approach, Journal of Computer Science and Cybernetics, 33 (1) (2017), 86–109.

A. Tarski, A. Mostowski, and R. Robinson, Undecidable Theories. North-Holland, 1953

Cat Ho Nguyen, Thi Lan Pham, Cam Ha Ho, Thu Anh Nguyen, A real-world-semantics approach to the interpretability problem of linguistic summaries, IEEE Transactions on Fuzzy Systems (Submited)

C.H. Nguyen, W. Pedrycz, T. L. Duong, T. S. Tran - A genetic design of ling. terms for fuzzy rule based classiﬁers, Int. J. Approx. Reason., 54 (2013)1–21.

C.H. Nguyen, T. S. Tran, D.P. Pham - Modeling of a semantics core of linguistic terms based on an extension of hedge algebrasemantics and its application, Knowl-Based Syst., 67 (2014) 244-262.

M. Antonelli, P. Ducange, B. Lazzerini, F. Marcelloni - Learning concurrently data and rule bases of Mamdani fuzzy rule-based systems by exploiting a novel interpretability index. Soft Comput., 15 (2015)1981–1998.

Thu Anh Nguyen, Cat Ho Nguyen, On the computational interpretability of linguistic fuzzy rules based systems at the low level, Proc. National Conferrence season 19: Some selected matters about Information Technology, Hanoi, Oct 2016, 274-281

DOI: https://doi.org/10.15625/2525-2518/57/2/13129 Display counter: Abstract : 41 views. PDF : 59 views.

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