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Application of Fuzzy Systems and Neural Nets to Chemical Engineering Problems
Published in Shintaro Furusaki, John Garside, L.S. Fan, The Expanding World of Chemical Engineering, 2019
Kazuhiko Suzuki, Hayatoshi Sayama, Shuzo Ohe
The idea of “YOUNG”, illustrated as dotted line in Figure 2.1, is the classical example of a fuzzy set and illustrates the intrinsic properties of fuzzy spaces. The domain of this set, indicated along the horizontal axis, is the range of youth between 10 years old and 50 years old. The degree of membership or truth function is indicated on the vertical axis to the far left. In general, the membership goes from zero (no membership) to one (complete membership.) The membership function and the domain are connected, in this case, by a simple curve. Now, given a value for age, we can determine its degree of membership in the fuzzy set.
Technology of Intelligent Systems
Published in James A. Momoh, Mohamed E. El-Hawary, Electric Systems, Dynamics, and Stability with Artificial Intelligence Applications, 2018
James A. Momoh, Mohamed E. El-Hawary
The degree of membership is known as the membership or truth function since it establishes a one-to-one correspondence between an element in the domain and a truth value indicating its degree of membership in the set. It takes the form, () μA(x)←f(x∈A)
Fuzzy Sets
Published in K. Sundareswaran, A Leaner’s Guide to Fuzzy Logic Systems, 2019
The numerical value is termed “degree of membership” or “truth function” or more commonly “membership grade”. This membership value makes a one-to-one correspondence between the element and the fuzzy set. This is indicated as µLOW SALARY(x) like a discriminant function. Thus, a salary of Rs.25,000 has a membership of 0.5 in LOW SALARY and 0.4 in HIGH SALARY. Hence, each variable has a certain degree of membership in each fuzzy set.
Sequent-type rejection systems for finite-valued non-deterministic logics
Published in Journal of Applied Non-Classical Logics, 2023
In this section, as a first step towards our general method to generate many-sided anti-sequent calculi for any given Nmatrix, we generalise the concept of a complementary partial normal form, as introduced by Bogojeski and Tompits (2020), as a device to encode the semantic functions of Nmatrices into two-valued logic. The basic idea of an ith complementary partial normal form for a connective is to encode the situations in which the truth function for does not take the ith truth value. This idea goes back to the concept of an ith partial normal form for a connective (Rosser & Turquette, 1952), which encodes in turn the situations where does take the ith truth value.
Parameterized simplification logic I: reasoning with implications and classes of closure operators
Published in International Journal of General Systems, 2020
Pablo Cordero, Manuel Enciso, Angel Mora, Vilem Vychodil
Residuated lattices were initially studied in Ward and Dilworth (1939) and later became popular as general structures of truth values in multiple-valued and fuzzy logics (Cintula, Hájek, and Noguera 2011; Gottwald 2013; Esteva and Godo 2001; Goguen 1969; Hájek 1998), see also Belohlavek, Dauben, and Klir (2017) for a historic overview. In fuzzy logics, elements of residuated lattices are considered as degrees of truth and operations of residuated lattices are taken as truth functions for general (fuzzy) logical connectives. Typically, one works with a residuated lattice satisfying the following form of adjointness: for all ; ⊗ (so-called multiplication) is considered as truth function of “fuzzy conjunction” and (so-called residuum) is considered as truth function of “fuzzy implication”. In contrast, we use (4) with the intention to have a general way of expressing operations ⊕ and ⊖ generalizing set union and set difference, respectively.
Basic level of concepts and formal concept analysis 2: examination of existing basic level metrics
Published in International Journal of General Systems, 2020
Radim Belohlavek, Martin Trnecka
We then utilize the principles of fuzzy logic to obtain the truth degrees , , and of these propositions, respectively, in a manner analogous to how we proceeded in the definitions of the truth degrees , , and when formalizing Rosch's approach to basic level (Belohlavek and Trnecka 2020). Finally, we put where ⊗ is again an appropriate truth function of many-valued conjunction (Gottwald 2001), for which we use the product in our experiments.