Paper:

# How to Describe Conditions Like 2-out-of-5 in Fuzzy Logic: A Neural Approach

## Olga Kosheleva^{*}, Vladik Kreinovich^{**}, and Hoang Phuong Nguyen^{***,†}

^{*}Department of Teacher Education, University of Texas at El Paso

500 West University Avenue, El Paso, Texas 79968, USA

^{**}Department of Computer Science, University of Texas at El Paso

500 West University Avenue, El Paso, Texas 79968, USA

^{***}Division Informatics, Math-Informatics Faculty, Thang Long University

Nghiem Xuan Yem Road, Hoang Mai District, Hanoi, Vietnam

^{†}Corresponding author

In many medical applications, we diagnose a disease and/or apply a certain remedy if, e.g., two out of five conditions are satisfied. In the fuzzy case, i.e., when we only have certain degrees of confidence that each of *n* statement is satisfied, how do we estimate the degree of confidence that *k* out of *n* conditions are satisfied? In principle, we can get this estimate if we use the usual methodology of applying fuzzy techniques: we represent the desired statement in terms of “and” and “or,” and use fuzzy analogues of these logical operations. The problem with this approach is that for large *n*, it requires too many computations. In this paper, we derive the fastest-to-compute alternative formula. In this derivation, we use the ideas from neural networks.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.24, No.5, pp. 593-598, 2020.

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