Optimization under Fuzzy Constraints: Need to Go Beyond Bellman-Zadeh Approach and How It Is Related to Skewed Distributions

Authors

Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Nguyen Hoang Phuong, Thang Long UniversityFollow

Publication Date

5-2020

Comments

Technical Report: UTEP-CS-20-46

Abstract

In many practical situations, we need to optimize the objective function under fuzzy constraints. Formulas for such optimization are known since the 1970s paper by Richard Bellman and Lotfi Zadeh, but these formulas have a limitation: small changes in the corresponding degrees can lead to a drastic change in the resulting selection. In this paper, we propose a natural modification of this formula, a modification that no longer has this limitation. Interestingly, this formula turns out to be related for formulas for skewed (asymmetric) generalizations of the normal distribution.