EA solutions and EA solvability to general interval linear systems

ABSTRACT

S. Shary introduced the notion of quantifier solutions to interval systems, in which the uncertainty on the coefficients of a system is modelled by a selecting predicate, allowing an alternation in an arbitrary order of the logical quantifiers (∀ and ∃). AE solutions, a particular type of quantifier solutions, in which all the occurrences of the universal quantifier ∀ precede the occurrences of the existential quantifier ∃, have been studied by many authors. In this work we deal with EA solutions, another type of quantifier solutions to general interval linear systems, such that, in the selecting predicate, all the occurrences of the existential quantifier ∃ precede the occurrences of the universal quantifier ∀. The EA solutions can be considered as a dual form of AE solutions. We provide a full characterization of EA solutions. Moreover, we develop a necessary condition for EA solvability of the general interval linear systems, as well as a necessary and sufficient condition for a certain subcase.

Keywords:

• Interval linear systems
• EA solutions
• EA solvability

Mathematics Subject Classification (2010):

• 15A39
• 65G40

Acknowledgements

The authors would like to thank anonymous referees and the editor for their very valuable comments and suggestions that helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors were partially supported by the NNSF of China (Grant No. 11701506).