Why Lattice-valued fuzzy values? A mathematical justification | Zendy

Rujira Ouncharoen | Zendy; Владик Крейнович | Zendy; Hung T. Nguyen | Zendy

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Why Lattice-valued fuzzy values? A mathematical justification

Author(s) -

Rujira Ouncharoen,

Владик Крейнович,

Hung T. Nguyen

Publication year - 2015

Publication title -

journal of intelligent and fuzzy systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.331

H-Index - 57

eISSN - 1875-8967

pISSN - 1064-1246

DOI - 10.3233/ifs-151558

Subject(s) - upper and lower bounds , lattice (music) , mathematics , certainty , combinatorics , fuzzy set , interval (graph theory) , complete lattice , fuzzy logic , discrete mathematics , mathematical economics , computer science , physics , mathematical analysis , condensed matter physics , geometry , artificial intelligence , universality (dynamical systems) , acoustics

To take into account that expert's degrees of certainty are not always comparable, researchers have used partially ordered set of degrees instead of the more traditional linearly (totally) ordered interval (0, 1). In most cases, it is assumed that this partially ordered set is a lattice, i.e., every two elements have the greatest lower bound and the least upper bound. In this paper, we prove a theorem explaining why it is reasonable to require that the set of degrees is a lattice.

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