Affiliations: [a] Department of Mathematics, Chiang Mai University, Chiang Mai, Thailand | [b] Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, USA | [c] Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA | [d] Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand
Correspondence:
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Corresponding author. Rujira Ouncharoen, Department of Mathematics, Chiang Mai University, Chiang Mai, Thailand. rujira.o@cmu.ac.th.
Abstract: 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.
