Premium
Many‐valued Logic in Multistate and Vague Stochastic Systems
Author(s) -
Sellers Kimberly F.,
Singpurwalla Nozer D.
Publication year - 2008
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2008.00049.x
Subject(s) - vagueness , context (archaeology) , set (abstract data type) , theoretical computer science , state (computer science) , computer science , function (biology) , inference , feature (linguistics) , limiting , set theory , set function , mathematics , artificial intelligence , algorithm , programming language , mechanical engineering , paleontology , philosophy , engineering , biology , fuzzy logic , linguistics , evolutionary biology
Summary The state of the art in coherent structure theory is driven by two assertions, both of which are limiting: (1) all units of a system can exist in one of two states, failed or functioning; and (2) at any point in time, each unit can exist in only one of the above states. In actuality, units can exist in more than two states, and it is possible that a unit can simultaneously exist in more than one state. This latter feature is a consequence of the view that it may not be possible to precisely define the subsets of a set of states; such subsets are called vague . The first limitation has been addressed via work labeled ‘multistate systems’; however, this work has not capitalized on the mathematics of many‐valued propositions in logic. Here, we invoke its truth tables to define the structure function of multistate systems and then harness our results in the context of vagueness. A key contribution of this paper is to argue that many‐valued logic is a common platform for studying both multistate and vague systems but, to do so, it is necessary to lean on several principles of statistical inference.