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On a Class of General Type-n Normal Fuzzy Sets Synthesized from Subject Matter Expert Inputs
  • John Rickard ,
  • Janet Aisbett ,
  • J. Tyler Rickard
John Rickard
Meraglim Holdings Corporation

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Janet Aisbett
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J. Tyler Rickard
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Abstract

Knowledge of fuzzy concepts defined on real-valued domains may be imprecise due to differing interpretations of the concept as well as to respondents’ lack of confidence in their own judgements.  This second source of imprecision has largely been ignored.  We describe a novel procedure to form an interval type-3 fuzzy set on the domain from two interval type-2 (IT2) fuzzy sets that model each of these sources of imprecision.  The first IT2 fuzzy set is on the real-valued domain and represents a consensus of opinions about the concept description.  The second IT2 fuzzy set is on the unit interval and represents a consensus of respondents’ sentiment about their own judgements.  These sets are either generated from interval inputs using the Hao-Mendel Approach, or from respondents’ selections from ordinal vocabularies whose words have IT2 representations as described by Hao and Mendel.  We show more generally how imprecision in hierarchical estimates of knowledge can be incorporated into type-n fuzzy set representations of concepts.  These representations belong to a class of general fuzzy sets constructed from IT2 fuzzy sets that support efficient type reduction.