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\title{Interval Valued Fuzzy Sets and Measures}
\author{I. B. Turksen}

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\markright{APIC'95, El Paso,
Extended Abstracts,
A Supplement to the international journal of {\rm Reliable
Computing}\ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ }

\maketitle

  
\auffil{The author is a
                Principal Investigator with MRCO,
                Department of Industrial Engineering,
                University of Toronto,
                Toronto, Ontario, Canada M5S 1A1.}

\begin{abstract}
Three classes of connectives generate three classes of interval valued
fuzzy sets due to a separation between the disjunctive and conjunctive
normal forms. The three classes are identified by the axiomatic conditions,
These are:
 \begin{itemize}
\begin{itemize}
\item[(i)] boundary, monotonicity and involutive complementation; 
\item[(ii)]
conditions in (i) plus commutativity and associativity; and 
\item[(iii)]
conditions in (ii) plus idempotency.
\end{itemize}
\end{itemize}

Furthermore, the selection of a particular involutive complement together
with some crisp disjunction and conjunction results in a new interpretation
of the classical laws such as ``Excluded Middle", ``Contradiction",
``Equivalence", etc. These laws must now be interpreted as ``a matter of
degree". That is, we ought not state, for example, that the ``Law of Excluded
Middle" holds or not, but rather that 
it holds to a degree that is generated for
a given membership value.

Finally, one can introduce fuzzy measures over the interval valued fuzzy
sets, such as ``non-specificity", ``belief", etc. These measures provide a
new direction for evidential reasoning. 
\end{abstract}

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