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34) for all a, where S denotes the statement "Pa E Pa[a), Pb E Pb[a), Pab E Pada), E po[a), Pa + Pb + Pab + Po = I". Define pw[a] = (PWl(a),pw2(a)) for w = a,b,ab,o. Let P(O')[a) = [Onl(a),On2(a)). 34) to get Onl (a), but this set of p;s is not feasible. 82 and there is no value of Po E PolO) that can make the sum equal to one. Therefore we need to use some numerical method to compute these a-cuts. We used "simplex" in Maple (2). 1. 2. 2 Resistance to Surveys Pollsters are concerned about the increased level of resistance of people to answer questions during surveys.

Buckley and Y. Qu: On Using a-cuts to Evaluate Fuzzy Equations, Fuzzy Sets and Systems, 38 (1990), pp. 309-312. 9. Feuring: Fuzzy Mathematics in Economics and Engineering, Physica-Verlag, Heidelberg, Germany, 2002. 10. Feuring and YHayashi: Solving Fuzzy Problems in Operations Research, J. Advanced Computational Intelligence, 3(1999), pp. 171-176. 11. Hayashi: Multi-Objective Fully Fuzzified Linear Programming, Int. J. Uncertainty, Fuzziness and Knowledge Based Systems, 9(2001), pp. 605-622 12.

21) x=o and 2 Q2(0:) = max{l - x=o CHAPTER 4. 2 for all a. Let k()") = 1 - [I:~=o h()")]. Then dkjd).. 2(a))]. 3. To finish this section we now compute the fuzzy mean and the fuzzy variance of the fuzzy Poisson probability mass function. 12) of Chapter 3, are (l::: xh()") I).. , the expression ]I[a] = {AI).. \[a]}. 24) Hence, ]I = )... So the fuzzy mean is just the fuzzification of the crisp mean. Let the fuzzy variance be £12 and we obtain its a-cuts as co £12[a] = (l)x - p)2h()") I)..

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