Quantifiers in the formulation of multiple objective decision functions

doi:10.1016/0020-0255(83)90029-4

Information Sciences

Volume 31, Issue 2, November 1983, Pages 107-139

https://doi.org/10.1016/0020-0255(83)90029-4 Get rights and content

Abstract

We discuss the interpretation of linguistically quantified statements using fuzzy sets. We indicate that there are two methods of interpreting these statements, the algebraic approach and the substitution approach. We then use quantified statements to express overall decision functions involving multiple objectives. These statements are of the type “A solution should satisfy many of the objectives”. Using the algebraic and substitution approach, we develop a whole family of forms for combining multiple objectives. We show that algebraic approach corresponds to situations in which we are unconcerned about the allocation of satisfaction amongst the objectives but just interested in getting much satisfaction. The substitution approach on the other hand leads to forms which are dependent upon the allocation of satisfaction between the objectives.

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There are more references available in the full text version of this article.

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Each of the linguistic terms is mapped to a fuzzy quantifier function. Yager [42] pointed out that the aggregation by fuzzy intersection is not appropriate, because the final overall decision is, of course, required to satisfy ‘all’ the criteria. Owing to the complexity of judgments, the hierarchical multiple criteria are mostly satisfied to achieve the final best course of decision-making action.
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^∗: Currently on leave of absence from: Machine Intelligence Institute, Iona College, New Rochelle, New York 10801.

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Quantifiers in the formulation of multiple objective decision functions

Abstract

Internat. J. Man-Machine Studies

Internat. J. Man-Machine Studies

Internat. J. Man-Machine Studies

Internat. Man-Machine Studies