One of the most controversial issues in uncertainty modeling and information sciences is the relationship between probability theory and fuzzy sets The literature pertaining to this debate is surveyed The authors address some classical misunderstandings between fuzzy sets and probabilities They consider probabilistic interpretations of membership functions that may help in membership function assessment Nonprobabilistic interpretations of fuzzy sets are identified The literature on possibility-probability transformations is examined, and some lurking controversies on that topic are clarified Several subfields of fuzzy set research where fuzzy sets and probability are conjointly used are discussed >

Fuzzy sets and probability: misunderstandings, bridges and gaps

Overview on the development of fuzzy random variables

Possibility theory was coined by L.A. Zadeh in the late seventies as an approach to model flexible restrictions constructed from vague pieces of information, described by means of fuzzy sets. Possibility theory is also a basic non-classical theory of uncertainty, different from but related to probability theory. This chapter discusses the basic elements of the theory: possibility and necessity measures (as well as two other set functions associated with a possibility distribution), the minimal specificity principle which underlies the whole theory, the notions of possibilitic conditioning and possibilistic independence, the combination, and projection of joint possibility distributions, as well as the possibilistic counterparts to integration. The relations and differences between this approach and other uncertainty frameworks, and especially probability theory, are pointed out. The difference between probability theory and fuzzy set theory is thus tentatively clarified. Lastly, decision-theoretic justifications of possibility theory are given.

Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps

Fuzzy sets, probability and measurement

The process of evaluating tenders is considered to be largely dependent on subjective judgment when cost is not the only criterion used. A systematic procedure based on fuzzy set theory and multicriteria modeling is proposed for the selection of bid contracts. The proposed procedure is suitable for a general tender evaluation process that may involve many decision‐making parties and noninteractive multiple criteria. Illustrative examples are given for cases involving three major criteria: cost, present bid information, and past experience of tenderers.

Tender evaluation by fuzzy sets

For decision problems in the real world, states of nature, information, and actions should be viewed as fuzzy events. The application of the fuzzy sets theory and the statistical decision theory to the decision problems in fuzzy events leads to a specific formulation of fuzzy decision problems and the definitions of entropy, worth of information, and quantity of information. Some results which are analogous to those in the statistical decision theory are given in this paper.

T. Okuda

Papers

A formulation of fuzzy decision problems with fuzzy information using probability measures of fuzzy events