Theoretical and semantic distinctions of fuzzy, possibilistic, and mixed fuzzy/possibilistic optimization

Theoretical, semantic, and algorithmic distinctions among fuzzy, possibilistic and mixed fuzzy/possibilistic optimization are presented and illustrated. The theory underlying fuzzy, possibilistic, and mixed fuzzy/possibilistic optimization is developed and demonstrated and points to the appropriate use of distinct solution methods associated with each type of optimization dependant on the semantics of the problem. Semantics is key to both the input where one is obtaining the data and constructing the optimization model in the presence of uncertainty and the output where the meaning of the results is necessary for understanding solutions. The case in which the optimization model arises from the data that is a combination of fuzzy and possibilistic distributions is also derived. Lastly, examples illustrate the theory. This paper is a modification and an amplification of a presentation made at IFSA’05 [W.A. Lodwich, K.D. Jamison, Theory and semantics for fuzzy and possibilistic optimization, in: Fuzzy Logic, Soft Computing and Computational Intelligence, Eleventh Internat. Fuzzy Systems Association World Congress, July 28–31, 2005, Beijing, China, Vol. III, pp. 1805–1810 [26]].