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

Authors:
Weldon A. Lodwick;K. David Jamison
Affiliations:
Department of Mathematics, University of Colorado at Denver, Campus Box 170, P.O. Box 173364, Denver, CO 80217-3364, USA;Watson & Wyatt Company, 950 17th Street, Suite 1400, Denver, CO 80202, USA
Venue:
Fuzzy Sets and Systems
Year:
2007

Citing 11
Cited 6

The mean value of a fuzzy number

Fuzzy Sets and Systems - Fuzzy Numbers
Relationships between modality constrained programming problems and various fuzzy mathematical programming problems

Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications

Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets as a basis for a theory of possibility

Fuzzy Sets and Systems
Fuzzy linear programming using a penalty method

Fuzzy Sets and Systems
Fuzzy Sets and Systems: Theory and Applications

Fuzzy Sets and Systems: Theory and Applications
Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis

SIAM Review
Weighted Constraint Aggregation in Fuzzy Optimization

Constraints
The construction of consistent possibility and necessity measures

Fuzzy Sets and Systems - Possibility theory and fuzzy logic
Fuzzy modeling in terms of surprise

Fuzzy Sets and Systems - Special issue: Interfaces between fuzzy set theory and interval analysis
Solving Large-Scale Fuzzy and Possibilistic Optimization Problems

Fuzzy Optimization and Decision Making

On starshaped fuzzy sets

Fuzzy Sets and Systems
The Relationship between Interval, Fuzzy and Possibilistic Optimization

MDAI '09 Proceedings of the 6th International Conference on Modeling Decisions for Artificial Intelligence
Solving fuzzy linear programming problems with interval type-2 RHS

SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Computing optimal solutions of a linear programming problem with interval type-2 fuzzy constraints

HAIS'12 Proceedings of the 7th international conference on Hybrid Artificial Intelligent Systems - Volume Part I
Multi-period Mixed Production Planning with uncertain demands: Fuzzy and interval fuzzy sets approach

Fuzzy Sets and Systems
A stepwise fuzzy linear programming model with possibility and necessity relations

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

Quantified Score

Hi-index	0.21

Visualization

Abstract

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]].