On fuzzy convexity and parametric fuzzy optimization
Fuzzy Sets and Systems
Fuzzy multiple objective programming and compromise programming with Pareto optimum
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Some properties of convex fuzzy sets
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy logic: intelligence, control, and information
Fuzzy logic: intelligence, control, and information
Fuzzy Sets and Systems
Pareto-optimality of compromise decisions
Fuzzy Sets and Systems
A property on convex fuzzy sets
Fuzzy Sets and Systems
Fuzzy convexity and multiobjective convex optimization problems
Computers & Mathematics with Applications
Convexity and upper semicontinuity of fuzzy sets
Computers & Mathematics with Applications
Fuzzy Φ-convexity and fuzzy decision making
Computers & Mathematics with Applications
Preincavity and fuzzy decision making
Fuzzy Sets and Systems
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Concave properties play a dominate role in solving both classic and fuzzy optimization problems. However, since fuzzy problems are generally represented by sets, not crisp numbers, various aggregation schemes are needed to manipulate and to combine the different elements in a fuzzy optimization problem. Based on these different aggregations, various concavity properties can be formulated and explored. In this paper, the intersection aggregation and the convex combination aggregation are explored based on the supp-@F"1-concave fuzzy sets. First, the concept of @F"1-convexity, which covers a wider class of sets and functions, is extended to fuzzy sets. Supp-@F"1-concave and supp-@F"1-quasiconcave fuzzy sets are then introduced; and some useful aggregation and composition rules are developed. Based on these aggregation and composition rules and the generalized concave properties, fuzzy multiple objective decision making problems are formulated and the conditions to ensure local-global maximum property are discussed.