Browsing by Author "Fang, Shu-Cherng"

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Citation - WoS: 10
Citation - Scopus: 10
Convex Optimization on Mixed Domains
(Amer Inst Mathematical Sciences-Aims, 2012) Adıvar, Murat; Fang, Shu-Cherng
This paper aims to study convex analysis on some generalized domains, in particular, the domain of the product of closed subsets of reals. We introduce the basic concepts and derive analytic properties regarding convex subsets of mixed domains and convex functions defined on convex sets in mixed domains. The results obtained may open an avenue for modeling and solving a new type of optimization problems that involve both discrete and continuous variables at the same time.
Citation - WoS: 7
Citation - Scopus: 7
Non-L Type Fuzzy Parameters in Mathematical Programming Problems
(IEEE-Inst Electrical Electronics Engineers Inc, 2014) Hu, Cheng-Feng; Adıvar, Murat; Fang, Shu-Cherng
The triangular norm-based operations in fuzzy logic usually lead to non-L-R type fuzzy sets. This study considers mathematical programming problems with non-L-R type fuzzy parameters. It shows that the fuzzy solutions to such problems can be obtained by solving an optimization problem on a mixed domain. The necessary and sufficient conditions for solving the resulting optimization problems are investigated by employing the theory of convex optimization on mixed domains. This is the first attempt to solve the fuzzy optimization problem with non-L-R type membership functions in view of optimization problems on a mixed domain.