Book ChapterDOI
Fuzzy Optimization and Mathematical Programming: A Brief Introduction and Survey
Janusz Kacprzyk,Sergei A. Orlovski +1 more
- pp 50-72
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Some general concepts and ideas related to fuzzy optimization as, e.g., a fuzzy constraint, fuzzy goal (objective function), fuzzy optimum, etc are introduced and a general fuzzy optimization problem involving these elements is formulated and solved.Abstract:
Some general concepts and ideas related to fuzzy optimization as, e.g., a fuzzy constraint, fuzzy goal (objective function), fuzzy optimum, etc. are introduced first. A general fuzzy optimization problem involving these elements is formulated and solved. The cases of single and multiple objective functions are dealt with. Secondly, basic classes of fuzzy mathematical programming are discussed, including: fuzzy linear programming (with single and multiple objective functions), fuzzy integer programming, fuzzy 0–1 programming and fuzzy dynamic programming. Finally some newer, knowledge-based approaches are mentioned. An extended list of literature is included.read more
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Journal ArticleDOI
Material Requirement Planning with fuzzy constraints and fuzzy coefficients
TL;DR: A new fuzzy mathematical programming model for production planning under uncertainty in an industrial environment that considers fuzzy constraints related to the total costs, the market demand and the available capacity and fuzzy coefficients for the costs due to the backlog of demand and for the required capacity.
Journal ArticleDOI
Capacity and material requirement planning modelling by comparing deterministic and fuzzy models
TL;DR: In this paper, a model for the capacity and material requirement planning problem with uncertainty in a multi-product, multi-level and multi-period manufacturing environment is proposed, which takes into account the uncertainty that exists in both the market demand and capacity data, and the uncertain costs for backlog.
Journal ArticleDOI
Capital Budgeting Decisions With Fuzzy Projects
Chui-Yu Chiu,Chan S. Park +1 more
TL;DR: A capital budgeting model under uncertainty in which cash flow information is specified as a special type of fuzzy number—triangular fuzzy numbers is proposed and a new project dominance method is proposed to determine the preference of fuzzy projects.
Journal ArticleDOI
Analysis of structure in fuzzy linear programs
TL;DR: Fuzzy linear programming problems are analyzed within the fuzzy set context to uncover redundancies, infeasibilities, variables whose values are fixed, and implied bounds on rows and columns.
Journal Article
Understanding of fuzzy optimization: theories and methods
TL;DR: This summary is made on aspects of fuzzy modelling and fuzzy optimization, classification and formulation for the fuzzy optimization problems, models and methods.
References
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Book
Decision-making in a fuzzy environment
Richard Bellman,Lotfi A. Zadeh +1 more
TL;DR: A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
Journal ArticleDOI
Fuzzy programming and linear programming with several objective functions
TL;DR: It is shown that solutions obtained by fuzzy linear programming are always efficient solutions and the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution are shown.
Journal ArticleDOI
Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming
TL;DR: This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy via set containment.
Journal ArticleDOI
A computational approach to fuzzy quantifiers in natural languages
TL;DR: The computational approach to fuzzy quantifiers which is described in this paper may be viewed as a derivative of fuzzy logic and test-score semantics.
Journal ArticleDOI
Decision-making with a fuzzy preference relation
TL;DR: It is shown that unfuzzy nondominated solutions to the decision-making problem exist, provided the original fuzzy relation satisfies some topological requirements, and a simple method of calculating these solutions is indicated.