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A dual approach in fuzzy linear programming.

José M. Cadenas, Fernando Jiménez (1996)

Mathware and Soft Computing

In this paper, we propose a relationship of fuzzy duality. We use the Decomposition Theorem and some properties about Linear Programming with interval coefficients to define this relationship. Thus, a linear programming problem with fuzzy costs represented by membership functions L-R can be solved by means of two dual problems (linear programming problems with fuzzy constraints). Moreover, these results can be applied to multiobjective problems whose coefficients of the objective function are fuzzy...

A fuzzy logic approach to assembly line balancing.

Daniel J. Fonseca, C. L. Guest, Matthew Elam, Charles L. Karr (2005)

Mathware and Soft Computing

This paper deals with the use of fuzzy set theory as a viable alternative method for modelling and solving the stochastic assembly line balancing problem. Variability and uncertainty in the assembly line balancing problem has traditionally been modelled through the use of statistical distributions. This may not be feasible in cases where no historical data exists. Fuzzy set theory allows for the consideration of the ambiguity involved in assigning processing and cycle times and the uncertainty contained...

A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors

Masahiro Inuiguchi (2006)


In this paper, a necessity measure optimization model of linear programming problems with fuzzy oblique vectors is discussed. It is shown that the problems are reduced to linear fractional programming problems. Utilizing a special structure of the reduced problem, we propose a solution algorithm based on Bender’s decomposition. A numerical example is given.

A Note on Application of Two-sided Systems of ( max , min ) -Linear Equations and Inequalities to Some Fuzzy Set Problems

Karel Zimmermann (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The aim of this short contribution is to point out some applications of systems of so called two-sided ( max , min ) -linear systems of equations and inequalities of [Gavalec, M., Zimmermann, K.: Solving systems of two-sided (max,min)-linear equations Kybernetika 46 (2010), 405–414.] to solving some fuzzy set multiple fuzzy goal problems. The paper describes one approach to formulating and solving multiple fuzzy goal problems. The fuzzy goals are given as fuzzy sets and we look for a fuzzy set, the fuzzy intersections...

Additivities in fuzzy coalition games with side-payments

Milan Mareš (1999)


The fuzzy coalition game theory brings a more realistic tools for the mathematical modelling of the negotiation process and its results. In this paper we limit our attention to the fuzzy extension of the simple model of coalition games with side-payments, and in the frame of this model we study one of the elementary concepts of the coalition game theory, namely its “additivities”, i. e., superadditivity, subadditivity and additivity in the strict sense. In the deterministic game theory these additivites...

Batch scheduling problem with due-date and fuzzy precedence relation

Xuesong Li, Hiroaki Ishii, Minghao Chen (2012)


A single-machine batch scheduling problem is investigated. Each job has a positive processing time and due-date. Setup times are assumed to be identical for all batches. All batch sizes cannot exceed a common upper bound. As in many practical situations, jobs have to be subject to flexible precedence constraints. The aim of this paper is to find an optimal batch sequence. The sequence is to minimize the maximal completion time and maximize the minimum value of desirability of the fuzzy precedence....

Chance constrained bottleneck transportation problem with preference of routes

Yue Ge, Minghao Chen, Hiroaki Ishii (2012)


This paper considers a variant of the bottleneck transportation problem. For each supply-demand point pair, the transportation time is an independent random variable. Preference of each route is attached. Our model has two criteria, namely: minimize the transportation time target subject to a chance constraint and maximize the minimal preference among the used routes. Since usually a transportation pattern optimizing two objectives simultaneously does not exist, we define non-domination in this...

Completely generalized nonlinear variational inclusions for fuzzy mappings

Nan-jing Huang (1999)

Czechoslovak Mathematical Journal

In this paper, we introduce and study a new class of completely generalized nonlinear variational inclusions for fuzzy mappings and construct some new iterative algorithms. We prove the existence of solutions for this kind of completely generalized nonlinear variational inclusions and the convergence of iterative sequences generated by the algorithms.

Détermination d'une période économique robuste dans le cadre du modèle de Wilson

Philippe Vallin (2010)

RAIRO - Operations Research

This paper presents results about the optimal order interval in a context of fuzzy information about inventory management. The classical inventory model is based on well known cost and demand rate. In practice, this accurate estimation is very difficult to obtain, even impossible. Consequently, we propose a solution, not optimal in a classical sense, but allowing to choose an action which is not far from the optimal policy whatever the economic parameters may be. These parameters belong to a...

Distributed fuzzy decision making for production scheduling.

Thomas A. Runkler, Rudolf Sollacher, Wendelin Reverey (2004)

Mathware and Soft Computing

In production systems, input materials (educts) pass through multiple sequential stages until they become a product. The production stages consist of different machines with various dynamic characteristics. The coupling of those machines is a non-linear distributed system. With a distributed control system based on a multi-agent approach, the production system can achieve (almost) maximum output, where lot size and lot sequence are the most important control variables. In most production processes...

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