scholarly journals The Karush-Kuhn-Tucker Optimality Conditions for the Fuzzy Optimization Problems in the Quotient Space of Fuzzy Numbers

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Nanxiang Yu ◽  
Dong Qiu
Keyword(s):  
Optimality Conditions ◽  
Fuzzy Numbers ◽  
Quotient Space ◽  
Optimization Problems ◽  
Lagrange Function ◽  
Fuzzy Optimization ◽  
Solution Concepts ◽  
Kkt Optimality Conditions

We propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. The Karush-Kuhn-Tucker (KKT) optimality conditions are elicited naturally by introducing the Lagrange function multipliers. The effectiveness is illustrated by examples.

scholarly journals An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

2021 ◽  
Author(s):  
Mingxuan Zhao ◽  
Yulin Han ◽  
Jian Zhou
Keyword(s):  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Fuzzy Programming ◽  
Planning Problem ◽  
Monotone Functions ◽  
Solution Strategy ◽  
Deterministic Equivalent ◽  
The One ◽  
Short Time

Abstract The operational law put forward by Zhou et al. on strictly monotone functions with regard to regular LR fuzzy numbers makes a valuable push to the development of fuzzy set theory. However, its applicable conditions are confined to strictly monotone functions and regular LR fuzzy numbers, which restricts its application in practice to a certain degree. In this paper, we propose an extensive operational law that generalizes the one proposed by Zhou et al. to apply to monotone (but not necessarily strictly monotone) functions with regard to regular LR fuzzy intervals (LR-FIs), of which regular fuzzy numbers can be regarded as particular cases. By means of the extensive operational law, the inverse credibility distributions (ICDs) of monotone functions regarding regular LR-FIs can be calculated efficiently and effectively. Moreover, the extensive operational law has a wider range of applications, which can deal with the situations hard to be handled by the original operational law. Subsequently, based on the extensive operational law, the computational formulae for expected values (EVs) of LR-FIs and monotone functions with regard to regular LR-FIs are presented. Furthermore, the proposed operational law is also applied to dispose fuzzy optimization problems with regular LR-FIs, for which a solution strategy is provided, where the fuzzy programming is converted to a deterministic equivalent first and then a newly-devised solution algorithm is utilized. Finally, the proposed solution strategy is applied to a purchasing planning problem, whose performances are evaluated by comparing with the traditional fuzzy simulation-based genetic algorithm. Experimental results indicate that our method is much more efficient, yielding high-quality solutions within a short time.

The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems

2015 ◽  
Vol 15 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Y. Chalco-Cano ◽  
W. A. Lodwick ◽  
R. Osuna-Gómez ◽  
A. Rufián-Lizana
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Fuzzy Optimization

LEXICOGRAPHIC METHOD FOR MATRIX GAMES WITH PAYOFFS OF TRIANGULAR FUZZY NUMBERS

2008 ◽  
Vol 16 (03) ◽  
pp. 371-389 ◽  
Author(s):  
DENG-FENG LI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Programming Models ◽  
Matrix Game ◽  
Triangular Fuzzy Numbers ◽  
Matrix Games ◽  
Lexicographic Method

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology.

Interval Methods and Fuzzy Optimization

1997 ◽  
Vol 05 (03) ◽  
pp. 239-249 ◽  
Author(s):  
Weldon A. Lodwick ◽  
K. David Jamison
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Interval Analysis ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Interval Methods

In this paper, we describe interval-based methods for solving constrained fuzzy optimization problems. The class of fuzzy functions we consider for the optimization problems is the set of real-valued functions where one or more parameters/coefficients are fuzzy numbers. The focus of this research is to explore some relationships between fuzzy set theory and interval analysis as it relates to optimization problems.

scholarly journals Generalized derivatives and optimization problems for n-dimensional fuzzy-number-valued functions

2020 ◽  
Vol 18 (1) ◽  
pp. 1451-1477
Author(s):  
Ting Xie ◽  
Zengtai Gong ◽  
Dapeng Li
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Directional Derivative ◽  
Fuzzy Optimization ◽  
Optimality Criteria ◽  
Generalized Derivatives ◽  
Duality Theorems ◽  
Generalized Derivative ◽  
Partial Orderings

Abstract In this paper, we present the concepts of generalized derivative, directional generalized derivative, subdifferential and conjugate for n-dimensional fuzzy-number-valued functions and discuss the characterizations of generalized derivative and directional generalized derivative by, respectively, using the derivative and directional derivative of crisp functions that are determined by the fuzzy mapping. Furthermore, the relations among generalized derivative, directional generalized derivative, subdifferential and convexity for n-dimensional fuzzy-number-valued functions are investigated. Finally, under two kinds of partial orderings defined on the set of all n-dimensional fuzzy numbers, the duality theorems and saddle point optimality criteria in fuzzy optimization problems with constraints are discussed.

scholarly journals Optimality conditions for invex interval valued nonlinear programming problems involving generalized H-derivative

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2121-2138 ◽  
Author(s):  
Izhar Ahmad ◽  
Deepak Singh ◽  
Bilal Dar
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Generalized Convexity ◽  
Optimal Solutions ◽  
Solution Concepts ◽  
Lagrangian Multipliers ◽  
Kkt Optimality Conditions ◽  
Generalized Hukuhara Differentiability ◽  
Interval Valued

In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu [7] and Chalco-Cano et al. [34]. By considering generalized Hukuhara differentiability and generalized convexity (viz. ?-preinvexity, ?-invexity etc.) of interval valued functions, the KKT optimality conditions for obtaining (LS and LU) optimal solutions are elicited by introducing Lagrangian multipliers. Our results generalize the results of Wu [7], Zhang et al. [11] and Chalco-Cano et al. [34]. To illustrate our theorems suitable examples are also provided

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