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Duality theorems in fuzzy mathematical programming problems based on the concept of necessity

Hsien-Chung Wu
2003 Fuzzy sets and systems (Print)  
The fuzzy-valued Lagrangian function for the fuzzy mathematical programming problem via the concept of the fuzzy scalar (inner) product is proposed.  ...  A solution concept of fuzzy optimization problems, which is essentially similar to the notion of Pareto solution in multiobjective programming problems, is also introduced by ranking the fuzzy numbers  ...  . f U * (x) + u;g U * (x) ¿f U * ( x) Conclusions The duality theorems in fuzzy mathematical programming problems based on the necessity indices have been successfully discussed in this paper by introducing  ... 
doi:10.1016/s0165-0114(02)00575-4 fatcat:7fs2pbdezfgx3dh5ys42zw2k5q

Duality in fuzzy linear programming: a survey

Guido Schryen, Diana Hristova
2013 OR spectrum  
The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed, comprehensively and practically applied in an abundance of cases.  ...  However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent.  ...  Results in these areas can contribute to duality theory in FLP as the appendix shows.  ... 
doi:10.1007/s00291-013-0355-2 fatcat:byci47dltjhlpfqafon3by7klu

Duality theory in fuzzy mathematical programming problems with fuzzy coefficients

Cheng Zhang, Xue-hai Yuan, E. Stanley Lee
2005 Computers and Mathematics with Applications  
Furthermore, the concept of saddle-points and mimmax theorems under fuzzy environment is discussed The results obtained are used to formulate the Lagranglan dual of fuzzy programming.  ...  In this paper, the notions of subgradmnt, subdifferentla[, and differential with respect to convex fuzzy mappings are investigated, whmh provides the basis for the fuzzy extremum problem theory We consider  ...  In this paper, the duality theory of fuzzy programming or the saddle-point problem are formulated based on the concept of convexity and convex fuzzy mapping.  ... 
doi:10.1016/j.camwa.2004.12.012 fatcat:oknxev7u7bcgxm2zlyisf57cxm

Page 1712 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
The paper is devoted to multi-objective linear fractional program- ming with fuzzy parameters and extends the ordinary Pareto opti- mality concepts based on the concepts of possibility and necessity for  ...  A multiobjective fractional programming problem is studied, using a feasible direction version of efficient solution. A duality theorem is proved for a dual problem using Dini derivatives. Bruce D.  ... 

The solution and duality of imprecise network problems

Mehdi Ghatee, S. Mehdi Hashemi, Behnam Hashemi, Mehdi Dehghan
2008 Computers and Mathematics with Applications  
Also, based on fuzzy relations, Ramik [14] introduced the concepts of feasibility and A-efficiency for the solutions of fuzzy linear problems.  ...  For nonlinear programming, in [32], the near results were obtained and a fuzzy-valued Lagrangian function for fuzzy mathematical programming problems via the concept of the fuzzy inner products was proposed  ...  Christee Zimmermann for managing the review process.  ... 
doi:10.1016/j.camwa.2007.10.023 fatcat:gsq7ofkchjcolnfdhpvavjiyci

Page 5282 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
The main purpose of this paper is the study of multi-objective nonlinear programming problems with fuzzy parameters which can be represented by means of fuzzy sets of the real line known as fuzzy numbers  ...  Assuming differentiability, quasiconvexity and pseudoconvexity of the functions involved, weak, strong and converse duality theorems are established.  ... 

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

Ting Xie, Zengtai Gong, Dapeng Li
2020 Open Mathematics  
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  ...  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  ...  [13] discussed the convex fuzzy mappings and discussed the duality theory in fuzzy mathematical programming problems with fuzzy coefficients based on the ordering of two fuzzy numbers proposed in [  ... 
doi:10.1515/math-2020-0081 fatcat:cvktmla36jhyla5tuiplh5bbjq

Page 3001 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
Even the concept of infinite sets is suggested by some apparently unend- ing processes, and by the physical space-time continuum. Thus mathematics is not based on human intelligence alone.  ...  Another reason why the term logicism is not used any more is that its program—to derive mathematics from logic in the wider sense—has been fully accomplished.”  ... 

A stepwise fuzzy linear programming model with possibility and necessity relations

Adel Hatami-Marbini, Per J. Agrell, Madjid Tavana, Ali Emrouznejad
2013 Journal of Intelligent & Fuzzy Systems  
In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function.  ...  Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency.  ...  This research is partially supported by the French Community of Belgium ARC project on managing shared resources in supply chains.  ... 
doi:10.3233/ifs-2012-0616 fatcat:6d2zmn6hfnfxngdfxrfpkypgoa


2009 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.  ...  In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed.  ...  Acknowledgements This work is supported by National Natural Science Foundation of China (No. 60874067).  ... 
doi:10.1142/s0218488509005954 fatcat:6vlbmg3ygza7lputlketrouwvy

Page 3647 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
Solution of the problem of completeness with respect to expressibility in a 5-valued nonchain extension of duality intuitionistic logic. (Russian. English, Russian and Moldavian summaries) Izv. Akad.  ...  Summary: “Although the concept of topos can lead naturally to the logical operations on the class of sets, SetH cannot be connected to the logical operations on fuzzy sets, due to the fact that SetH has  ... 

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

Guang Wang, Yixuan Shen, Yujiao Jiang, Jiahao Chen
2021 Symmetry  
Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law.  ...  As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold  ...  In addition, the authors would like to acknowledge the gracious support of this work by the National Natural Science Foundation of China and Shandong Provincial Natural Science Foundation of China.  ... 
doi:10.3390/sym13081428 fatcat:4dseol7jqnedtptfik3g3zoivy

A Fuzzy Approach Using Generalized Dinkelbach's Algorithm for Multiobjective Linear Fractional Transportation Problem

Nurdan Cetin, Fatma Tiryaki
2014 Mathematical Problems in Engineering  
Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem.  ...  We consider a multiobjective linear fractional transportation problem (MLFTP) with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time,  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/702319 fatcat:kdbhve2oxbaefarblggo6k36r4

Credible Fuzzy Classification basedTechnique on Self Organized Features Maps and FRANT IC-RL

Mona Gamal, Elsayed Radwan, Adel M.A.
2014 International Journal of Advanced Computer Science and Applications  
FRANT IC-SRL builds the fuzzy classification rule set using the ranked credibility variables in a simultaneous process. Moreover, the whole fuzzy system is evaluated based on the credibility value.  ...  Based on the credibility theory, a fuzzy clustering approach that improves the classification accuracy is targeted by this work.  ...  The fuzzy programming problem has been widely studied in a variety of fields, which are all based on the fuzzy set theory [7] and the concept of possibility measure [14] .  ... 
doi:10.14569/ijacsa.2014.051011 fatcat:dhx6esjdvfhetiwtch75ty233i

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

Sudipta Midya, Sankar Kumar Roy, Gerhard Wilhelm Weber
2021 Reserche operationelle  
We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters.  ...  The optimal solution which belongs to the "surely region" is better (as these are minimum values) than the one in the "possible region" and other cases.  ...  The authors are very thankful to the respected Editor-in-Chief Professor Nelson Maculan and the anonymous reviewers for their invaluable suggestions, which have improved the quality of the article significantly  ... 
doi:10.1051/ro/2021078 fatcat:2xqvdba5uzf5hcyrjabz7x2tv4
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