Fuzzy linear programming using a penalty method

Jamison, K. David; Lodwick, Weldon A.

doi:10.1016/s0165-0114(99)00082-2

Cited by 63 publications

(51 citation statements)

References 13 publications

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“…Our solution for the interval case with maximinity, although arrived at differently, essentially reduces to the approach of Soyster [9]; further results in this vein can be found in the domains of inexact and robust optimization [5,1]. The possibility distribution case has been analyzed from a very wide range of angles by the fuzzy sets community-all nevertheless differing from ours; the approach of Jamison & Lodwick [6] is one to mention, because they also pursue a penalty idea, but use a different optimality criterion.…”

Section: Introductionmentioning

confidence: 97%

Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty

Quaeghebeur

Huntley

Shariatmadar

et al. 2012

Communications in Computer and Information Science

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We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possibility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncertainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them.

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Section: Introductionmentioning

confidence: 97%

Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty

Quaeghebeur

Huntley

Shariatmadar

et al. 2012

Communications in Computer and Information Science

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“…Duality theory defines the comparison of fuzzy numbers using a binary relation and uncertainty raises from the fuzzy order will be lost as the comparison between fuzzy numbers.(iii). The ranking function used to prove duality theorems by allowing them to do all the proof analogously to the crisp case [7].…”

Section: Review Of Literaturementioning

confidence: 99%

Computing with words using intuitionistic fuzzy logic programming

Dutta¹

2018

IJET

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Computing with words is the terminology to indicate a set of numbers and words. It is the base for natural language processing and computational theory of perceptions. It is the art to combine both human and machine perception and find a solution for the real world problems left unsolved due to improper mechanism. Animal voice interpreter, lie detector, driving a vehicle in heavy traffic, and natural language interpreter are the applications need to be automated for the next generation. The computational theory is a group of perceptions used to express propositions in a natural language. The concept of the research is to utilize intutionistic fuzzy logic to interpret perceptions to solve vague problems. The output of the research shows that the performance of proposed method is better than the existing methods.

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“…Pos(A) so defined, is a possibility measure since Thus, Pos( A) defined by (13) satisfies (1) and (2) and so it is a possibility. Given this definition of possibility (13), the following holds.…”

Section: Is the "Fuzzified" Number The Set Of Numbers For Which The mentioning

confidence: 99%

“…Given a fuzzy interval, one can generate a possibility/necessity pair using (13) and (3) such that (14) holds.…”

Section: [14] Given An Unknown Cumulative Distribution Function F(x) mentioning

confidence: 99%

An overview of flexibility and generalized uncertainty in optimization

Lodwick

2012

Comput. Appl. Math.

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Abstract.Two new powerful mathematical languages, fuzzy set theory and possibility theory, have led to two optimization types that explicitly incorporate data whose values are not real-valued nor probabilistic: 1) flexible optimization and 2) optimization under generalized uncertainty. Our aim is to make clear what these two types are, make distinctions, and show how they can be applied. Mathematical subject classification: 90C70, 65G40.

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Fuzzy linear programming using a penalty method

Cited by 63 publications

References 13 publications

Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty

Maximin and Maximal Solutions for Linear Programming Problems with Possibilistic Uncertainty

Computing with words using intuitionistic fuzzy logic programming

An overview of flexibility and generalized uncertainty in optimization

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