A note on “Solving linear programming problems under fuzziness and randomness environment using attainment values”

Chou, Shuo‐Yan; Lin, Jen‐Yang; Julian, Peterson

doi:10.1016/j.ins.2009.08.013

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…Moreover, our paper not only revises the questionable results in Hop [13], but also extends Hop [13] and Chou et al [14]. For two fuzzy numbers̃and̃, in Hop [13] and Chou et al [14], they only considered, (̃,̃), the lowerside attainment index of̃tõsuch that, in their definition, they assumed that̃≤̃.…”

Section: Introductionsupporting

confidence: 53%

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An Improvement for Fuzzy Stochastic Goal Programming Problems

Lin

Tuan

Julian

2017

Mathematical Problems in Engineering

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We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

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Section: Introductionsupporting

confidence: 53%

“…For two fuzzy numbers̃and̃, in Hop [13] and Chou et al [14], they only considered, (̃,̃), the lowerside attainment index of̃tõsuch that, in their definition, they assumed that̃≤̃. It means that if̃and̃are two triangular fuzzy numbers, with̃= ( , , ) and̃= (V, , ), then they assumed that ≤ V.…”

Section: Introductionmentioning

confidence: 99%

An Improvement for Fuzzy Stochastic Goal Programming Problems

Lin

Tuan

Julian

2017

Mathematical Problems in Engineering

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“…When the intersection does not exist, ( , ) D U V   equals to zero (Chou et al 2009). The average lower-side attainment degree index proposed above can effectively transform fuzzy relationships between fuzzy numbers into corresponding deterministic ones and reflect the attainment degree of two fuzzy numbers without any additional constraints.…”

Section: Given Two Fuzzy Numbers ( )mentioning

confidence: 99%

Planning of Electric Power Generation Systems under Multiple Uncertainties and Constraint-Violation Levels

Huang²,

Cai

et al. 2014

J ENV INFORM

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ABSTRACT. Regional electric power generation systems (REPGS) planning involves multiple sectors, multiple facilities, and multiple uncertainties, leading a variety of complexities. In this study, lower-side attainment degrees based inexact fuzzy chance-constraint programming (LA-IFCCP) was proposed to support the planning of REPGS under such a complex situation. LA-IFCCP was developed by integrating lower-side attainment degrees based fuzzy programming (LA-FLP) into an interval chance-constraint programming (ICCP) framework. It was able to tackle uncertainties expressed as intervals, fuzzy sets, probabilistic distributions as well as their combinations. At the same time, fuzzy relationships between conversion efficiencies of technologies and availabilities of energy resources could be transformed into corresponding deterministic ones via the lower-side attainment degree index without introducing any additional constraints, and thus guaranteed enhanced computation efficiency. Moreover, constraintviolation levels about renewable energy resource availabilities could be quantified through the adoption of various pi levels, which could represent the reliability of the system. The relationships between systems costs and reliability could be reflected via analyzing the solutions under different pi levels, which was very important for the management of power generation. A hypothetical but representative regional electric power generation system was adopted for demonstrating its applicability. Reasonable solutions were generated. They provided desired plans regarding energy supply, electricity generation, capacity expansion and emission mitigation to achieve a minimized system cost.

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“…It should be noted that these can be obtained only when the intersection between the right side ofŨ u; a; b ð Þ and the left side of V v; c; d ð Þ exists. However, such an intersection does not always exist (Chou et al 2009). When the intersection does not exist, k Ã which represents the membership degree of the intersection between the right side ofŨ u; a; b ð Þand the left side ofṼ v; c; d ð Þ, does not exist.…”

Section: Proposition 2 (Fan 2008) Given Two Fuzzy Numbersmentioning

confidence: 99%

“…Based on this method, relationships among fuzzy/fuzzy-random parameters are reflected by varying lower-side attainment degrees, and transformed into their corresponding deterministic ones without additional constraints leading to a sharp decline in computational process compared to conventional approaches. Though LA-FSLP can deal with dual uncertainties expressed as probability and possibility distributions, it still does not result in superior performance because it neglects some relevant and inevitable theoretical essentials (e.g., the case comparing the relative vicinity degrees among two or more groups of fuzzy number, and/or the case that the intersection between the right hand side ofŨ and the left side ofṼ does not exist) (Chou et al 2009). Also, it encounters difficulty to deal with uncertainties represented as intervals or fuzzy boundary intervals.…”

mentioning

confidence: 99%

Inexact fuzzy two-stage programming for water resources management in an environment of fuzziness and randomness

Huang

Liu

et al. 2011

Stoch Environ Res Risk Assess

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A standard lower-side attainment values based inexact fuzzy two-stage programming (SLA-IFTSP) approach is proposed for supporting multi-water resources management under multi-uncertainties. The method improves upon the existing inexact two-stage stochastic programming by the introduction of a standard average lower-side attainment values based fuzzy linear programming. Multi-uncertainties such as intervals, probabilistic and/or possibilistic distributions and their combinations in water resources management can be directly communicated into the water allocation process. The risk of infeasibility caused by the random water availabilities can be analyzed by imposing economic penalties when the designed water allocations would not be satisfied after the occurrence of random seasonal flows. Based on the standard average lower-side attainment index, the fuzzy random relationships representing various subjective judgments in the model can be transformed into corresponding deterministic ones without additional constraints, and thus guarantee a higher computational efficiency. A hypothetical case regarding two-source water resources management is adopted for demonstrating its applicability. Reasonable solutions have been generated. They provide desired water allocations with maximized system benefit under different water availability levels. The solutions of intervals with different probabilities can be used for generating decision alternatives. Comparisons between the solutions from SLA-IFTSP and those from ITSP are also undertaken. They show that SLA-IFTSP can generate more reasonable water allocation patterns with higher net system benefits than ITSP.

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A note on “Solving linear programming problems under fuzziness and randomness environment using attainment values”

Cited by 7 publications

References 24 publications

An Improvement for Fuzzy Stochastic Goal Programming Problems

An Improvement for Fuzzy Stochastic Goal Programming Problems

Planning of Electric Power Generation Systems under Multiple Uncertainties and Constraint-Violation Levels

Inexact fuzzy two-stage programming for water resources management in an environment of fuzziness and randomness

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