• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.163-163
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• 1988

This research shows that fuzzy set theory can be useful in modeling and solving flow shop scheduling problems with uncertain processing times and illustrates a method for solving job sequencing problem which the opinions of experts disagree in each processing time. In this study, FCDS (Fuzzified Campbell-Dudek-Smith) algorithm and FNEH (Fuzzified Nawaz-Enscope-Ham) algorithm are proposed to improve the fuzzified Branch & Bound algorithm that requires long run-time and computational complexities to find the optimal sequence. These proposed algorithms are also designed to treat opinions of experts. In this paper, Fuzzy processing times are expressed as triangular fuzzy numbers and comparison method use Lee-Li method and ranking method based on the dominance property. On the basis of the proposed method, an example is presented.

• Korean Management Science Review
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• v.13 no.2
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• pp.163-175
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• 1996

This research shows that fuzzy set theory can be useful in modeling and solving flow shop scheduling problems with uncertain processing times and illustrates a method for solving job sequencing problem which the opinions of experts disagree in each processing time. In this study, FCDS (Fuzzified Campbell-Dudek-Smith) algorithm and FNEH (Fuzzified Nawaz-Enscope-Ham) algorithm are proposed to improve the fuzzified Branch & Bound algorithm that requires long run-time and computational complexities to find the optimal sequence. These proposed algorithms are also designed to treat opinions of experts. In this paper, Fuzzy processing times are expressed as triangular fuzzy numbers and comparison method use Lee-Li method and ranking method based on the dominance property. On the basis of the proposed method, an example is presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.18 no.1
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• pp.139-157
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• 1993

This paper presents possibilistic job scheduling based on the membership function as an alternative to probabilistic job scheduling and illustrates a methodology for solving job sequencing problem which the opinions of experts greatly disagree in each processing time. Triangular fuzzy numbers are used to represent the processing times of experts. Here, the comparison method is based on the dominance property. The criteria for dominance are presented. By the dominance criteria, for each job, a mojor TFN and a minor TFN are selected and apessimistic sequence with mojor TFNs and an optimistic sequence with minor TFNs are computed. The three-machine flow shop problem is considered as an example to illustrate the approach.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.17 no.3
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• pp.249-258
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• 2004

We investigated structural phases of potassium intercalated into carbon nanotubes using a structural optimization process applied to atomistic simulation methods. As the radius of carbon nanotubes increased, structures were found in various phases from an atomistic strand to multishell packs composed of coaxial cylindrical shells and in helical, layed, and crystalline structures. Numbers of helical atom rows composed of coaxial tubes and orthogonal vectors of a circular rolling of a triangular network could explain multishell phases of potassium in carbon nanotubes.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.265-275
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• 2004

In this paper, multi-objective models for designing 3D trajectory of horizontal wells are developed in a fuzzy environment. Here, the objectives of minimizing the length of the trajectory and the error of entry target point are fuzzy in nature. Some parameters, such as initial value, end value, lower bound and upper bound of the curvature radius, tool-face angle and the arc length of each curve section, are also assumed to be vague and imprecise. The impreciseness in the above objectives have been expressed by fuzzy linear membership functions and that in the above parameters by triangular fuzzy numbers. Models have been solved by the fuzzy non-linear programming method based on Zimmermann [1] and Lee and Li [2]. Models are applied to practical design of the horizontal wells. Numerical results illustrate the accuracy and efficiency of the fuzzy models.

• Journal of Mechanical Science and Technology
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• v.16 no.4
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• pp.549-556
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• 2002

An investigation on the fully developed heat transfer and friction factor characteristics has been made in rectangular ducts with one-side roughened by five different shapes. The effects of rib shape geometries as well as Reynolds numbers are examined. The rib height-to-duct hydraulic diameter, pitch-to-height ratio, and aspect ratio of channel width to height are fixed at e/De=0.0476, P/e=8, and W/H=2.33, respectively. To understand the characteristics of heat transfer enhancements, the friction factors are also measured. The data indicates that the triangular type rib has a substantially higher heat transfer performance than any other ones.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.128-133
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• 2002

The heat transfer characteristics of a turbulent flow in a ribbed two-dimensional channel have been investigated numerically. The fully elliptic governing equations, coupled with a four-equation turbulence model, $\kappa-\omega-\bar{t^2}-\epsilon_t$, are solved by a finite volume method of SIMPLE type. Calculations have been carried out for three rib cross-sections : square, triangular, and semicircular, with various rib pitches and Reynolds numbers. The procedure appears to be satisfactory as the results for the square rib compare favorably with available experimental data and earlier calculation. The optimal rib pitch that yields the maximum heat transfer has been identified. It is also found that the square rib is most effective in enhancing the heat transfer. The semicircular rib, on the other hand, incurs the least amount of pressure drop but the improvement in heat transfer is substantially lower.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.11-23
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• 1998

This paper presents a more efficient evaluation of alternatives by use of multi-criteria decision making methodlogy under fuzzy intersectional dependence relations. The performance evaluation of most systems such as weapons, enterprise systems etc. are multiple criteria decision making problems. The descriptions and judgements on these systems are usually linguistic and fuzzy. The traditional methods of Analytic Hierarchy Process(AHP) are mainly used in crisp(non-fuzzy) decision applications with a very unbalanced scale of judgements and rank reversal. To overcome these problems, we will propose a new, general decision making method for evaluation models using fuzzy AHP(FAHP) under fuzzy intersectional dependence relations. The T.M.S alternatives A, B and C will be evaluted by the Fuzzy Analytic Hierachy Process (FAHP) based on entropy weight in this study. We will use symmetric triangular fuzzy numbers to indicate the relative strength of the elements in the hierachy and degree of intersection between criteria. These problems are evaluated by five criteria : tactical criteria, technology criteria, maintenance criteria, economy criteria, advacement criteria.

• Journal of the Korean Chemical Society
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• v.57 no.3
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• pp.352-356
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• 2013

In this work, a new cadmium complex $[Cd(L)(CH_3COO)_2].2H_2O$ (1) with the ligand L, N,N'-bis(2-pyridinecarboxalidene)-1,2-cyclohexanediamine was prepared and identified by elemental analysis, FT-IR, Raman, $^1H$ NMR spectroscopy and single-crystal X-ray diffraction. The cadmium atom in the crystal structure of 1 has distorted triangular dodecahedral geometry by coordination of the four nitrogen atoms of L and four oxygen atoms of the two acetate ions. Two water molecules are also incorporated in the crystal network. The $O-H{\cdots}O$ hydrogen bonds present in the crystal structure of 1. In this work, three structural surveys including coordination numbers of the cadmium atom, coordination modes of L and resonance in pyridine-2-ylmethanimine-based compounds are presented.

• International Journal of Computer Science & Network Security
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• v.21 no.12
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• pp.223-227
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• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.