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By D. G. Hulbert, D. J. Oosthuizen, D. de V. van der Spuy

Expert Online, as a software system, is aimed at providing plant operators in the minerals industry with effective training and on-the-job assistance. It incorporates a number of features to achieve this goal, of which the most important is its ability to explain the dynamics of the plant and control system in simple language, mimicking an informed plant expert who has online access to the inner workings of the plant and control system. This is made possible by a novel form of Artificial Intelligence, called the Interpreting Expert System. Previous implementations of the IES were only capable of explaining controller actions. Expert Online will extend this capability to also perform the more difficult task of explaining process behaviour. Expert Online will implement three main processes, namely the accumulation of data from the controllers and plant models, the interpretation, processing and filtering of that data and lastly communicating the relevant information to the user, both as written messages and in other audio-visual forms. Although Expert Online is aimed at the operator, other plant personnel, like supervisors and plant managers, will also benefit from it. This paper focuses on the structural and functional design of Expert Online for implementation on the latest version of Mintek’s open control platform, PlantStar, highlighting advances and additions since the previous implementations of the Interpreting Expert System and concluding with an example illustrating some of the principles.

Jan 1, 2003

By M. Handley

The Witwatersrand Basin contains by far the most gold ever found, and has hosted mining from its discovery in 1886 to the present. For many years, South Africa was the world’s largest producerof gold, nearly all of which came from the Witwatersrand. Since 2000, South Africa has fallen back several positions because of declining gold output. There are many complex and varied reasons for this; however, declining gold resources in the Witwatersrand Basin are not one of them. As far as the author knows, there are no qualified estimates in the literature of gold remaining in the Witwatersrand Basin. This paper collects mining data from several sources and then, using elementary gold accounting and error analysis, attempts to estimate the amount of gold remaining in the Witwatersrand Basin. It includes gold underground in existing and defunct mines, in evaluated ore resources, and dumps. Compiled data from 1887 to 2019 shows that 50 200 t of gold were produced by Witwatersrand mines, while it is estimated that a further 48 100 t remainunderground, both within and outside of mine leases, a further 1 600 t on the surface in tailings,and an unknown amount in rock dumps. Nearly all of this gold will remain inaccessible with current mining methods, and major technical developments in mining will be necessary before any of the gold can be categorized as a code-compliant resource or reserve. To win this prize, the mining industry will have to rethink its approach to mining, both in old mining leases and in the unexploited ground. It will also have to find effective means of preventing gold theft and informal mining, which are on the rise.

Apr 5, 2023

By A. Haines, O. Varaud, I. Baidoo

Abosso Goldfields Limited (AGL) is in the process of developing an expansion of their Damang Open Pit gold mine in Ghana. AGL acquired the Damang mine in January 2002, with SRK participating in the geotechnical investigation and design for the project since 2001. A deep resource drilling program, completed during 2004, intersected an extension of the orebody below the then planned final pit floor. A feasibility study has been completed to determine the economic extraction of this deep ore with an expanded pit shell. The Damang mine is in a stockwork sulphide deposit at the culmination of the Damang anticline. The deposit occurs as hydrothermal mineralisation associated with dominantly east dipping thrusts and sub-horizontal quartz veins. Primary gold mineralisation also occurs in the conglomerates of the Tarkwaian Formation. The geological units consist of steep easterly dipping dolerite, sandstone, siltstone and phyllite beds, with the weathering profile comprising saprolites overlying a relatively thin joint oxidized horizon. It is planned to deepen the current open pit to a final depth of up to 270 m, primarily by the development of a push-back of the eastern and western walls. The edge of the Eastern Tailings Storage Facility (ETSF) is currently located within 80 to 100 m of the crest of the existing pit. The geotechnical design focused on the optimization of the bench face angle and finally recommended a ?Steep Slope Strategy?, involving 24m high near vertical benches. Limiting bench stack heights of 96m at a maximum of 66° were derived from the influence of major structures and the variation in rock mass conditions. The overall slope angles in each pit sector were developed around the requirement for haulage ramps. One of the main design challenges was to optimise the standoff distance between the final pit crest and the ETSF. This process had to consider maximum access to the resource without undue influence on or from the nearby tailings dam. A planned increase to the height of the dam wall was an additional factor in the design. Dewatering of the pit walls was also a major consideration in this tropical environment.

Jan 1, 2006

By P. J. K Leeuw, E. Uludag, M. J. Nong

Efficient drill-and-blast performance is pivotal to the profitability of deep-level mines, where high operating costs and declining grades demand maximum throughput. This study investigated persistent fragmentation problems at a longhole stoping operation that suffered from simultaneous oversized rock blockages in 300 mm × 300 mm grizzlies and excessive fines. Fifty-one muckpile images from five blasted stopes were analysed with Split-Desktop. Although the overall F₈₀ was 287 mm, nominally suitable for the grizzly aperture, the Rosin- Rammler uniformity index of 0.80 revealed a highly inconsistent size distribution containing both boulders and fines. Existing drill patterns were then evaluated with the Aegis underground software, which showed negligible crack overlap at the toe owing to inadequate spacing and burden. Insufficient energy overlap between blastholes, particularly at the toe, was found to contribute to the coarse fragmentation, while excessive fines were attributed to the crushing and severely fractured zones of blastholes. Optimisation simulations demonstrated that an 89 mm blasthole diameter on a 2 m × 2 m pattern would overlap, aligning with Aegis requirements of balancing powder factor, break angle, and energy distribution. Implementing this revised pattern is expected to reduce secondary breaking, prevent ore-pass blockages, lower fines, and ultimately improve overall production efficiency. The methodology illustrates how integrated image analysis and modelling software can effectively diagnose and address fragmentation issues, particularly in underground longhole mining, where challenging blasting conditions require a balance between achieving optimal fragmentation and maintaining stope stability. This approach offers a cost-effective pathway to improving comminution performance in deeplevel mines.

Oct 2, 2025

By G. A. Brown

Major mining projects are developed with the assistance of lending institutions who provide hundreds of millions of dollars in funding over several years, and of course expect those funds to be returned with interest. Two Australian banks have adopted the Equator Principles, an emerging financial industry benchmark for assessing and managing environmental and social risk in project financing. Project financiers have encountered environmental and social issues that are both complex and challenging, particularly with respect to projects in the emerging markets of Asia-Pacific and elsewhere. There are many recent and historical examples of failures by resource companies to effectively manage their environmental, social, safety and security risks, some of which have caused the project to fail completely, and some of which have caused the temporary cessation of production. These events put the financial institutions' funds at risk through inadequate management capacity and non-compliance adversely affecting the ability of the borrowers to repay the loans. They can also reflect adversely on the reputation of the lending institutions. In assessing these risks, lenders are increasingly looking at the track record of the borrower in its country of origin and in other countries where it operates. Lenders are wary of companies that have one standard for operations in a developed country, where the regulatory environment may tightly control what they do, and another standard for operations in countries where the regulatory regime is perhaps less stringent. Lenders may require environmental and social reviews or audits to be conducted on their behalf by competent third parties prior to a loan being approved, and annually over the life of the relationship. The mining industry's concept of the unwritten `social licence to operate' is highly relevant in relation to the delivery of community benefits that are sustainable post-mine closure. This paper provides examples of recent practices that support financial viability and sustainable development, as well as examples of some failures that have put lenders at risk.

Jan 1, 2007

By Patrick J. Foster

This paper summarises a behavioural safety project undertaken in seven quarries in the UK in order to investigate its applicability as a means of raising the standards of health and safety in the UK quarrying industry. A behavioural safety methodology was developed and trialled at two quarry sites in the UK. During the study the number of unsafe acts and minor accidents had decreased and at one of the quarries there was a 95% reduction in the number of working days lost. It was then introduced at a further five sites of varying sizes and within this focused specifically on lone workers as well as behaviours that affected quality and environmental issues. Positive improvements were noted in most of these operations. The project also looked at the effectiveness of health and safety performance indicators. Here, the common lead and trailing indicators for both safety and health that are commonly used by industry were identified. In consultation with the UK quarrying industry these were then used to identify specific performance measurement criteria that can be used by the quarrying sector to measure performance. Following on from this a quarry specific health and safety management system specification was developed for large and small quarries.

Jan 1, 2008

By H. S. Sichel

"The valuation of diamond ferous deposits depends on (i) the density distribution, (ii) the size distribution of stones and (iii) the selling price structure prevailing at a particular time.In the density distribution the stochastic variable is defined as the Dumber of individual stones found per sample unit irrespective of the stone size. The density distribution is discrete and allows for barren sample units.As diamonds often occur in clusters, a Poisson mixture distribution is derived which is entirely new, as existing discrete distributions cannot represent the stone number frequencies found in nature.For the sizes of diamonds, which are measured by weight, a new compound logarithmic normal distribution is developed.Combination of (i), (H) and (iii) leads to a meaningful appraisal of diamond ferous ground expressed in monetary value per production unit of mining.Finally, confidence limits are calculated which allow for inference from sampling to recovery."

Jan 1, 2014

By Nielen van der Merwe

Mr Janisch' s comment' in the August issue on Dick Stacey's remarks about safety factors indeed requires wider debate. The example he quoted to illustrate the successful application of the safety factor concept in coal mining, namely the Salamon formula, is to my knowledge the only recognized application of that concept. Not only that, but that particular formula should be used only for what it was intended, namely to prevent major disasters. It was never intended to indicate long-term pillar stability, and it should not be used for that.

Jan 1, 1993

By T. C. Alex, K. M. Godiwalla, R. K. Jana

Manganese nodule, available in ocean beds, is a potential resource of the future for copper, nickel and cobalt. Recovering only these metals, containing less than 3% by weight, will result in the generation of large amount of residue. In addition to the material losses, several environmental and ecological problems arise out of this. The present study has been aimed at reducing the environmental and ecological problems associated with massive generation of this residue together with utilization of the resources. Presence of ~ 20% manganese and ~16% silicon in the residue has prompted us to check its suitability as a raw material for silicomanganese production. Lower manganese content and lower Mn/Fe ratio of the residue than that required for silicomanganese production has been corrected in this study by suitable blending. The efficacy of blending and its thermodynamic aspects using FACTSAGE software are discussed. The studies conducted indicate viability of bulk utilisation of the residue through silicomanganese production and thereby reducing the burden on environment to a great extent.

Jan 1, 2007

By B. I. Matshediso, J. Kaavera, E. Shemang, T. K. Dintwe, L. S. Teseletso, K. Fichani

The minerals sector continues to draw attention from policy makers who would want to see both old and new mineral projects add value to the minerals in the host country. The current technological development in the leaching of manganese oxide ores to produce a high-purity manganese sulphate monohydrate, a compound that is used in the manufacture of batteries for electric vehicles or long-life storage cells for the renewable energy market, has led to junior mining companies spearheading this technology in new projects across the globe. In this paper, we researched the high-purity manganese sulphate monohydrate project pipeline and used projected production volumes and C1 cash costs to construct the industry supply curve for six projects, including the K.Hill project owned by Giyani Metals Corporation near Kanye, in the southern part of Botswana. The aim was to determine the ideal conditions that would provide a comparative advantage for further local value addition to high-purity manganese sulphate monohydrate and to the end user product. The results showed that while the estimated C1 cash costs would place the K.Hill project as the second highest cost producer from among five projects, it would nonetheless have healthy profit margins due to the high projected price of high-purity manganese sulphate monohydrate. The study recommended policy options, which, if implemented, could further encourage the exploitation and value addition of battery metals in Botswana.

May 27, 2025

By X. B. Zhao, J. G. Cai

The purpose of this paper is to incorporate the dynamic BB model of rock fracture normal behaviour into Universal Distinct Element Code (UDEC), and to conduct UDEC modelling to predict stress wave propagation across rock fractures. With the incorporation of new dynamic model of fractures, the UDEC is improved in the capability of modelling wave propagation across fractures. In this study, the case of normally incident P-wave transmission across a fracture is modelled, and the effect of dynamic normal behaviour of fracture is concentrated on. Wave transmission coefficient for wave transmission across the fracture with the dynamic BB model is obtained for various combinations of fracture dynamic parameters, as well as different wave amplitudes and frequencies.

Jan 1, 2003

By D. Botha, J. F. Cronjé

"SynopsisAlthough women all over the world have been involved in mining activities for centuries, mining has always been considered a very masculine industry due to its heavily male-dominated workforce as well as the physicality of mining work. The mining industry has not been an obvious career choice and preferred place of employment for women; women were mainly employed in administrative and advisory positions. Until 1994, women were legislatively prohibited from being employed in underground operations in South Africa, but the Mines Health and Safety Act, No. 29 of 1996, removed these restrictions. In addition, new mining legislation (the Mineral and Petroleum Resources Development Act, No. 28 of 2002) and the accompanying Mining Charter make specific provisions for the inclusion of women in core mining activities and require 10% of core positions to be filled by women.This article voices perceptions of the physical ability of women employed in core mining positions. Findings are drawn from empirical work undertaken at platinum, phosphate, and copper mines. Quantitative and qualitative research paradigms are used. It is evident that women find it extremely difficult to perform mine work that requires physical strength and stamina. Practical recommendations, informed by the literature review and empirical findings, are made with the objective of contributing to the sustainable deployment of women in the mining industry.IntroductionFor many years, mining has been considered the foundation of the South African economy. Although the mining industry in South Africa is currently under considerable pressure and experiences various challenges, including escalating operational costs, electricity tariff increases, safety-related issues and associated production stoppages, poor productivity, labour unrest, and reduced demand both globally and domestically, it remains a key contributor to the national economy and development of the country (IDC, 2013, p. 9).Until 1994, women were legislatively prohibited from meaningful participation in the mining industry and were denied access to skills and jobs, self-employment, and entrepreneurship. The newly elected democratic government in 1994 initiated substantial socio-political and economic transformation in South Africa. Nearly every sector in the country was transformed and re-shaped, primarily through sector-specific legislation, but also through negotiations between government, industry, and labour unions to create and refine the so-called sector charters, which included the Mining Charter. The vision of the new regime, the African National Congress (ANC), was to ‘transfer power to the people and transform society into a non-racial, non-sexist, united, democratic one, and change the manner in which wealth is shared, in order to benefit all the people’ (ANC, 2007)."

Jan 1, 2015

By S. Erçayhan, B. Derin, O. Yücel

In the present study, the production of low carbon ferrochromium (LC-FeCr) from chromite concentrates containing 55.09% Cr2O3 and 13.06% Fe via metallothermic process was investigated. For this aim, in the experiments, the aluminothermic reduction method was applied in an open crucible. 10% CrO3 + 10% NaClO3, 15% CrO3 + 5% NaClO3 and 20% CrO3 by weight of concentrate were added to the charge, respectively and the charge was reduced with aluminium. The experiments were done with the additions of 90, 100, 110, 120 and 130% of stoichiometric requirement of aluminium. The highest Cr content in alloys was found as 71.7% at 120% of stoichiometric Al whereas the highest Cr recovery in alloys was found as 71.8% at 130% of stoichiometric Al when the both charge contained 15% CrO3 + 5% NaClO3 by weight of chromite concentrate.

Jan 1, 2004

By J. Muralha

The paper presents the limit equilibrium equations for the analysis of toppling blocks on a rock slope. The safety conditions are assessed by a numeric procedure implemented in an Excel worksheet. The UDEC numerical program was exploited to validate the procedure. A probabilistic model considering the spacing variability of the discontinuities was developed to define the most relevant parameters in this kind of problems. La communication presente les equations d’équilibre limite pour l’analyse de blocs rocheux sur une pente. Les conditions de securité sont évaluées par une procédure numérique en Excel. Le logiciel UDEC a été exploité pour valider cette procedure. Un modèle probabilistique a été developpé pour définir les plus importants paramètres dans ces problèmes. Das Referat stellt die Grenzgleichgewichtsgleichungen für die Analyse von umstrürzenden Blök-ken auf eines Felshang vor. Die Sicherheitsbedingungen werden durch ein numerisches Verfahren mit Excel beurteilt. Um die Gültigkeit des Verfahrens festzustellen, wurde das Programm UDEC benutzt. Ein die Klufabstandsvariabilität berücksichtigendes probabilistisches Modell wurde entwickelt, um die wichtigsten Parameter dieser Probleme zu bestimmen.

Jan 1, 2003

By N. A. Barcza

This publication records the proceedings of the Tenth International Ferroalloys Congress, INFACON X, and the third INFACON hosted in South Africa. The Proceedings of the previous two South African congresses in 1974 and 1992 serve, as this volume does, as a valuable record of the papers presented at these important events. This publication comes at a time in South Africa?s democratic development where the theme ?Transformation Through Technology? is very appropriate. The ferroalloy industry has played an increasingly significant role in transformation and black economic empowerment in South Africa, particularly through the advancement and sharing of technology. INFACON X plays an important role in this process, and the stakeholders and organisers of this Congress are thankful for the opportunity to hold this event at this time of transformation in our country. The world of ferroalloys, as well as that of the steel and stainless steel industries, has continued to change rapidly. Recent innovations, better use of resources, increased awareness of environmental issues and ongoing efforts to improve occupational health and safety are among the topics addressed at INFACON X and in these Proceedings. The theme of ?Transformation Through Technology? has been chosen to reflect the regional and global developments in the ferroalloy industry, and the crucial role that technology plays. The Proceedings of INFACON X, the first Congress in Southern Africa of the new millenium, represent a milestone in the technical developments in this major global industry. It contains almost eighty papers in twenty Sessions, from authors in twenty countries, covering raw materials, reductants, energy, electrodes, refractories, furnace design, post taphole services, modelling, simulation, control, sensors, fundamental issues and the applications of ferroalloys as related topics. The major ferroalloys, namely ferrochromium and ferromanganese, are covered extensively in many interesting papers. This comes as no surprise, since South Africa is the leading producer of ferrochromium and also plays a major role in the supply of manganese ore and alloys. Papers on ferronickel, silicon and ferrosilicon ensure that all the large-volume ferroalloys are addressed. These Proceedings of refereed papers of high quality will serve the ferroalloy industry for many years to come, as has been the case with previous INFACON events. For the first time in the history of INFACON, the Proceedings will be available both in bound and in a searchable electronic CD-ROM format. We appreciate the time and effort that the authors and referees have devoted to making this publication a really valuable document. Their contributions are recorded for posterity and reflect the advancements they and their colleagues have made to benefit the ferroalloy industry. Without these ongoing improvements, the industry would stagnate and not fulfil its role in the advancement of mankind. All papers included in these Proceedings were peer-reviewed by at least two referees. About 130 referees were sourced internationally to fulfill this function, and their valuable technical and editing inputs are gratefully acknowledged. Finally, I would like to thank the Technical Programme and Publication committees, led by Dr. Lloyd Nelson and Dr. Noël Machingawuta respectively. Without the tireless efforts of these individuals and their Committee members, the technical programme and these Proceedings would not have been the success they certainly are.

Jan 1, 2004

By D. Nyembe, B. Mamba, Antoine F. Mulaba-Bafubiandi

Copper and cobalt are generally electro-won from their aqueous sulphate solutions. After optimised leaching of their ores, concentrates or calcine bearing minerals, the leachate is clarified and suitably purified prior to the electrolytic extraction of the metal of pursuit (Pearcy, 2006). Solvent extraction (SX) using appropriate organic solvents and ion exchange (IX) with relevant resins are known purification processes used for copper and cobalt recovery (Stanely, 1970).As zeolites in general and natural zeolites in particular, demonstrate ion exchange properties (Korkuna et al., 2005), an attempt has been made to use Southern African natural clinoptilolite in the recovery of copper and cobalt from their aqueous sulphate solutions. Initially, synthetic Co and Cu solutions were prepared. Preceded by laboratory ore leachate, plant solutions are to be used. AAS, XRF, XRD, Mossbauer spectroscopy and BET were characterization techniques used. Natural clinoptilolite was used as-received as well as acid activated; and cobalt and copper extractions were performed at room temperature.

Jan 1, 2007

By J. -H. Wu, S. Nishiyama, Y. Ohnishi

The behaviors and stress distributions of the inclined jointed rock masses with different dip angles obtained from DDA are compared to the results of laboratory tests. By calculating the block stress distributions, it is confirmed that DDA can reproduce the arching around the trap door when lowering the trap door. The shapes of arching change with the angles of inclined layers. In addition, the earth pressures acting on the trap door shows non-symmetrical distributions when the layers are not horizontal. The stress concentration occurs in one side of the rock masses close to the trap door. Furthermore, the surface settlements are also related to the inclined angle, and the loosening zone in rock masses can be different from Terzghi’s theory [1]. Since, simulations have good agreements with the laboratory test , it demonstrates the applicability of DDA to explain the mechanical behaviors of tunnel, such as arching phenomenon, non-symmetrical earth pressure distributions acting on the trap door, and the surface settlement profile in the jointed rock masses. Dans cet article est décrite l’étude numérique du perçage d’un tunnel dans un massif de couches rocheuses jointes inclinées. La simulation à l’aide de l’Analyse de Déformation Discontinue (DDA), en faisant varier l’angle d’inclinaison des couches de roche, nous apporte des résultats en termes de distributions de contraintes et de comportement des couches, résultats qui sont ensuite comparés avec des résultats de tests en laboratoire. Les résultats confirment le fait que la DDA est capable de reproduire le phénomène d’arcage autour de la trappe lorsque la trappe s’abaisse. Les formes d’arcage varient selon l’angle d’inclinaison des couches de roche. Par ailleurs, lorsque les couches ne sont pas horizontales, la distribution de pression agissant sur la trappe est assymmétrique. La concentration de contraintes se produit du coté proche de la trappe. De plus, les tassements de surface dépendent eux aussi de l’angle d’inclinaison. En conséquence, les résultats de simulation sont en accord avec les tests en laboratoire, ce qui prouve que la DDA permet d’expliquer des comportements mécaniques du tunnel tels que l’arcage, les distributions assymmétiques de pression du sol sur la trappe, ainsi que le profil du tassement de surface dans la masse de roches jointes. Dieser Beitrag beschreibt eine numerische Studie über Tunnel im geklüftetem Fels. Das Verhalten und die Druckverteilungen in den unterschiedlich geneigten und geklüfteten Felsenmassen wird mit Hilfe des Discontinuous Deformation Analysis Programms (DDA) simuliert, und mit Laborversuchen verglichen. Die Resultate bestätigen, dass DDA der Gewölbewirkung im „Trapdoor“ Experiment gut reproduzieren kann. Die Form des Gewölbes, ändert sich mit unterschiedlichen Neigungswinkeln der Schichten. Bei geneigten Schichten entstehen unsymmetrische Druckverteilungen. Auch die Oberflächenabsenkung ist von dem Neigungswinkel abhängig. Die gute Übereinstimmung der Simulationen mit den Laborversuchen zeigt, dass die DDA-Methode gut geeignet ist, um das mechanische Verhalten von Tunneln, wie z.B. den Effekt der Gewölbewirkung, die unsymmetrischen Druckverteilungen bei geneigten Schichten, oder die Oberflächenabsenkung in geklüfteten Felsenmassen, zu erklären.

Jan 1, 2003

By R. Romano

Some topics, which difficult the effective use of RMR for dam foundations, are reviewed and a new geomechanics classification system, DMR (Dam Mass Rating), is proposed -as an adaptation of RMR- giving guidelines for several practical aspects in dam engineering and appraisal of dam foundation. On revise quelques problems qui ont fait difficile l’application du RMR pour les fondations des barrages. On propose un nouveau classification système, DMR (Dam Mass Rating)-comme un désarroi du RMR-qui donne recommendations pour quelques problèmes pratiques dans le projet et construction des barrages, et de ses fondations. Es werden einige die praxisgerechte Nutzung des RMR (Rock mass Rating) erschwerende Themen betrachtet und ein neues Geomechanisches Einteilungssystem, das DMR (Dam Mass Rating), eine Anpassung des RMR, vorgeschlagen. Daraus resultieren neue Richtlinien für verschiedene praktische Aspekte beim Dammbau und bei der Beurteilung von Dammunterbauten

Jan 1, 2003

By F. T. Cawood

This paper focuses on the role of the coal mine surveyor at the start of the 21st century. It demonstrates that surveyors must look beyond their legal appointment and pursue opportunities to add value at an operational or corporate level of the company. It also exposes the shortfall of statutory appointments in defining the surveyor?s role in terms of key business drivers of the company. One such an opportunity is the potential role of the surveyor in mineral accounting and quality assurance to meet mine requirements, market specifications and standards pertaining to corporate governance and reporting. Finally, some thoughts are expressed on what can be done to elevate current practice to best practice and how to achieve this goal

Jan 1, 2007

By M. Yavuz

Two different methods of fuzzy multiple criteria decision making have been proposed to solve the problem of mining method selection in the paper titled ?Mining method selection by multiple criteria decision making tool, by Bitarafan and Ataei. This problem is really important and also difficult to solve because of the need of handling many criteria simultaneously in the process of decision making. Bitarafan and Ataei have selected 15 criteria for the case study in their paper and those criteria have not been clustered/grouped yet. The number of selected criteria is only 15, although there are more criteria that should be handled in a real case, because they have used Saaty?s method in the section ?Fuzzy multiple attribute decision making? in their paper. Saaty?s method considers the pair wise comparison of criteria and uses random indexed which have already been derived and published. Available random indexes, however, have been derived for maximum 15 criteria so far.

Jan 1, 2007