Küresel bulanık ahp ve topsıs entegrasyonu ile profesyonel ses sistemi seçim probleminin analizi
Analysis of the professional loudspeaker selection problem through the integration of spherical fuzzy and topsis
- Tez No: 1024902
- Danışmanlar: DOÇ. DR. TUNCAY ÖZCAN
- Tez Türü: Yüksek Lisans
- Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2026
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Lisansüstü Eğitim Enstitüsü
- Ana Bilim Dalı: İşletme Mühendisliği Ana Bilim Dalı
- Bilim Dalı: İşletme Mühendisliği Bilim Dalı
- Sayfa Sayısı: Belirtilmemiş.
Özet
Bu çalışmada, hoparlör sistemlerinin seçim problemi çok kriterli karar verme (ÇKKV) yaklaşımı çerçevesinde ele alınmış ve belirsizlik içeren karar ortamlarında daha gerçekçi sonuçlar elde edebilmek amacıyla küresel bulanık küme teorisine dayalı yöntemler kullanılmıştır. Profesyonel ses sistemlerinin seçiminde performans, maliyet, tasarım ve güç gibi birden fazla kriterin birlikte değerlendirilmesi gerekmekte olup, bu kriterler arasındaki ilişkiler ürün seçim problemlerinde genellikle kesin ve net olarak ifade edilememektedir. Bu durum, klasik karar verme yöntemlerinin yetersiz kalmasına neden olmaktadır. Bu çalışmada, karar verme süreci dört ana kriter ve bu kriterlere bağlı toplam on bir alt kriter üzerinden yapılandırılmıştır. Ana kriterler; performans (C1), maliyet (C2), tasarım (C3) ve güç (C4) olarak belirlenmiştir. Bu ana kriterlere bağlı olarak performans kriteri altında be¸s alt kriter (C11-C15), maliyet kriteri altında iki alt kriter (C21-C22), tasarım kriteri altında iki alt kriter (C31-C32) ve güç kriteri altında iki alt kriter (C41-C42) tanımlanmıştır. Kriter ağırlıklarının belirlenmesi amacıyla Küresel Bulanık Analitik Hiyerar¸si Prosesi (SF-AHP) yöntemi uygulanmıştır. Bu doğrultuda, alanında deneyimli toplam beş uzmandan ikili karşılaştırma verileri toplanmıştır. Uzman değerlendirmeleri, küresel bulanık sayılar kullanılarak üyelik (µ), karşıt üyelik (ν) ve tereddüt (π) derecelerini içerecek şekilde modellenmiştir. Elde edilen bireysel değerlendirmeler, küresel ağırlıklı geometrik ortalama (SWGM) operatörü kullanılarak birleştirilmiş ve kriterlerin global ağırlıkları hesaplanmıştır. Alternatiflerin değerlendirilmesi ve sıralanması aşamasında ise Küresel Bulanık TOPSIS (SF-TOPSIS) yöntemi kullanılmıştır. Çalışmada dört farklı hoparlör alternatifi değerlendirilmiştir. Bu kapsamda, alternatiflerin her bir kritere göre performansları belirlenmiş, ağırlıklı karar matrisi oluşturulmuş ve küresel bulanık pozitif ideal çözüm ile negatif ideal çözüme olan uzaklıklar hesaplanmıştır. Daha sonra hesaplanan yakınlık katsayıları aracılığı ile alternatiflerin sıralanması sağlanmıştır. Elde edilen sonuçlara göre, karar verme sürecinde en yüksek öneme sahip kriterin RMS (Root Mean Square) güç olduğu belirlenmiştir. Bunu sırasıyla kompaktlık, satış fiyatı ve tepe güç (peak power) kriterleri takip etmektedir. Alternatiflerin sıralanması sonucunda ise üçüncü alternatifin en uygun seçenek olduğu tespit edilmiştir. Bu durum, yüksek ağırlığa sahip kriterler açısından daha dengeli performans sergileyen alternatiflerin karar sürecinde avantaj sağladığını göstermektedir. Sonuç olarak, küresel bulanık AHP ve küresel bulanık TOPSIS yöntemlerinin birlikte kullanılması, belirsizlik içeren mühendislik problemlerinde daha esnek, tutarlı ve güvenilir kararlar alınmasına olanak sağlamaktadır. Önerilen yaklaşım, yalnızca hoparlör seçimi problemi için değil, benzer çok kriterli karar verme problemleri için de uygulanabilir niteliktedir.
Özet (Çeviri)
Intensifying global competition and rapid technological change have made product selection decisions increasingly consequential for manufacturing firms. In the professional loudspeaker industry, choosing the most appropriate product from a set of candidate designs cannot be reduced to technical performance alone; cost, aesthetic design, physical footprint and power capacity must be weighed simultaneously. Because loudspeakers are developed for acoustically and functionally heterogeneous environments homes, cafes, restaurants, hotels and clubs the evaluation problem is inherently multi-dimensional, and an inappropriate choice translates directly into wasted development time and lost competitive advantage. A further difficulty is that expert judgments in this domain are rarely expressed as crisp numbers. Although several attributes (frequency limits, sound pressure level, rated power) are measurable, the perceived quality of bass, midrange and treble reproduction is assessed auditorily and communicated linguistically. Classical multi-criteria decision-making (MCDM) methods, which presume precise inputs, therefore struggle to represent the vagueness and hesitancy embedded in such evaluations. This thesis addresses that gap by formulating professional loudspeaker selection as an MCDM problem under spherical fuzzy uncertainty and by developing an integrated, reproducible decision-support model for it. The study therefore pursues two objectives: to determine which criteria genuinely drive the selection of professional sound systems and to produce a defensible ranking of alternative loudspeaker models that remains stable under plausible shifts in decision-maker priorities. The literature review covers MCDM applications to product selection and design published between 1999 and 2026, together with the comparatively small body of work that addresses audio equipment specifically. Prior studies have combined AHP with TOPSIS, QFD, VIKOR, DEMATEL, BWM and axiomatic design in contexts ranging from concept screening and green product design to supplier and equipment selection. Within the audio domain, earlier contributions have applied hybrid fuzzy group decision models to concept loudspeaker prototypes, DEMATEL-based frameworks to Hi-Fi system evaluation, and fuzzy multi-attribute methods to studio monitor selection. A recurring finding is that no single technique suffices on its own; weighting and ranking are best handled by complementary methods. Spherical fuzzy sets, introduced by Kutlu Gündo˘ gdu and Kahraman, extend earlier fuzzy set generalisations by allowing the degrees of membership (µ), non-membership (ν), and hesitancy (π) to be specified independently, provided that the sum of their squared values does not exceed one. This three-dimensional representation offers decision-makers a broader preference domain for expressing uncertainty and hesitation during the evaluation process. Such flexibility is particularly advantageous in engineering decision-making applications. For example, an audiophile expert who evaluates the bass response of a loudspeaker enclosure as“good, but not with complete confidence”can express this uncertainty explicitly through spherical fuzzy sets instead of being constrained to a single crisp assessment. A two-stage hybrid framework is adopted. In the first stage, the Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) is used to derive criterion weights. Experts complete pairwise comparison matrices using a linguistic scale whose terms are mapped to spherical fuzzy numbers. Before aggregation, each expert's matrix is converted into its corresponding score-index values and subjected to a classical consistency check, a consistency ratio (CR) below 0.10 is required for the judgments to enter the model. Consistent matrices are then combined with the Spherical Weighted Geometric Mean (SWGM) operator, aggregated criterion values are obtained with the Spherical Weighted Arithmetic Mean (SWAM) operator, defuzzified through the score function, and normalised to yield local weights. Global sub-criterion weights are obtained by multiplying local sub-criterion weights by the weight of their parent criterion. In the second stage, the Spherical Fuzzy TOPSIS (SF-TOPSIS) method ranks the alternatives. Expert assessments of each alternative against each sub-criterion are aggregated with the SWAM operator, the resulting spherical fuzzy decision matrix is multiplied by the SF-AHP weights, and the weighted matrix is defuzzified in order to identify the spherical fuzzy positive ideal solution (SF-PIS) and the spherical fuzzy negative ideal solution (SF-NIS) for every criterion. Normalised euclidean distances from each alternative to these two reference points are computed, and alternatives are ordered using the revised closeness ratio proposed by Kutlu Gündoğdu and Kahraman, which corrects the tendency of the original Zhang-Xu formulation to return zero or negative values. Under this measure the best alternative attains a value of zero and larger values indicate poorer performance. The model is applied to four loudspeaker models developed by a firm operating in the professional sound system sector. A1 is a compact system with a six-inch mid-bass driver and a high-frequency driver, intended for medium-sized venues. A2 is a multi-driver active system with an internal amplifier, wireless connectivity and mobile application support. A3 is a high-performance tower system with an integrated subwoofer, DSP and internal amplification and A4 is an active, DSP-supported system offering high power capacity and wide coverage. The alternatives were deliberately chosen to differ in technical specification, intended use and cost structure. The evaluation hierarchy comprises four main criteria, performance (C1), economic factors (C2), physical suitability (C3) and power capacity (C4) and eleven sub-criteria. Five experts with professional experience in loudspeaker design and audiophile listening supplied both the pairwise comparisons and the alternative assessments, all expressed linguistically. Their comparison matrices produced consistency ratios between 0.043 and 0.090, all below the 0.10 threshold, so no expert had to be excluded.At the main-criterion level, performance received the highest weight (0.333), followed by power capacity (0.276), physical suitability (0.218) and economic factors (0.174). The most influential single sub-criterion in the model is RMS power (C41, 0.176), followed by compactness (C31, 0.128), selling price (C21, 0.109) and peak power (C42, 0.100). The lowest weight is assigned to the lower frequency limit (C11, 0.040). Substantively, this ordering indicates that the experts value sustained, stable output over transient peak capability, and that once continuous power is secured, spatial efficiency and price become the decisive considerations. It is notable that the highest-ranked sub-criterion does not belong to the highest-weighted main criterion the influence of the decision drivers is distributed across the hierarchy rather than concentrated within performance. The SF-TOPSIS stage produces the ranking A3 > A4 > A2 > A1. Alternative A3 lies closest to the positive ideal solution and farthest from the negative ideal solution, attaining a revised closeness ratio of zero. Its advantage stems from balanced, favourable values on precisely those sub-criteria that carry the greatest weight RMS power, compactness and selling price, illustrating that in weighted-distance models alternatives which avoid weakness on heavily weighted criteria outperform those that excel only on lightly weighted ones. Since the criterion weights are derived from expert judgments, a sensitivity analysis was conducted to evaluate the robustness of the proposed decision model. A total of eighteen scenarios were examined, including the original weighting scheme, an equal-weight scenario in which all four main criteria were assigned identical importance, and sixteen additional scenarios generated by increasing and decreasing the weight of each main criterion by 25% and 50%. In each case, the remaining criterion weights were proportionally adjusted to ensure that the total weight remained equal to one. For every scenario, the weighted decision matrix was reconstructed, the positive and negative ideal solutions were recalculated, and the corresponding closeness coefficients were obtained. The sensitivity analysis demonstrated that the proposed decision model is highly robust. Across all eighteen scenarios, A3 consistently retained the highest ranking, whereas A1 remained the lowest-ranked alternative in every case except the equal-weight scenario, where it improved by one position. The ranking order remained unchanged in eleven scenarios. In the remaining seven scenarios, only the second and third positions were interchanged, reflecting the relatively small difference between their closeness coefficients. The most noticeable variation occurred when the weight of the cost criterion was reduced by 50%, resulting in a decrease in the ranking of A2, which originally benefited from this criterion, and producing the order A3 > A2 > A4 > A1. These findings indicate that the proposed model reacts to variations in criterion weights in a consistent and predictable manner, while preserving the stability of the overall ranking. The study demonstrates that the integration of SF-AHP and SF-TOPSIS provides a structured, flexible and reliable decision-support framework for loudspeaker selection under uncertainty. The simultaneous treatment of membership, non-membership and hesitancy degrees allows linguistic and hesitant expert judgments to be modelled more realistically than classical fuzzy approaches permit, while the two-stage architecture separates the question of what matters from the question of which alternative performs best. The sensitivity results indicate that the recommended choice does not depend on a single weight configuration and is therefore defensible in practice. Several limitations should be acknowledged. Expert evaluations of sound quality depend on auditory perception, and human hearing sensitivity varies with age and environmental exposure each expert effectively judges within their own audible frequency range. Future studies could therefore screen participants through audiometric testing and enlarge the expert panel to include acoustic engineers, sales specialists and end users. In addition, the alternatives here are drawn from a single manufacturer's portfolio extending the analysis across brands would improve generalisability. Methodologically, the framework invites comparison with other spherical fuzzy techniques (SF-VIKOR, SF-WASPAS, SF-CODAS, SF-MARCOS, SF-EDAS) and with alternative weighting schemes such as SF-BWM, SWARA or DEMATEL, the last of which would additionally capture causal interdependence among criteria richer structures such as picture fuzzy and T-spherical fuzzy sets may model hesitancy more finely still. Finally, implementing the model as a decision-support application would make it directly usable in the sector, and the same architecture could be transferred to supplier selection, equipment selection and investment appraisal problems of comparable uncertainty.
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