Engineering, Technology & Applied Science Research Vol. 8, No. 1, 2018, 2568-2571 2568 www.etasr.com Umar et al.: Taxonomy of Fuzzy Multi-Attribute Decision Making Systems in Terms of Model, Inventor … Taxonomy of Fuzzy Multi-Attribute Decision Making Systems in Terms of Model, Inventor and Data Type Rusydi Umar Department of Informatics Engineering Universitas Ahmad Dahlan Yogyakarta, Indonesia rusydi_umar@rocketmail.com Sunardi Department of Electrical Engineering Universitas Ahmad Dahlan Yogyakarta, Indonesia sunardi@mti.uad.ac.id Yasinta Bella Fitriana Department of Informatics Engineering Universitas Ahmad Dahlan Yogyakarta, Indonesia yasintabella13@gmail.com Abstract—Decision support systems are one of the choices decision-makers make in an attempt to cope with the problems related to the time length required in decision-making process. Such systems are known to improve the efficiency and accuracy in the decision-making processes. In developing a decision support system, a certain calculation method is required as part of its processing. One of the most commonly used methods is FMADM. This research discusses the clustering of decision support system using FMADM in an attempt to provide a taxonomy of decision support system based on FMADM. Keywords-artificial intelligence; decision support system; fuzzy; taxonomy I. INTRODUCTION A decision support system (DSS) is a computerized system that will provide results in the form of ranking based on the assessment aspects determined by decision makers. DSSs are derived from expert systems and are part of the artificial intelligence (AI) field and of the applications that aim to help solving common knowledge-based cases [1]. DSSs are systems that try to gather and exploit human knowledge and experience in artificial intelligence systems so that they may assist in, or even perform, decision making [2]. Some examples of research on expert systems are stroke detection [3], animal disease identification [4, 5] and motor engine damage detection [6]. One of the algorithms used in DSSs is the Multiple Criteria Decision Making (MCDM) algorithm. However, MCDM is divided into several types. This paper, following a similar approach to the one in [7], provides a short literature review on MCDM taxonomy focusing on Multi Attribute Decision Making (MADM) aiming to provide a taxonomy of Fuzzy Multi-Attribute Decision Making Systems in Terms of Model, Inventor, and Data Type Methods. II. RESULT AND DISCUSSION MCDM is a decision-making method that can be used to establish the best choice from a number of alternatives based on certain criteria, e.g. size, standard etc [8]. However, MCDM has a minor disadvantage: if the data provided by the decision maker or the attribute of the data is incomplete, then the resulting decision will contain uncertainty. The problem of uncertainty can be caused by several things, namely: 1. Information that cannot be calculated, 2. Incomplete information, 3. Unclear information and 4. Partial abandonment [9]. To solve these problems, some research on the use of Fuzzy MCDM began to be conducted in order to find methods that proved to have excellent performance. FMCDM can be divided into 2 models: fuzzy multi objective decision making (FMODM) and fuzzy multi attribute decision making (FMADM). FMADM model then can be further divided into 2 models namely the Yager and the Baas & Kwakernaak model. Based on the type of data, FMADM can be divided into 3 types, namely fuzzy data, crisp data, fuzzy and crisp data [10]. While based on the method of application, FMADM can be divided into 3 types, namely SAW method, WP method and TOPSIS. FMADM taxonomies are shown in Figures 1-4 and are presented below. A. FMADM Inventor-Based Taxonomy 1) Yager Model The Yager model FMADM is the standard form of FMADM. According to [11],Yager model has 5 completion stages, which are: 1. Set a pairwise comparison matrix between attributes M based on Saaty’s hierarchy procedure. 2. Determine the consistent weight of wj for each attributes for each attribute based on the eigenvector method of Saaty. 3. Calculate the value of 4. Determine the intersection of all 5. Select with the largest membership degree in , and set the optimal alternatives. One of the researches related to DSS using Yager method is [12] which emphasize on theapplication of DSS to solve cases about the determination of families as poor. A similar research, [13], was conducted to solve the best customer selection case. Both researches resulted in a desktop-based decision support system that was able to assist the decision-making process in their respective cases. mo oft Th ran set the wh of bro B. Engineeri www.etas Fig 2) Baas In contrast odel is not a ften used by s he Baas &Kw nking of som ts[14].Accord e following ste 1. Evaluate follows: here w = (w1, f μZi is defined m Through the ought to a fuzs The value 2. The best ∈ | ̅ FMADM Da 1. Crisp dat obtained their re considere ing, Technology sr.com Fig. 1. FM g. 2. FMADM & Kwakernaa to the Yager standard form some research wakernaak mod me aspects ding to[11]Baa eps: each alterna ∑∑ ... , wm ; r1, .. as follows : in ,.. g function, th zy set sup ̅ ̅) is an alternative is ̅ ,∀ ∈ ata-Type-Base ta, also called directly from spective attr ed less suitabl gy & Applied Sc Umar et al.: T MADM taxonom inventor-based ta ak Model r model, the m of FMADM hers for furthe del is a metho of an altern as and Kwaker ative ai, thro .. , rm ). The m , ,.. he fuzzy set, with m n alternative en chosen as foll , and 1, ed Taxonomy d standard data m the source [ ributes. Use le. cience Research Taxonomy of F my axonomy Baas &Kwak M, but the con er developmen od that describ native using rnaakmodel co ough function (1 membership fu (2 , membership fun (3 nd value ai. lows: …, . (4 a is the origin [15] and grou of crisp d h Fuzzy Multi-Att kernaak ncept is nt [10]. bes the fuzzy ontains n g as ) unction ) will be nction: ) ) nal data uped by data is C. th m we att no all [1 alt Th pr th co W de de ra att ca W cr Vol. 8, No. 1, tribute Decision 2. Fuzzy d overcom request. been tran generaliz function members Fig . FMADM Ap 1) Simp SAW[17] is he most comm multi-attribute eighted sum o tributes[10]. ormalizing the l alternative ju 8] : where rij is ternatives in t he preference ∑ A larger V referred/chose 2) Weig The WP me he rating of orresponding a∏ Where i = 1,2, enotes the crit enotes the crit ank for the att tribute of cos an be given as ∏∏ Where V denote riteria, and w d 2018, 2568-25 n Making Syste data, this dat me the problem In this case th nsformed into zation of th , the fuzzy se ship value bei g. 3. FMADM pplicator-Base ple Additive W s known as th monly used val decisions. T of performanc SAW meth e decryption m udgments. The the normaliz the attributeC value for each Vivalue indic n. ghted Product ethod [19] uses each attribute attribute weigh ..., m, S repre terionvalue, w teria number. tribute of gain st. The relativ : ∗ es alternative denotes the we 71 ems in Terms of ta is chosen m of uncerta he fuzzy data o fuzzy set. Th he concept t has an uncle ing in the rang data-type-based ed Taxonomy Weighting (SAW he linear weigh uation method The basic con e ratings on e hod requires matrix (x) to a e normalized zed performan Cj; i = 1,2, ..., h alternative (V cates that th t (WP) s the normaliz e must be ra hts. This proce esents an alte w denotes the The rank wj n, and is nega ve preferences preferences, x eight of criteri 2569 of Model, Inven as the solu ain decision m is crisp data t he fuzzy set [ of a charac ear boundary w ge 0 to 1 [15]. taxonomy W) hting combina ds for making ncept is to ach alternativ s the proce scale proporti formula is as ( nce rating of m and j = 1, Vi) is given as (6) he Ai alterna zation process aised first w ess is given by (7 rnative prefer criterion’s we is a positive atively valued s of each alte (8 x denotes the v ia. ntor … ution to maker’s that has 16] is a cteristic with its ation or g simple find a e on all ess of ional to follows (5) f the Ai ,2, ...,n. s: ative is s, where with the y (7). 7) rence, x eight, n -valued for the ernative 8) value of Ide lim alt po ne de on wh sol ba wh wh sol sol Engineeri www.etas 3) Techn eal Solution (T TOPSIS is a mited alternat ternative mus ositive solutio gative solutio sribed as follo 1. Create a 2. Create a 3. Determe matrices 4. Determin alternativ negative 5. Determin TOPSIS req n each of the n ∑ here i =1, 2, lution A+ and ased on the nor here i = 1, 2, .. A+ = 1 , 2 A- = 1 , 2 Whereas and herej = 1,2,...n The distance lution is formu ∑ 1 The distance lution is formu ∑ The preferen ing, Technology sr.com nique for Or (TOPSIS) a multi-criteri tives. The ba st have the s on and the f on [17]. In g ows [10]: normalized de weighted norm the matrix of negative id ne the distan ve with posi ideal solution ne the preferen quiresperforma normalized Cj c ∑ ..., m; and j the ideal nega rmalized weig ..., m; and j = 2 ,… , 2 ,… , ; ; ; ; n. e between alte ulated as: 2 ; e between alte ulated as: ; nce value for e gy & Applied Sc Umar et al.: T rder Preferen ia method to asic principle shortest dista furthest distan general, TOP ecision matrix malized decisi of positive deal solutions; nce between itive ideal s n matrix; nce value for e ance rating of criteria, namel = 1, 2, ..., n ative solution ghted rating (y 1, 2, ..., n. ernative Ai wi 1, ernative Ai wi each alternativ cience Research Taxonomy of F nce by Simila identify soluti is that the ance from the nce from the SIS procedur x ion matrix ideal solution the value o olution matri each alternativ f each alterna ly: (9 n.The ideal p A-can be dete yij) as: (1 (1 (1 (1 (1 ith the ideal p ,2,… , (1 ith the ideal n 1,2,…, (1 ve (Vi) is given h Fuzzy Multi-Att arity to ions of chosen e ideal e ideal res can ns and of each ix and ve. ative Ai ) positive rmined 0) 1) 2) 3) 4) positive 5) egative 6) n as: de in de is of m [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 [1 [12 Vol. 8, No. 1, tribute Decision A largerVi s Fig The MCDM ecision making nformation is eveloped as a presented in f fuzzy multi- model, inventor ] E. D. Rikh Mendiagnosa Dempster Sha 1–10, 2013 ] Y. N. Istiqom Saluran Penc Sarjana Tekni ] P. Wijayanti, Stroke Mengg Informatika, V ] M. J. Wahy Penyakit Uda Sarjana Tekni ] S. Triyanto, Kelinci Berba 1, pp. 701-71 ] S. Purnama, Kerusakan Telecommuni pp. 33–38, 20 ] R. Umar, Su System Base Journal of Inn pp. 206–211, ] O. E. Turban, Intelligent Sy Andi Publishe ] C. Chen, C. M problems”, Fu 0] S. Kusumade Attribute Dec 1] H. -J. Zimme Academic Pub 2] D. Kartini, A MADM Yage Miskin (Studi Tanah Laut)”, 191–198, 201 2018, 2568-25 n Making Syste ; score indicates g. 4. FMADM III. C M method is g due to the u provided. F solution to th this paper in -attribute deci r and data type Re hiana, A. Fadlil Penyakit Dalam afer”, Jurnal Sarja mah, A. Fadlil, “S cernaan Menggun ik Informatika, V , A. Fadlil, “Sis gunakan Metode Vol. 2, No. 1, pp yudi, A. Fadlil, ang Galah Deng ik Informatika, V A. Fadlil, “Sist asis Web”, Jurna 1, 2014 F. Firdausy, A Mesin Motor ication Computin 007 unardi, Y. B. Fi ed on Software novative Science 2017 , J. E. Aronson, T ystems (Sistem P er, 2005 M. Klein, “An ef uzzy Sets and Sys ewi, S. Hartati, cision Making (FU ermann, Fuzzy S blishers, 1991 A. Saputra, O. er Pada Sistem P i Kasus : Desa K , Seminar Ilmiah 5 71 ems in Terms of 1,2,…, s that Ai altern applicator-based CONCLUSION s not conside uncertainty in uzzy MCDM hat issue. A sh an attempt to ision making e. ferences l, “Implementas m Pada Manusi ana Teknik Infor Sistem Pakar Untu nakan Metode D Vol. 1, No. 1, pp. 3 stem Pakar Men Certainty Factor p. 691–700, 2014 “Sistem Pakar gan Metode The Vol. 1, No. 1, pp. tem Pakar Untuk al Sarjana Teknik A. Yudhana, “S Menggunakan ng Electronics an itriana, “Taxonom and Calculation and Research T T. -P. Liang, Dec endukung Keput fficient approach stems, Vol. 88, N A. Harjoko, R. UZZY MADM), Sets Theory and Soesanto, “Impl Pendukung Keput Karang Rejo Keca Nasional Teknol 2570 of Model, Inven (1 natives are pre taxonomy ered appropri results if inco M method ha hort literature provide a tax systems in te si Sistem Paka a Menggunakan rmatika, Vol. 1, N uk Mendiagnosa Dempster Shafer 32–41, 2013 ndiagnosa Jenis r”, Jurnal Sarjan Untuk Mengid eorema Bayes 1 11–20, 2013 k Mendiagnosa k Informatika, Vo Sistem Pakar Pe Borland Del nd Control, Vol. my of Decision n Method”, Inte echnology, Vol. cision Support Sy tusan dan Sistem to solving fuzzy No. 1, pp. 51–67, Wardoyo, Fuzz Graha Ilmu, 2006 Its Applications lementasi Metod tusan Penentuan amatan Jorong K logi Komputer, V ntor … 17) eferred. iate for omplete as been review xonomy erms of ar Untuk n Metode No. 1, pp. Penyakit r”, Jurnal Penyakit na Teknik dentifikasi ”, Jurnal Penyakit ol. 2, No. endeteksi lphi 7”, 5, No. 1, Support ernational 2, No. 9, ystem and m Cerdas), y MADM 1997 zy Multi- 6 s, Kluwer de Fuzzy Keluarga Kabupaten Vol. 1, pp. Engineering, Technology & Applied Science Research Vol. 8, No. 1, 2018, 2568-2571 2571 www.etasr.com Umar et al.: Taxonomy of Fuzzy Multi-Attribute Decision Making Systems in Terms of Model, Inventor … [13] R. B. Permana, “Pemilihan Pelanggan Terbaik Dengan Model Yager Pada PT. Aesha Surabaya”, available at: http://ppta.stikom.edu/upload /upload/file/04410100234MAKALAH_TA.pdf [14] H. Kwakernaak, “An algorithm for rating multiple-aspect alternatives using fuzzy sets”, Automatica, Vol. 15, No. 5, pp. 615–616, 1979 [15] E. Prasetyo, “Fuzzy Database”, available at: http://www.slideserve.com /moeshe/fuzzy-database, 2012 [16] C. Praseptyo, A. Pujiyanta, “Media Pembelajaran Himpunan Fuzzy Berbasis Multimedia”, Jurnal Sarjana Teknik Informatika, Vol. 2, No. 2, pp. 1176-1185, 2014 [17] I. Kaliszewski, D. Podkopaev, “Simple additive weighting—A metamodel for multiple criteria decision analysis methods”, Expert Systems with Applications, Vol. 54, pp. 155-161, 2016 [18] Y. Melia, “Multi Attribute Decision Making Using Simple Additive Weighting and Weighted Product in Investment Introduction”, International Academic Institutefor Science and Technology, Vol. 3, No. 7, pp. 1–15, 2016 [19] A. Ahmadi, D. T. Wijayanti, “Implementasi Weighted Product (WP) dalam Penentuan Penerima Bantuan Langsung Masyarakat PNPM Mandiri Perdesaan”, Seminar Nasional Aplikasi Teknologi Informasi, pp. Α19–Α22, 2014