ENRICHING PROCESS OF ICE-CREAM RECOMMENDATION USING COMBINATORIAL RANKING OF AHP AND MONTE CARLO AHP

ENRICHING PROCESS OF ICE-CREAM RECOMMENDATION USING COMBINATORIAL RANKING OF AHP AND MONTE CARLO AHP 1 AKASH RAMESHWAR LADDHA, 2 RAHUL RAGHVENDRA JOSHI, 3 Dr.PEETI MULAY 1 M.Tech, Department of Computer Scence and Engneerng, Symboss Insttute of Technology, Pune 2,3 Asst. Prof., Department of Computer Scence and Engneerng, Symboss Insttute of Technology, Pune Afflated to Symboss Internatonal Unversty, Pune, Inda E-mal: 1 akash.laddha@stpune.edu.n, 2 rahulj@stpune.edu.n, 3 preet.mulay@stpune.edu.n ABSTRACT Dabetes dsease s the curse to human lfe and t s one of the worst nghtmares of everyone s lfe. The patent needs to keep count on the sugar level each tme when he/she consumes food, sugar free ce-creams are not spared from ths and are favorte dessert of every one. Very less systems exst whch can gude dabetc and non-dabetc persons about the contents of sugar free ce-creams. Many methodologes exst to recommend the ce-creams whch are based on some tradtonal technques lke collaboratve flterng and content recommendatons. But most of the tme ther results are not up to the mark and they may wrongly recommend the ce-cream whch may adversely dsturb blood sugar level of the person. So, proposed methods put forward an dea of recommendng sugar free ce-creams based on ts ngredents lke carbohydrates, fats, protens and detary fbers, whch play a vtal role n affectng blood glucose levels of dabetcs and non-dabetcs. The proposed system uses advanced technques lke Analytc Herarchy Process (AHP) and Monte Carlo AHP (MCAHP) whch can be powered wth Goal programmng and classfcaton process. It s observed that rankngs obtaned from these two technques are same for ce creams under consderaton. Ths paper manly focuses on the technques of AHP and MCAHP for the rankng of consdered sugar free ce-creams. Keywords: Analytc Herarchy Process (AHP), Sugar Free, Ice-creams, Monte Carlo AHP (MCAHP), Rankng etc. 1. INTRODUCTION The frst part of the paper presents how tradtonal AHP can be formulated for rankng and recommendng the sugar free ce-cream or a combnaton of those sugar free products to dabetc as well as non-dabetc persons. In the later part, Monte Carlo AHP s used to apply to same multcrtera problem. Thus, the paper culmnates development and a comparatve study between tradtonal Analytc Herarchy Process (AHP) and Monte Carlo Analytc Herarchy Process (MCAHP). The paper reveals the obtaned results to encourage selecton process n mult-crtera decson problem (MCDP). 2. ANALYTIC HIERARCHY PROCESS (AHP) 2.1 Introducton to Analytc Herarchy Process (AHP) Decsons made usng ntellgence, creatvty and wsdom tend to satsfy the needs and desres. Analytc Herarchy Process (AHP) s one of the modern popular mult-crtera analytcal technques used to get best sutable soluton for the problem or goal under consderaton from avalable alternatves consderng multple mpactful crtera and choces. AHP s used to get out of the complex decsons whch are merely mpossble to overcome usng standard methods [1]. Ths modern method of AHP s developed by Thomas Saaty n order to effcently optmze decson makng from qualtatve, quanttatve, conflctng factors under consderaton. It helps n dervng or selectng the soluton or alternatve that proves to be best to satsfy the desred goal among avalable dfferent 298

alternatves consderng multple crtera (such as costs, rsks nvolved, benefts derved, losses from decson made) [2]. Recently, AHP s used to rank state IT polcy documents n Inda by consderng a partcular perspectve [3]. In AHP, the crtera or factors consdered to affect decson makng have competng prortes and rankngs aganst each other. Thomas Saaty desgned the technque of AHP to evaluate decson made from avalable choces by prortzng the measures (crtera). Characterstcs of Analytc Herarchy Process (AHP) make t effcent to use n solvng multcrtera decson problems. AHP can be effcently used n operaton research, engneerng, desgn for sx sgma (DFSS) stuatons. The research elaborates the novel approach for recommendng the ce-creams to the patents who are sufferng from the dabetes dsease [4]. For detecton of true or false condton.e. whether ce-cream should be recommended to the patent or not, four mportant ngredents are consdered whch are normally observed n the ce-cream vz. sugar, cholesterol, detary fber and proten. For understandng purpose a clear graph s gven by the author who precsely shows the percentage of each of these ngredents n the ce-cream. The expermental evaluaton s done through MATALAB smulaton tool. Another good use of the AHP s n vehcle routng system [5]. Presents a study whch makes use of AHP and fuzzy logc remote gudance system on vehcle. The sad system s also synonym as Dynamc Route Gudance System (DRGS). It observes the traffc pattern and the traffc nformaton to accomplsh the task. The man advantage of the AHP-Fuzzy combnaton s that t greatly clarfes the problem statement of the decson strategy and the multple crterons. The man motto behnd the use of fuzzy s that t effectvely deals wth the uncertanty of the nput data and solves the stuaton. Today s ndustry hghly suffers the problem of project complexty, day by day complexty of project s ncreasng and t hghly requres the sklled person to manage the huge projects [6]. Many systems were proposed to get out of these scenaros. AHP s one of the best technques to solve the gven problem. AHP can be used to get best sutable soluton from a range of alternatves and stuatons that nvolve subjectve judgments, multple decson makng. It also deals effcently wth fnte objectve as well as subjectve attrbutes [7].AHP represents the problem (decson stuaton) along wth ts attrbutes nto herarchy of dstnct levels as level 0, level 1, and level 2 and so on and sub-levels as requred. These levels consst of problem defnton, crtera, and optons avalable. AHP can be vewed to have 4 steps. Frst step clearly defnes the goal or objectve. Second step presents the crtera (factors) that nfluence the decson made. These crtera can be further arranged nto levels and sublevels. Thrd step nvolves makng pared comparsons of all the crtera wth each other. AHP uses weghted matrx algebra to calculate Egen values, Egen vectors, consstency measures.e. consstency ndex (CI), consstency rato (CR). The fourth and last step s to rank the alternatves avalable to reach the fnal choce. AHP s manly based on the use of Saaty scale of relatve mportance. 2.2 SAATY Scale of Relatve Importance Fg 1: Saaty scale for factor rankng Fgure 1 descrbes the dfferent factor rankng based on Saaty scale of relatve mportance. On the bass of respectve mportance of the enttes n AHP and Saaty scale, the measures (crtera) are ranked aganst each other. AHP allows calculatng consstent weghts and evaluatng composte performance score of alternatves to get the rank of consdered alternatves. Rank depends on performance score. Hgher s rank f hgher s the performance. Consder two tems and j. Comparng and j.e. aj would range from values 9(max) to 1/9(0.111). (Item ) 9-8-7-6-5-4-3-2-1-2-3-4-5-6-7-8-9 (Item j ) If tem s strongly mportant than that of j, we have aj =5.e. (1/aj)=aj=1/5=0.2. 2.3 Prorty and Rankng Usng Weghted Comparson Matrces AHP ensures comparsons between all possble pars of crtera usng weghted matrx algebra and 299

constructs comparson matrces. The comparson matrces represent mportance of crtera wth respect to each other. Weghts of crtera are nputs to matrx to calculate Egen values and Egen vectors to compute consstency measures. However, outputs obtaned by matrx operatons may be nconsstent. Consder three tems say A, B and C. Let tem A be preferable and mportant than tem B. whereas, tem B s mportant than tem C. Ths mples that, tem A must be mportant and preferable than tem C, the transtve property. If ths does not hold good, comparsons made are nconsstent. 2.4 Mathematcal Model for AHP C s = (1) mat Where, c s represents sum of elements n each column, mat stands for weghted matrx, s number of rows.. mat d( mat) Cs Where, d( mat ) s dvson matrx, mat, j, j = (2) represents each matrx element. Evector = dj (3) Where, E vector s the matrx of Egen vector, j s column number. E value = s vector (4) Where, ( λmax ) C * E ( ) ( ) E ( value max ) proposed methodology. λ stands for Egen value 2.5 Pseudo Code for AHP The pseudo code for AHP s desgned as n the below fgure 2[8]: Fg 2: Pseudo code for AHP 3. APPLYING AHP FOR SUGAR FREE ICE- CREAMS Ths paper delberates three dfferent sugar free ce-creams vz. Sugar Free Vanlla, Rpple and and four ngredents of sugar free ce-creams as multple crtera. Carbohydrate content of the sugar free cecream s the most mportant and mpactful crtera on person s blood sugar level, whch s followed by fats. Protens and detary fbers present n sugar free ce-creams have very less mpact as compared to carbohydrates and fats. Analytc Herarchy Process s used to get the best sutable sugar free ce-cream or combnaton of sugar free ce-creams, based on nutrtonal nformaton, to recommend for dabetcs and non-dabetcs. Patent s detals are not consdered as crteron, to make analyss of the cecreams easer. The followng table 3.1 lsts out the nutrtonal values of the ce-creams consdered as alternatves. 300

Table 3.1: Crtera And Alternatves For Recommendng Sugar Free Ice-Cream(S) Attrbutes (n mllgrams) Vanlla Rpple Carbohydrates 13 16 15.086 Fats 4 6 4.526 Protens 2 1 3.017 Detary Fbers 4 0 2.011 Accordngly, thrd step s to have pared comparsons of all the crtera wth each other and the ce-cream alternatves. For every weghted matrx, normalzed Prncpal Egen vector (Prorty vector) s computed. For Egen vector, every element n matrx s dvded by sum of all elements n ts column followed by addng resultant elements n rows. From the obtaned results, Prncpal Egen value (λ max ) s computed. Obtaned Egen value s used to get Consstency Index (C.I.). C.I. s used to compute Consstency Rato (C.R.). Herarchcal structure of levels consstng of crtera and alternatves n analytc herarchy process s gven n fgure 3 as below: Table 3.2: AHP For Consdered Sugar Free Ice-Creams (Alternatves) Crtera Preferences Carbohydrate -s Fats Prot ens Detary Fbres Carbohydrates 1 3 7 9 Fats 1/3 1 5 7 Protens 1/7 1/5 1 3 Detary Fbres 1/9 1/7 1/3 1 Vanlla Rpple CI: 0.0549 CR: 0.0617 λ: 4.1648 Table 3.3: AHP For Carbohydrates Vanlla Rpple 1 5 3 1/5 1 ¼ 1/3 4 1 CI: 0.0428 CR: 0.0824 λ: 3.085 Table 3.4: AHP For Fats Vanlla Rpple Fg.3: Herarchcal structure of proposed AHP model Along wth the expert advce, the scale of relatve mportance mentoned n secton 2.2 and by consderng compostons of sugar free ce- creams to be ranked, the followng tables 3.2 to 3.6 represent relatve weghts assgned to crtera and alternatves consdered. Followng are the pared comparsons for each crtera and alternatves for every ndvdual crtera separately. Vanlla Rpple 1 7 3 1/7 1 ¼ 1/3 4 1 Vanlla Rpple CI: 0.0162 CR: 0.0311 λ: 3.0323 Table 3.5: AHP For Protens Vanlla Rpple 1 2 ¼ ½ 1 1/5 4 5 1 CI: 0.0120 CR: 0.0232 λ: 3.0241 301

Vanlla Rpple Table 3.6: AHP For Detary Fbers Vanlla Rpple 1 ½ 3 2 1 3 1/3 1/3 1 CI: 0.0266 CR: 0.0511 λ: 3.0532 4. RESULTS OBTAINED AND ANALYSIS Analytc Herarchy Process model can be effectvely used to recommend the sugar free cecreams to dabetcs as well as non-dabetc persons. AHP ranks the alternatves and crtera (.e. sugar free ce-creams consdered and ther nutrtonal components). On the bass of Saaty scale and weghted matrx computatons, the followng results are obtaned. Fg.5 reveals the mportance of multple crtera consdered n AHP model. It s clear that recommendaton of sugar free ce-creams manly depends on carbohydrates content of the products. Carbs play a vtal role n affectng persons blood sugar level and hence the most mportant crtera. AHP ranked carbohydrates as 58.31 to be most mportant n all crtera, followed by fats wth rank of 28.95, protens to have 8.49 wth detary fbers havng least mpact on persons blood glucose level and hence, AHP method ranked detary fbers to just 4.25. AHP can be used to evaluate the beneft/cost rato so as to decde the benefts of alternatves chosen on the bass of cost. Fg. 6: Benefts-Cost Analyss Fg.6 depcts the beneft-cost analyss obtaned usng AHP for sugar free ce-creams. Fg.4: Rankng Of Alternatves Fg.4 shows the rankngs obtaned from AHP model. Snce, Vanlla has less carb content than others, t s preferred and recommended the most, and hence ts rank s obtaned as 58.72. Ths s followed by sugar free ce-cream wth rank of 30.31.e. the second most recommended sugar free product. Sugar-free Rpple s the hghest to contan carbohydrates and hence AHP ranks t as 10.97 to be least preferred among those sugar free products. Fg5:AHP Rankng Of Crtera 5. MONTE CARLO ANALYTIC HIERARCHY PROCESS 5.1 Introducton to Monte Carlo AHP Tradtonal AHP lacks of usng probablty dstrbuton n rankng the alternatves. Rosenbloom(1997) suggested to use the values for pared comparsons a(j,)=1/a(,j) and a(,)=1 by usng Saaty s scale of mportance, as random varables. Monte Carlo AHP (MCAHP) uses probablty dstrbutons to convert value of every pared comparson a (, j) to a dscrete random varable by replcatng ranges for the gven values for n tmes [9]. Usng tradtonal AHP, one can make judgements and get decsons usng sngle numerc preferences by makng par wse comparsons of all the alternatves and crtera n AHP. The rankngs of alternatves obtaned can t be tested aganst the statstcal sgnfcance and varatons (Paulson & Zahr 1995, Rosenbloom 1996, Scott 2002). To overcome the lmtatons of tradtonal AHP, MCAHP ncorporates probablstc dstrbutons to focus on uncertanty n derved judgements. Thus, MCAHP ncorporates analyss 302

of rankngs. It can effcently deal wth manageral (soft) aspects of mult-dmensonal problems. MCAHP s effectve dealngs wth manageral aspects lead to have:. More clear understandng of the context of problem.. Clear structure of the problem.. Enhanced results. v. Generaton of new nsghts n results obtaned. To fgure out the qualty of the dental servce, research [10] presents an AHP-Monte Carlo AHP (MCAHP) based approach for detectng the qualty of dental servce. Here MCAHP s used for analyzng and prortzng the attrbutes from the huge set of attrbutes. For showng the expermental evaluaton the system s compared wth the real world dental clnc. After comparson t had been observed that the system effectvely fnds the attrbutes havng hgh qualty. Paper [11] also presents the effectve use of Monte Carlo AHP to fnd the assocated samplng methods. 5.2 Flowchart of Monte Carlo AHP 5.3 Mathematcal Model of MCAHP n µ = = 1 ( Ch / F / P / DF) / n (1) Where, µ= mean for carbohydrates, fats, protens and detary fbers, n = number of sugar free ce-creams, Ch = value of carbohydrate content for th sugar free ce-cream, F = value of fat content n th sugar free cecream, P = proten content of th ce-cream, DF = detary fber content n th sugar free cecream. n σ = µ = 1 ( Ch / / / ) 2 F P DF / n (2) Where, σ =standard devaton for carbohydrates, fats, protens, detary fbers. f ( x µ, σ) ( x µ ) 1 2 2 2σ = (3) e σ 2π Where, x = random possble value of the nutrton factors n between ther respectve mnmum and maxmum lmts. 6. APPLYING MONTE CARLO AHP FOR SUGAR FREE ICE-CREAMS Selectng a sngle nutrtonal factor at any gven nstance and then arrange them n ascendng order. Then, for every sugar free ce-cream two ranges have been set wthn past and current values. Startng from zero and ends at last ce-cream that s sorted n ascendng order. The weght of ther respectve possbltes s beng dentfed and counted and then based on ths weght, the fnal sugar free products are ranked. 7. RESULTS OBTAINED Table 7.1: Results of AHP and MCAHP Fg 6: Flow Chart Depctng Steps In Monte Carlo AHP For N Number Of Iteratons 303

Table 7.1 represents rankng of consdered sugar free ce- creams and they are ranked on the bass of ther weghts obtaned for methodologes under consderaton. The ce- cream that has more prorty s ranked hgher followed by those that are havng less prortes. The above table depcts the fact that both AHP and Monte Carlo AHP yeld the same result for dfferent ce-creams. AHP uses the beneft cost as the major constrant to measure the rankng of the ce-creams. On the other hand Monte Carlo AHP uses the probablty weghts to measure the rankng. Above obtaned results clearly ndcate that the rankng parameters of tradtonal AHP are havng a mnute dfference whch eventually makes tough to take decsons about rankng. Whereas, Monte Carlo AHP rankng parameters are clear and dstnct whch help us to take better rankng decsons for the sugar free ce-creams. 8. CONCLUSION The proposed method of recommendaton for ce-creams to the dabetc patents clearly provdes best result due to successful ncorporaton of the AHP for the gven crterons. Whereas the proposed system generates dstrbuton of the ngredent values s been calculated successful random probabltes through whch normal usng Gaussan functon. Due to usage of the combnatoral values of the both AHP and Monte Carlo AHP systems, t leads to decrease n the possbltes of the mproper recommendaton to ts low level and ncrease the better chances to the recommendaton seekers. REFRENCES: [1] Dpt, Sengar. "Mantanablty Estmaton of Component Based Software Development Usng Fuzzy AHP." Internatonal Journal of Emergng Trends n Scence and Technology 1.03 (2014). [2] de Acedo Lzarraga, ML Sanz, MT Sanz de Acedo Baquedano, and María Cardelle-Elawar. "Factors that affect decson makng: gender and age dfferences." Internatonal Journal of Psychology and Psychologcal Therapy7.3 (2007): 381-391. [3] Josh, Rahul Raghvendra, et al. "PBR: Perspectve Based Rankng of Selected State IT Polcy Documents n Inda usng AHP." Internatonal Journal of Appled Engneerng Research 10.20 (2015): 41353-41356. [4] Gakwad, Suhas Machhndra, Preet Mulay, and Rahul Raghvendra Josh. "Analytcal Herarchy Process to Recommend an Ice-cream to a Dabetc Patent Based on Sugar Content n t." Proceda Computer Scence 50 (2015): 64-72. [5] L, Caxa, Sreenatha G. Anavatt, and Tapabrata Ray. "Analytcal herarchy process usng fuzzy nference technque for real-tme route gudance system." Intellgent Transportaton Systems, IEEE Transactons on 15.1 (2014): 84-93. [6] Vdal, Ludovc-Alexandre, Franck Marle, and Jean-Claude Bocquet. "Usng a Delph process and the Analytc Herarchy Process (AHP) to evaluate the complexty of projects." Expert systems wth applcatons 38.5 (2011): 5388-5405. [7] Ghamgosar, M., et al. "Multcrtera decson makng based on analytcal herarchy process (AHP) n GIS for toursm." Mddle-East Journal of Scentfc Research 10.4 (2011): 501-507. [8] Alexander, Melvn. "Decson-Makng usng the Analytc Herarchy Process (AHP) and SAS/IML'." Avalable from (Last checked 28th July 2014) (2012). [9] Moman, Amer M., and Abdulazz A. Ahmed. "Materal handlng equpment selecton usng hybrd Monte Carlo smulaton and analytc herarchy process." World Academy of Scence, Engneerng and Technology 59 (2011): 953-958. [10] Hsu, Tsuen-Ho, and Frank FC Pan. "Applcaton of Monte Carlo AHP n rankng dental qualty attrbutes." Expert Systems wth Applcatons 36.2 (2009): 2310-2316. [11] Hastngs, W. Keth. "Monte Carlo samplng methods usng Markov chans and ther applcatons." Bometrka 57.1 (1970): 97-109. 304