neutrosophic logic for mental model elicitation and analysis

Neutrosophic Sets and Systems, Vol. 2, 2014 31 31 Neutrosophic Logic for Mental Model Elicitation and Analysis Karina Prez-Teruel1, Maikel Leyva-Vzquez2 1Universidad de las Ciencias Informticas, La Habana, Cuba. E-mail: karinapt@uci.cu 2Universidad de las Ciencias Informticas, La Habana, Cuba. E-mail: mleyvaz@uci.cu Abstract.Mentalmodelsarepersonal,internalrepresentations ofexternalrealitythatpeopleusetointeractwiththeworld aroundthem.Theyareusefulinmultiplesituationssuchas muticriteriadecisionmaking,knowledgemanagement,complex systemlearningandanalysis.Inthispaperaframeworkfor mentalmodelselicitationandanalysisbasedon neutrosophicLogicispresented.Anillustrative exampleisprovidedtoshowtheapplicabilityofthe proposal.Thepaperendswithconclusionfuture research directions.Keywords: mental model, neutrosophic Logic, neutrosophic cognitive maps, static analysis. 1 Introduction Mentalmodelsareusefulinmultiplesituationssuchas muticriteria decision making [1], knowledge management, complexsystemlearningandanalysis[2].Inthispaper, weproposetheuseofaninnovativetechniquefor processinguncertaintyandindeterminacyinmental models. Theoutlineofthispaperisasfollows:Section2is dedicatedtomentalmodelsandneutrosophiclogicand neutrosophiccognitivemaps.Theproposedframeworkis presented in Section 3. An illustrative example is discussed inSection4.Thepapercloseswithconcludingremarks, and discussion of future work in Section 5.2 Mental Models and neutrosophic Logic Mentalmodelsarepersonal,internalrepresentationsof externalrealitythatpeopleusetointeractwiththeworld around them [3]. The development of more effective end-usermentalmodellingtoolsisanactiveareaofresearch [4]. Acognitivemapisformofstructuredknowledge representationintroducedbyAxelrod[5].Mentalmodels have been studied using cognitive mapping [6].Anotherapproachisbasedinfuzzycognitivemaps[7]. FCMutilizesfuzzylogicinthecreationofadirected cognitive map.FCM are a further extension of Axelrods definition of cognitive maps [7] . Neutrosophic logic is a generalization of fuzzy logic based onneutrosophy[8].Ifindeterminacyisintroducedin cognitivemappingitiscalledNeutrosophicCognitive Map (NCM) [9].NCMarebasedonneutrosophiclogictorepresent uncertaintyandindeterminacyincognitivemaps[8].A NCMis a directed graphin which atleast one edgeis an indeterminacy denoted by dotted lines [6]. 3 Proposed Framework The following steps will be used to establish a frameworkformentalmodelelicitationand analysis with NCM (Fig. 1). Figure 1: Mental model. Mental model development. ThisActivitybeginswithdetermination of nodes. Finally causal relationships, its weights and signs are elicited [10]. Mental model analysis Staticanalysisisdeveloptodefinethe importanceofeachnodebasedonthe degreecentralitymeasure[11].Ade-neutrosophicationprocessgivesan intervalnumberforcentrality.Finally the nodes are ordered. Mental model develoment Nodes determination Causal relationships determination. Weights and signs determination. Mental Model analysis Degree centrality determination De-neutrosophication process Karina Prez-Teruel, Maikel Leyva-Vzquez, Neutrosophic Logic for Mental Model Elicitation and Analysis 32Neutrosophic Sets and Systems, Vol. 2, 2014 32 4 Illustrative example In this section, we present an illustrative example in order toshowtheapplicabilityoftheproposedmodel.We selectedagroupofconceptsrelatedtopeoplefactorin agile software develoment projects sucess (Table 1) [12]. Table I. FCM nodes NodeDescription ACompetence and expertise of team members BMotivation of tem members CManagers knowledge of agile development DTeam trainingECustomerrelationship FCustomer commitment and presence The FCM is developed integrating knowledge from one expert. The FCM with weighs is represented in Fig. 4.ABD0.25CEF0.750.750.75 Figure 2: Mental model. Theneutrosophicscoreofeachnodebasedonthe centrality measure is as follows: A 1.75 B 0.75+I C 0.25+I D 0.75 E 0.75 F 0.75+2I Thenext stepis the de-neutrosophication process asproposesbySalmeronandSmarandache[13].I[0,1]isrepalacedbybothmaximumand minimum values. A1.75 B[0.75,1.75] C[0.25,1.25] D0.75 E0.75 F[0.75,2.75] Finallyweworkwithextremevalues[14]for giving a total order: Competenceandexpertiseofteammembers, Customer commitment and presence are the more important factors in his mental model.5 Conclusions Inthispaper,weproposeanewframeworkfor processinguncertaintyandindeterminacyin mentalmodels.Futureresearchwillfocuson conductingfurtherreallifeexperimentsandthe developmentofatooltoautomatetheprocess. 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Karina Prez-Teruel, Maikel Leyva-Vzquez, Neutrosophic Logic for Mental Model Elicitation and Analysis Neutrosophic Sets and Systems, Vol. 2, 2014 33 33 5.Axelrod,R.M.,I.o.p.p.studies,andI.o.i.studies, Structureofdecision:Thecognitivemapsofpolitical elites.Vol.1.1976:Princetonuniversitypress Princeton. 6.Salmeron,J.L.andF.Smarandache,Processing Uncertainty and Indeterminacy in Information Systems projects success mapping, in Computational Modeling inAppliedProblems:collectedpaperson econometrics,operationsresearch,gametheoryand simulation. 2006, Hexis. p. 94. 7.Gray, S., E. Zanre, and S. 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Received: December 23th, 2013. Accepted: January 5th, 2014 Karina Prez-Teruel, Maikel Leyva-Vzquez, Neutrosophic Logic for Mental Model Elicitation and Analysis