Generalized Net Model of the Process of European Awareness Scenario Workshop Method with Intuitionistic Fuzzy Estimation

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1 Fifth Internationa Workshop on IFs Banska Bystrica ovakia 19 Oct. 29 NIF 15 (29) Generaized Net Mode of the Process of European Awareness cenario Workshop Method with Intuitionistic Fuzzy Estimation otir otirov 1 Evdokia otirova 12 Yanisav Zheev 3 Maria Zheeva 3 1 Prof. Asen Zatarov University Bourgas-81 Bugaria e-mais: esotirova@btu.bg ssotirov@btu.bg 2 Centre of Biomedica Engineering Bugarian Academy of ciences Acad. G. Bonchev tr. B. 15 ofia-1113 Bugaria 3 Bourgas Free University Bourgas-81 Bugaria e-mais: jeev@bfu.bg mariaj@bfu.bg Abstract The present paper describes the process of the European Awareness cenario Workshop Method. For the purpose we use Generaized Nets. The opportunity of using GNs as a too for modeing such process is anayzed as we. The mode uses intuitionistic fuzzy sets for determine estimation for a creation of the masterpan. Keywords Generaized nets Modeing European Awareness cenario Workshop Method. 1 Introduction In a preview paper [5] we present a generaized net mode of the European Awareness cenario Workshop Method [4]. Now we use intuitionistic fuzzy sets for determine estimation for a creation of the masterpan. Intuitionistic Fuzzy ets (IFs) [1] are defined as etensions of ordinary fuzzy sets. A resuts which are vaid for fuzzy sets can be transformed here too. Aso a research for which the apparatus of fuzzy sets can be used can be used to describe the detais of IFs. On the other hand there have been defined over IFs not ony operations simiar to those of ordinary fuzzy sets but aso operators that cannot be defined in the case of ordinary fuzzy sets. Let a set E be fied. An IF A in E is an object of the foowing form: A = {< µ A () ν A ()> E} where functions µ A : E [ 1] and ν A : E [ 1] define the degree of membership and the degree of non-membership of the eement E respectivey and for every E: 4

2 µ A () + ν A () 1 For every E et π A () = 1 - µ A () - ν A (). Therefore the function π determines the degree of uncertainty. Obviousy for every ordinary fuzzy set π A () = for each E these sets have the form: {< µ A () 1-µ A ()> E}. In the contet of the present mode we incude some possibiities for the possibe ways for evauation of the European Awareness cenario Workshop Method (EAWM). To do this we can appy estimations of the IF on the basis of which some amendments may be undertaken. The estimations are represented by ordered pairs <µ ν> of rea numbers from the set [1] µ = 1 1 number of the peope who vote positive on current voting. number of the a peope who can vote on current voting (usuay the number is 4); ν = 2 where 2 number of the peope who vote negative on current voting. The degree of uncertainty π = 1- µ - ν refects the number of peopes who abstain from voting. 2 A GN-mode The GN-mode (see Fig. 1) is the reduced one from the mode from [5]. It contains 5 transitions and 23 paces. There are transitions that forming intuitionistic fuzzy sets for determine estimation for a creation of the masterpan (from Z 3 to Z 7 ). Initiay the foowing tokens enter in the GN: in pace token with characteristic: 11 = Group 1 The ist of the key words ; in pace token with characteristic: 12 = Group 2 The ist of the key words ; in pace token with characteristic: 13 = Group 3 The ist of the key words ; in pace token with characteristic: 14 = Group 4 The ist of the key words ; in pace thr - β thr -token with characteristic µ thr - threshod vaue for µ; ν thr - threshod vaue for ν. β thr = µ thr ν thr ; 41

3 Aso initiay when no suggestions has been eisting in paces and 29 a estimations take on initia vaues of <>. The generaized net [2 3] contains the foowing set of transitions А= {Z 3 Z 4 Z 5 Z 6 Z 7 } where the foowing transitions represent: Z 3 The work of the group 1; Z 4 The work of the group 2; Z 5 The work of the group 3; Z 6 The work of the group 4; Z 7 Creation of the Masterpan. 11 Z 3 16 Z Z thr E 13 9 Z Z 6 25 E Figure 1: GN mode of process of the EAWM with intuitionistic fuzzy estimation The forms of the transitions are the foowing. Z 3 = <{ } { } r 3 ( )> r 3 = Fase Fase Fase Fase W W W = The suggestions from group 1 are specified or a token from pace 31 is arrived 1816 W 1817 = W

4 The 11 token from paces 11 that enter pace 18 do not obtain new characteristic. It generates two β-tokens (β 16 and β 17 ) with characteristic uggestion 11 <µ 11 ν 11 >; uggestion 12 <µ 12 ν 12 >; ; uggestion 1n <µ 1 n ν 1 n >;. for the n-suggestions. Z 4 = <{ } { } r 4 ( )> r 4 = 32 W W W = The suggestions from group 2 are specified or a token from pace 32 is arrived 2119 W 212 = W The 12 token from paces 12 that enter pace 21 do not obtain new characteristic. It generates two β-tokens (β 19 and β 2 ) with characteristic uggestion 21 <µ 21 ν 21 >; uggestion 22 <µ 22 ν 22 >; ; uggestion 2n <µ 2 n ν 2 n > 212 Z 5 = <{ } { } r 5 ( )> r 5 = 33 W W W = The suggestions from group 3 are specified or a token from pace 34 is arrived 2422 W 2423= W The 13 token from paces 13 that enter pace 24 do not obtain new characteristic. It generates two β-tokens (β 22 and β 23 ) with characteristic uggestion 31 <µ 31 ν 31 >; uggestion 32 <µ 32 ν 32 >; ; uggestion 3n <µ 3 n ν 3 n > 2423 Z 6 = <{ } { } r 6 ( )> r 6 = 34 W W W = The suggestions from group 4 are specified or a token from pace 34 is arrived 2725 W 2726 = W The 14 token from paces 14 that enter pace 27 do not obtain new characteristic. It generates two β-tokens (β 25 and β 26 ) with characteristic uggestion 41 <µ 41 ν 41 >; uggestion 42 <µ 42 ν 42 >; ; uggestion 4n <µ 4 n ν 4 n >

5 Z 7 = <{ } { } r 7 ( )> r 7 = W2928 W 2928 = The suggestions from four groups are created. The β tokens from paces and 25 that enter pace 29 generate β-token that enters pace 28 with characteristic E ( 1 2 n-1 n ) i i-th suggestion i = 1 n Е function that sorts the suggestions in descending order by the degree of the acceptance of the suggestion i µ i and µ i µ thr and ν i ν thr. 3 Concusion The GN-mode constructed in this way is the net in a series of research eercises which the authors are currenty preparing. It can be used for simuation of the work of the European Awareness cenario Workshop Method. The echanged information can be evauated by means of intuitionistic fuzzy estimations. The mode use intuitionistic fuzzy sets for determine estimation for a creation of the masterpan. References [1] Atanassov K. Intuitionistic Fuzzy ets pringer Physica-Verag Berin [2] Atanassov K. Generaized nets Word cientific ingapore New Jersey London [3] Atanassov K. On Generaized Nets Theory Prof. M. Drinov Academic Pubishing House ofia 27. [4] Carsson Eine Europäische zenariowerkstattsmethode für partizipatives Panen und Bewußtseinsbidung. Monitorenausbidung in Wien 28 und 29 November IRC- BIT in Zusammenarbeit mit Hippopotamos Bidungsberatung. Broschüre. [5] Y. Zheev M. Zheeva E. otirova. otirov Generaized net mode of process of the European Awareness cenario Workshop Method Issues in Intuitionistic Fuzzy ets and Generaized Nets Warszaw