In this paper, two topological operators T and U over intuitionistic fuzzy sets are considered and applied. As a case study a parameter identification problem of E. coli fed-batch cultivation process model using genetic algorithms is investigated. A new result regarding T and U is established. The results obtained by the application of the topological operators over data processed by InterCriteria Analysis are discussed

Chountas, P.

Roeva, O.

Vassilev, P.

WestminsterResearch

WestminsterResearchhttp://www.westminster.ac.uk/westminsterresearch Application of Topological Operators over Data from InterCriteria AnalysisRoeva, O., Vassilev, P. and Chountas, P. This is an author's accepted manuscript of an article published in Christiansen H., Jaudoin H., Chountas P., Andreasen T., Legind Larsen H. (eds) Flexible Query Answering Systems. FQAS 2017. Lecture Notes in Computer Science, vol 10333. Springer, Cham.The final publication is available at Springer via:https://dx.doi.org/10.1007/978-3-319-59692-1_19The WestminsterResearch online digital archive at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners.Whilst further distribution of specific materials from within this archive is forbidden, you may freely distribute the URL of WestminsterResearch: ((http://westminsterresearch.wmin.ac.uk/).In case of abuse or copyright appearing without permission e-mail repository@westminster.ac.ukGeneralized Net Modelof Muscle Pain DiagnosingSimeon Ribagin1, Panagiotis Chountas2, Tania Pencheva11Institute of Biophysics and Biomedical Engineering,Bulgarian Academy of Sciences, Sofia, Bulgariasim ribagin@mail.bg, tania.pencheva@biomed.bas.bg2University of Westminster, Faculty of Science and Technology,FST, Dept. of Computer Science, London, UKP.I.Chountas@westminster.ac.ukAbstract. Pain is the most common symptom of the many muscu-loskeletal pathologies. Musculoskeletal pain affects the muscles, liga-ments, tendons, nerves and bones and might be caused by diverse factors.Musculoskeletal pain ranges from mild to severe. It can be local or dif-fuse, and acute or chronic. Due to the wide range of conditions that maycause such a symptom, diagnosing process is challenging and a systematicapproach is necessary. In this investigation we present a successful ex-ample of generalized nets application in medical diagnosing and proposea novel approach leading to the appropriate diagnostic considerations.The method proposed in this investigation accurately identifies the var-ious steps during the muscle pain diagnosing process and significantlyimproves the health care level. Obtained so far results could be used toassist in the decision making in the diagnostic processes.Keywords: Musculoskeletel Pain, Generalized Nets1 IntroductionThe diagnosis of musculoskeletal pain is made on the basis of the medical history,clinical examinations, diagnostic imaging techniques and simple laboratory in-vestigations. The basic issue associated with muscle pain diagnosing is to find theearly pointers to a likely diagnosis. Then as part of the assessment, it is essentialto establish a logical step-by-step approach to the medical history as well as aseries of screening investigations. Muscle pain may arise due to injury or overex-ertion, infections, inflammatory or systemic conditions. A number of conditionscan be associated with muscle pain, such as viral infections, fibromyalgia, auto-immune disorders, drug-induced disorders, metabolic disorders, etc. The purposeof the present study is to give an example how the apparatus of generalized netsmight be successfully applied to medical diagnosing and as such to be proposedas a novel mathematical approach for diagnosing the causes of the muscle pain.Generalized nets (GNs) (see [1], [2]) are an apparatus for modeling of paralleland concurrent processes, developed as an extension of the concept of Petri nets2 S. Ribagin, P. Chountas, T. Penchevaand some of their modifications. In general, the GNs may or may not have someof the components in their definition. GNs without some of their componentsform special classes called reduced GNs [2]. The presented GN-model shows sim-ilar features with previous models for medical diagnosing [3–5] but this is thefirst one highlighting the diagnostic algorithm for patients with muscle pain.2 Generalized Net Model of Muscle Pain DiagnosingA reduced GN-model which represents the plan for muscle pain diagnosing isdeveloped here. The proposed GN-model is shown in Fig. 1.Z1?l1gl3gl2g-----Z2?l4gl5g-- --Z3?---l9- g-gl6gl7l8g -Z4?----l10l11l12l13gggg--Z5?-l14g -Z6?----l15l16l17l18l19gggg- g-----Z7?-l20g-Figure 1. GN-model of muscle pain diagnosingThe GN-model has 7 transitions and 20 places with the following meanings:• Z1 represents the personal data of the patient;• Z2 – the current localization of the symptoms;• Z3 – the results from the medical history;• Z4 – the results from the physical examination;• Z5 – the set of laboratory tests;• Z6 – the results from the laboratory tests and possible diagnosis;• Z7 – the final diagnosis.The GN-model contains 5 types of tokens: α, β, µ, ν and pi. Some of themodel transitions contain the so called “special place” where a token stays andcollects information about the specific parts of the diagnosing process which arerepresented as follows:GN Model of Muscle Pain Diagnosing 3• place l3 collects the overall information obtained from the diagnostics stepsin the personal record (personal data);• place l9 – information obtained from the history of the patient;• place l13 – information about the results from physical examinations;• place l19 – information about the results from the laboratory tests.During the GM-model functioning, the α-tokens will unite with the tokensfrom the other types: β, µ, ν and pi. After that, some of these tokens can split inorder to generate new α-tokens obtaining corresponding characteristics. Whenthere are some α-tokens (α1, α2, α3 and, eventually, α4), on the next time-moment all they will unite with a token from another type.The token α enters the net in place l1 with an initial characteristic:“patient with muscle pain”.The transition Z1 has the following form:Z1 = 〈{l1, l3, l20}, {l2, l3}, r1〉wherer1 =l2 l3l1 false truel3 W3,2 truel20 false true• W3,2 = “information about the current symptoms, medical history and phys-ical examination is necessary”.The tokens from the three input places of transition Z1 enter place l3 andunite with token β with the above mentioned characteristic. On the next time-moment, token β splits to two tokens – the same token β and token α1. Whenpredicate W3,2 is true, the token α1 enters place l2 and there it obtains a char-acteristic:“obtain information about the current symptoms, medical history and physicalexamination”.The transition Z2 has the following form:Z2 = 〈{l2}, {l4, l5}, r2〉wherer2 =l4 l5l2 W2,4 W2,5and4 S. Ribagin, P. Chountas, T. Pencheva• W2,4 = “the muscle pain is local”;• W2,5 = “the muscle pain is diffuse with no history of trauma, overuse andstress”.When the predicate W2,4 is true, token α1 enters place l4 and there it obtainsa characteristic:“obtain information from the medical hystory of the patient”.When the predicate W2,5 is true, token α1 enters place l5 and there it obtains acharacteristic:“perform physical examination”.The transition Z3 has the following form:Z3 = 〈{l4, l9}, {l6, l7, l8, l9}, r3〉wherer3 =l6 l7 l8 l9l4 false false false truel9 W9,6 W9,7 W9,8 trueand• W9,6 = “there is a history of trauma”;• W9,7 = “there is a history of recent overexertion and stress ”;• W9,8 = ¬W9,6∨¬W9,7.The tokens from all input places of transition Z3 enter place l9 and unite withtoken µ with the characteristic as mentioned above. On the next time-moment,token µ splits to two tokens – the same token µ that stays permanently in theplace l9, and token α1. When the predicate W9,6 is true, token α1 enters placel6 and there it obtains a characteristic:“consider: muscle contusion, muscle strain, muscle rupture, ligament sprain;send patient to X-ray and/or MRI to determine the extent of the injury or toidentify possible additional injuries”.When the predicate W9,7 is true, token α1 enters place l7 and there it obtains acharacteristic:“consider: muscle cramps or delayed onset muscle soreness”.When the predicate W9,8 is true, token α1 enters place l8 and there it obtains acharacteristic:“perform physical examination”.GN Model of Muscle Pain Diagnosing 5The transition Z4 has the following form:Z4 = 〈{l5, l8, l13}, {l10, l11, l12, l13}, r4〉wherer4 =l10 l11 l12 l13l5 false false false truel8 false false false truel13 W13,10 W13,11 W13,12 trueand• W13,10 = “there is muscle weakness without loss of muscle mass”;• W13,11 = “there is muscle weakness and loss of muscle mass”;• W13,12 = ¬W13,10.The tokens from all input places of transition Z4 enter place l13 and unitewith token ν with the characteristic as mentioned above. On the next time-moment, token ν splits to two tokens – the same token ν that stays permanentlyin the place l12, and token α1. When the predicate W13,10 is true, token α1 entersplace l10 and there it obtains a characteristic:“perform a laboratory tests to rule in potential pathologies associated withmuscle pain and weakness”.When the predicate W13,11 is true, token α1 enters place l11 and there it obtainsa characteristic:“consider: muscular dystrophy; perform: muscle biopsy, aldolase test, creatinephosphokinase test”.When the predicate W13,12 is true, token α1 enters place l12 and there it obtainsa characteristic:“consider: fibromyalgia, psyhological disorders, spinal disorders, endocrinedisorders, polymyalgia rheumatica”.The transition Z5 has the following form:Z5 = 〈{l10}, {l14}, r5〉wherer5 =l14l10 trueThe token from place l10 of transition Z5 enter place l13 and there it obtainsa characteristic:“perform: erythrocyte sedimentation rate (ESR) test, serum alkalinephosphatase (SAP) test, creatine phosphokinase (CPT) test”.6 S. Ribagin, P. Chountas, T. PenchevaThe transition Z6 has the following form:Z6 = 〈{l14, l19}, {l15, l16, l17, l18, l19}, r6〉wherer6 =l15 l16 l17 l18 l19l14 false false false fals truel19 W19,15 W19,16 W19,17 W19,18 trueand• W19,15 = “erythrocyte sedimentation rate (ESR) is high”;• W19,16 = “serum alkaline phosphatase (SAP) is high”;• W19,17 = “creatine phosphokinase (CPT) is high”;• W19,18 = ¬W19,15∨¬W19,16.The tokens from all input places of transition Z6 enter place l19 and unite withtoken pi with the characteristic as mentioned above. On the next time-moment,token pi splits to two tokens – the same token pi that stays permanently in theplace l19, and token α1. When the predicate W19,15 is true, token α1 enters placel15 and there it obtains a characteristic:“consider: polymyalgia rheumatica, systemic lupus erythematosus, myositis orsecondary carcinomatosis”.When the predicate W19,16 is true, token α2 enters place l16 and there it obtainsa characteristic:“consider: liver diseases, osteoporosis, osteomalacia, viral infections, Pagetsdisease and hyperparathyroidism”.When the predicate W19,17 is true, token α3 enters place l17 and there it obtainsa characteristic:“consider: drug-induced disorders, inflammatory myopathies”.When the predicate W19,18 is true, token α4 enters place l18 and there it obtainsa characteristic:“consider: hypothyroidism, fibromyalgia, psyhogenic causes, myofascial painsyndrome”.The transition Z7 has the following form:Z7 = 〈{l15, l16, l17, l18}, {l20}, r7〉whereGN Model of Muscle Pain Diagnosing 7r7 =l20l15 truel16 truel17 truel18 trueThe tokens from the input places of transition Z7 enter place l20 and unite inone token β1 with some of the characteristics obtained from the previous time-step. The token β1 returns to transition Z1 and enters to place l3 to extend thepersonal record of the current patient.3 ConclusionsThe so described GN-model may provide a framework that can be used by pri-mary care practitioners to guide diagnostic processes for patients with musclepain, enabling more accurate and efficient identification of conditions that maylead to pain in the muscles and would assist in optimizing patient outcomes andmore effective treatment. The presented in this paper GN-model of diagnosticalgorithm for patient with muscle pain is a part of a series of studies for diag-nosing through GN-modeling assistance and can be improved in multiple waysto yield better results. This model significantly improves the accuracy of theprimary diagnosis and the reliability of the proposed algorithm.AcknowledgementsWork presented here is partially supported by the Grants: DFNP-142/2016 “Pro-gram for career development of young scientists, BAS” and DN02/10 “New In-struments for Knowledge Discovery from Data, and Their Modelling”References[1] Atanassov, K.,: Generalized Nets. World Scientific, Singapore (1991)[2] Atanassov, K.,: On Generalized Nets Theory. Prof. M. Drinov Academic PublishingHouse, Sofia (2007)[3] Ribagin, S., Atanassov, K., Shannon, A.: Generalized Net Model of Shoulder PainDiagnosis. Issues in Intuitionistic Fuzzy Sets and Generalized Nets 11, 55-62 (2014)[4] Ribagin, S., Roeva, O., Pencheva, T.: Generalized Net Model of AsymptomaticOsteoporosis Diagnosing. Proc. of 2016 IEEE 8th International Conference on In-telligent Systems (IS), Sofia, 604-608 (2016)[5] Shannon, A., Sorsich, J., Atanassov, K., Nikolov, N., Georgiev, P.: Generalized Netsin General and Internal Medicine, Vol. 1, Prof. M. Drinov Academic PublishingHouse, Sofia (1998)

Application of Topological Operators over Data from InterCriteria Analysis

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Application of Topological Operators over Data from InterCriteria Analysis

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