A modelforalarge network of"neurons" withagraded response (orsigmoid input-output relation) is studied. Thisdeterministic system hascollective properties in veryclose correspondence withtheearlier stochastic model based onMcCulloch-Pitts neurons. Thecontent-addressable memoryandother emergent collective properties oftheorigi- nalmodelalso arepresent inthegraded response model. The idea that suchcollective properties areusedinbiological sys- temsisgiven addedcredence bythecontinued presence ofsuch properties formorenearly biological "neurons." Collective analog electrical circuits ofthekinddescribed will certainly function. Thecollective states ofthetwomodels haveasimple correspondence. Theoriginal modelwill continue tobeuseful forsimulations, because its connection tograded response sys- temsisestablished. Equations that include theeffect ofaction potentials inthegraded response system arealsodeveloped. Recent papers (1-3) haveexplored theability ofasystem of highly interconnected "neurons" tohaveuseful collective computational properties. Theseproperties emergesponta- neously inasystem having alarge numberofelementary "neurons." Content-addressable memory(CAM)isoneof thesimplest collective properties ofsucha system. The mathematical modeling hasbeenbasedon"neurons" that aredifferent bothfromreal biological neurons andfromthe realistic functioning ofsimple electronic circuits. Someof these differences aremajor enough thatneurobiologists and circuit engineers alike havequestioned whether real neural orelectrical circuits wouldactually exhibit thekindofbe- haviors foundinthemodelsystem evenifthe"neurons" wereconnected inthefashion envisioned. Twomajor divergences between themodelandbiological orphysical systems stand out.Realneurons (andreal physi- caldevices suchasoperational amplifiers that might mimic them) havecontinuous input-output relations. (Action po- tentials areomitted until Discussion.) Theoriginal modeling usedtwo-state McCulloch-Pitts (4)threshold devices having outputs of0or1only. Realneurons andreal physical circuits haveintegrative timedelays duetocapacitance, andthetime evolution ofthestate ofsuchsystems should berepresented byadifferential equation (perhaps withaddednoise). The original modeling usedastochastic algorithm involving sud- den0-1or1-0changes ofstates ofneurons atrandom times. Thispaper showsthat theimportant properties oftheorigi- nalmodelremain intact whenthese twosimplifications of themodeling areeliminated. Although itisuncertain wheth- ertheproperties ofthese newcontinuous "neurons" areyet close enough totheessential properties ofrealneurons (and/or their dendritic arborization) tobedirectly applicable toneurobiology, amajor conceptual obstacle hasbeenelimi- nated. Itiscertain that aCAM constructed onthebasic ideas

Neurons withgraded response havecollective computational properties likethoseoftwo-state neurons

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and [0,1](2)-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m-polar fuzzy set (actually, [0,1] (m)-set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets. We also give examples to show how to apply m-polar fuzzy sets in real world problems.

/pdf/m-polar-fuzzy-sets-an-extension-of-bipolar-fuzzy-sets-5dbik37z3l.pdf

m-Polar fuzzy sets: an extension of bipolar fuzzy sets.

Personalized healthcare systems deliver e-health services to fulfill the medical and assistive needs of the aging population Internet of Things (IoT) is a significant advancement in the Big Data era, which supports many real-time engineering applications through enhanced services Analytics over data streams from IoT has become a source of user data for the healthcare systems to discover new information, predict early detection, and makes decision over the critical situation for the improvement of the quality of life In this paper, we have made a detailed study on the recent emerging technologies in the personalized healthcare systems with the focus towards cloud computing, fog computing, Big Data analytics, IoT and mobile based applications We have analyzed the challenges in designing a better healthcare system to make early detection and diagnosis of diseases and discussed the possible solutions while providing e-health services in secure manner This paper poses a light on the rapidly growing needs of the better healthcare systems in real-time and provides possible future work guidelines

/pdf/a-study-on-medical-internet-of-things-and-big-data-in-wuxmd5bwgx.pdf

A study on medical Internet of Things and Big Data in personalized healthcare system

In this paper, we have investigated the multiple attribute decision-making problems with bipolar fuzzy information. Motivated by the Hamacher operations, we have proposed bipolar fuzzy Hamacher weighted average operator, bipolar fuzzy Hamacher ordered weighted average operator, bipolar fuzzy Hamacher hybrid average operator, bipolar fuzzy Hamacher weighted geometric operator, bipolar fuzzy Hamacher ordered weighted geometric operator, bipolar fuzzy Hamacher hybrid geometric operator. We investigate the characteristics and special cases of these operators. Then, we have utilized these operators to develop some approaches to solve the bipolar fuzzy multiple attribute decision-making problems. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Bipolar Fuzzy Hamacher Aggregation Operators in Multiple Attribute Decision Making

Guiwu Weia,b, Mao Lua, Fuad E. Alsaadib, Tasawar Hayatc,d and Ahmed Alsaedid aSchool of Business, Sichuan Normal University, Chengdu, P.R. China bCommunications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia cDepartment of Mathematics, Quaid-I-Azam University 45320, Islamabad, Pakistan dNonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

Pythagorean 2-tuple linguistic aggregation operators in multiple attribute decision making

Social networks are absolutely a useful and important place for connecting people within the world. A basic issue in a social network is to identify the key persons within it. This is why different centrality measures have been found over the years. In this survey paper, we present past and present research works on measures of centrality in social network. For this plan, we discuss mathematical definitions and different developed centrality measures. We also present some applications of centrality measures in biology, research, security, traffic, transportation, drug, class room. At last, our future research work on centrality measure is given.

Study on centrality measures in social networks: a survey

Fuzzy k -competition graphs and p -competition fuzzy graphs

Recently, bipolar fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, at first we define three new operations on bipolar fuzzy graphs, viz. direct product, semi strong product and strong product. Likewise, sufficient conditions for each one of them to be complete are given. Also, it is proved that any of the products of strong bipolar fuzzy graphs are strong bipolar fuzzy graphs.

A study on bipolar fuzzy graphs

Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges. In addition, a comparative study between Kuratowski's graphs and fuzzy planar graph is made. A new concept of a strong fuzzy planar graph is introduced. Some related results are established. These results have certain applications in subway tunnels, routes, oil/gas pipelines representation, etc. It is also shown that an image can be represented by a fuzzy planar graph, and contraction of such an image can be made with the help of a fuzzy planar graph.

Fuzzy Planar Graphs

Presently, fuzzy graph theory has wide applications in engineering and social networks. Based on the applications, different types of fuzzy graphs are defined. Among them the competition graph is significantly used to model ecological problems. This graph is one kind of intersection graph. Different competitions of real world have been designed by fuzzy competition graphs. One generalization of fuzzy competition graph, called $$m$$
 -step fuzzy competition graph, is defined in this paper. Some related fuzzy graphs including fuzzy $$m$$
 -step neighbourhood graph, fuzzy economic competition graphs and fuzzy $$m$$
 -step economic competition graphs are introduced. Some properties of these new graphs have been investigated.

Sovan Samanta

Papers

Study on centrality measures in social networks: a survey

Fuzzy k -competition graphs and p -competition fuzzy graphs

A study on bipolar fuzzy graphs

Fuzzy Planar Graphs

$$m$$ m -Step fuzzy competition graphs