Pub Date : 2015-07-01DOI: 10.1016/j.psra.2015.11.002
Anton V. Dyshlyuk , Oleg B. Vitrik , Yuri N. Kulchin
We present a numerical analysis of surface plasmon resonance (SPR) excitation in a bent metal-coated single mode optical fibre with a low normalized frequency. It is shown that by choosing a proper combination of fibre parameters, such as bend radius and metal film thickness, a direct energy transfer can occur from the fundamental mode, guided by the fibre core, to the surface plasmon wave excited at the metal layer applied to the fibre cladding. The prospects for precision refractive index measurement based on the proposed configuration are discussed, with the spectral sensitivity and resolution estimated at 70 um/refractive index unit and 3⋅10−7, respectively.
{"title":"Application of optical fibres with reduced normalized frequency for SPR-based refractometry","authors":"Anton V. Dyshlyuk , Oleg B. Vitrik , Yuri N. Kulchin","doi":"10.1016/j.psra.2015.11.002","DOIUrl":"10.1016/j.psra.2015.11.002","url":null,"abstract":"<div><p>We present a numerical analysis of surface plasmon resonance (SPR) excitation in a bent metal-coated single mode optical fibre with a low normalized frequency. It is shown that by choosing a proper combination of fibre parameters, such as bend radius and metal film thickness, a direct energy transfer can occur from the fundamental mode, guided by the fibre core, to the surface plasmon wave excited at the metal layer applied to the fibre cladding. The prospects for precision refractive index measurement based on the proposed configuration are discussed, with the spectral sensitivity and resolution estimated at 70 um/refractive index unit and 3<em>⋅</em>10<sup>−7</sup>, respectively.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.11.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86445369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-01DOI: 10.1016/j.psra.2015.11.003
Yue Liu , Yanping Wang , Zhiping Yan
The development of digital PID controllers for adjustable boost DC–DC converters is discussed in this paper. The primary advantages of using digital signal processors over analogue circuits are higher immunity to environmental changes (such as temperature and ageing), increased flexibility by changing the software, more advanced control techniques, and a reduced number of components. Many engineers, scientists, and researchers rely only on the efficiency of MATLAB language to explore designs, but for system implementation, they were forced to translate high-level MATLAB algorithms into the lower-level language of C. Therefore, a type of advanced method of DSP software development is introduced. The Real-Time Workshop toolbox enables exploration and implementation to be brought together in the MATLAB platform. MATLAB is a technical computing language that can automatically generate readable, compact, and fast C code directly from its algorithms, which could be compiled using the Texas Instruments (TI) Code Composer Studio (CCS) I integrated development environment (IDE). With this capability, developers can maintain a single design source and use one language in one development environment from concept to implementation. This model-based development method has a unique value for rapid prototyping.
本文讨论了用于可调升压DC-DC变换器的数字PID控制器的研制。与模拟电路相比,使用数字信号处理器的主要优点是对环境变化(如温度和老化)具有更高的免疫力,通过改变软件增加了灵活性,更先进的控制技术,以及减少了组件数量。许多工程师、科学家和研究人员仅仅依靠MATLAB语言的效率来探索设计,但为了系统实现,他们被迫将高级MATLAB算法转换为低级c语言。因此,介绍了一种先进的DSP软件开发方法。实时研讨会工具箱使探索和实现在MATLAB平台中结合在一起。MATLAB是一种技术计算语言,可以直接从其算法中自动生成可读、紧凑和快速的C代码,这些代码可以使用德州仪器(TI) code Composer Studio (CCS) I集成开发环境(IDE)进行编译。有了这个功能,开发人员可以维护一个单一的设计源,并在一个开发环境中使用一种语言,从概念到实现。这种基于模型的开发方法对于快速原型设计具有独特的价值。
{"title":"Accelerating PID controller development with rapid prototyping and model-based design","authors":"Yue Liu , Yanping Wang , Zhiping Yan","doi":"10.1016/j.psra.2015.11.003","DOIUrl":"10.1016/j.psra.2015.11.003","url":null,"abstract":"<div><p>The development of digital PID controllers for adjustable boost DC–DC converters is discussed in this paper. The primary advantages of using digital signal processors over analogue circuits are higher immunity to environmental changes (such as temperature and ageing), increased flexibility by changing the software, more advanced control techniques, and a reduced number of components. Many engineers, scientists, and researchers rely only on the efficiency of MATLAB language to explore designs, but for system implementation, they were forced to translate high-level MATLAB algorithms into the lower-level language of C. Therefore, a type of advanced method of DSP software development is introduced. The Real-Time Workshop toolbox enables exploration and implementation to be brought together in the MATLAB platform. MATLAB is a technical computing language that can automatically generate readable, compact, and fast C code directly from its algorithms, which could be compiled using the Texas Instruments (TI) Code Composer Studio (CCS) I integrated development environment (IDE). With this capability, developers can maintain a single design source and use one language in one development environment from concept to implementation. This model-based development method has a unique value for rapid prototyping.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.11.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91532379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-01DOI: 10.1016/j.psra.2015.11.006
Sujit Kumar De , Shib Sankar Sana
This article describes an inventory model with several attributes. The primary purpose of an economic order quantity (EOQ) model is to select the best alternative in the face of uncertainty and other considerations. Unlike an intuitionistic fuzzy set (IFS), a hesitant fuzzy set (HFS) has an emergent implication in current decision-making problems. A membership function class is assumed, and a hesitant fuzzy decision matrix with elements that are membership grades is constructed. Using these values, the scores are derived with the help of hesitant fuzzy weighted geometric (HFWG), hesitant fuzzy geometric (HFG), hesitant fuzzy Einstein weighted geometric (HFEWG) and hesitant fuzzy Einstein ordered weighted geometric (HFEOWG) operators. Finally, a decision is made using the scores of each alternative.
{"title":"Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment","authors":"Sujit Kumar De , Shib Sankar Sana","doi":"10.1016/j.psra.2015.11.006","DOIUrl":"10.1016/j.psra.2015.11.006","url":null,"abstract":"<div><p>This article describes an inventory model with several attributes. The primary purpose of an economic order quantity (EOQ) model is to select the best alternative in the face of uncertainty and other considerations. Unlike an intuitionistic fuzzy set (IFS), a hesitant fuzzy set (HFS) has an emergent implication in current decision-making problems. A membership function class is assumed, and a hesitant fuzzy decision matrix with elements that are membership grades is constructed. Using these values, the scores are derived with the help of hesitant fuzzy weighted geometric (HFWG), hesitant fuzzy geometric (HFG), hesitant fuzzy Einstein weighted geometric (HFEWG) and hesitant fuzzy Einstein ordered weighted geometric (HFEOWG) operators. Finally, a decision is made using the scores of each alternative.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.11.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74627386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-01DOI: 10.1016/j.psra.2015.12.002
Yuriy N. Kulchin, Yuriy A. Zinin, Vladislav A. Kolchinskiy
In this article, the optical properties of a Bragg waveguide with an intermediate layer between the periodic cladding and the hollow core were investigated. The losses of the fibre modes were calculated using the method of transfer matrices. The possibility to reduce the optical losses by increasing the refractive index of the intermediate layer was shown. The thickness of the optimized intermediate layer must be selected to be in compliance with the anti-resonant condition.
{"title":"Bragg waveguide with an antiresonance intermediate layer","authors":"Yuriy N. Kulchin, Yuriy A. Zinin, Vladislav A. Kolchinskiy","doi":"10.1016/j.psra.2015.12.002","DOIUrl":"10.1016/j.psra.2015.12.002","url":null,"abstract":"<div><p>In this article, the optical properties of a Bragg waveguide with an intermediate layer between the periodic cladding and the hollow core were investigated. The losses of the fibre modes were calculated using the method of transfer matrices. The possibility to reduce the optical losses by increasing the refractive index of the intermediate layer was shown. The thickness of the optimized intermediate layer must be selected to be in compliance with the anti-resonant condition.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.12.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76025644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-01DOI: 10.1016/j.psra.2015.12.005
Vladimir P. Dzyuba, Yurii N. Kulchin, Andrey V. Amosov
The recently discovered, ultralow-threshold, nonlinear refraction of low-intensity laser radiation in dielectric nanostructures has an atypical dependence on radiation intensity in the pulsed and continuous modes. In this study, we present a theoretical explanation. The theory suggests that the nonlinearity is photoinduced in nature, rather than thermal, and depends directly on the nanoparticle electronic structure and the relationship between permittivities of the dielectric matrix and the nanoparticles.
{"title":"The theory of heterogeneous dielectric nanostructures with non-typical low-threshold nonlinearity","authors":"Vladimir P. Dzyuba, Yurii N. Kulchin, Andrey V. Amosov","doi":"10.1016/j.psra.2015.12.005","DOIUrl":"10.1016/j.psra.2015.12.005","url":null,"abstract":"<div><p>The recently discovered, ultralow-threshold, nonlinear refraction of low-intensity laser radiation in dielectric nanostructures has an atypical dependence on radiation intensity in the pulsed and continuous modes. In this study, we present a theoretical explanation. The theory suggests that the nonlinearity is photoinduced in nature, rather than thermal, and depends directly on the nanoparticle electronic structure and the relationship between permittivities of the dielectric matrix and the nanoparticles.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.12.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84767236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1016/j.psra.2015.11.001
Sergey I. Pokutnyi , Yury N. Kulchin , Vladimir P. Dzyuba
The theory of excitonic quasimolecules (biexcitons) formed of spatially separated electrons and holes in a nanosystem that consists of ZnSe quantum dots synthesized in a borosilicate glass matrix is developed within the context of the modified effective mass approximation. It is shown that biexciton formation that meets threshold characteristics is possible in a nanosystem in which the spacing between the quantum dots' surfaces is larger than a certain critical spacing.
{"title":"Excitonic quasimolecules in quasi-zero-dimensional nanogeterostructures: Theory","authors":"Sergey I. Pokutnyi , Yury N. Kulchin , Vladimir P. Dzyuba","doi":"10.1016/j.psra.2015.11.001","DOIUrl":"10.1016/j.psra.2015.11.001","url":null,"abstract":"<div><p>The theory of excitonic quasimolecules (biexcitons) formed of spatially separated electrons and holes in a nanosystem that consists of ZnSe quantum dots synthesized in a borosilicate glass matrix is developed within the context of the modified effective mass approximation. It is shown that biexciton formation that meets threshold characteristics is possible in a nanosystem in which the spacing between the quantum dots' surfaces is larger than a certain critical spacing.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.11.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82952887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1016/j.psra.2015.11.004
Alexander Yu. Popik , Evgeniy L. Gamayunov
The concentration of phytoplankton is often used to assess the ecological status of water bodies; it is determined by the fluorescence intensity of chlorophyll-a, which is located in microalgae cells. Investigators do not usually take into account the effect of the medium on the fluorescence intensity when determining the concentration of phytoplankton. This article describes the use of a fibre-optic spectrometer developed by the authors to identify the relationship between the fluorescence of the chlorophyll-a in phytoplankton cells and under environmental conditions, such as temperature and illumination. A mathematical model is used to calculate the chlorophyll-a concentration based on fluorescence measurements and takes the temperature and amount of light into account. Using the resulting proportionality coefficient can reduce the error in the chlorophyll-a concentration determined using fluorescence methods by a factor of two. In this article the, authors describe the results of applying the method they developed to performance monitoring in the waters of the Gulf of Peter the Great in September and October 2013.
{"title":"The dependence of the fluorescence spectrum of phytoplankton on external influences","authors":"Alexander Yu. Popik , Evgeniy L. Gamayunov","doi":"10.1016/j.psra.2015.11.004","DOIUrl":"10.1016/j.psra.2015.11.004","url":null,"abstract":"<div><p>The concentration of phytoplankton is often used to assess the ecological status of water bodies; it is determined by the fluorescence intensity of chlorophyll-a, which is located in microalgae cells. Investigators do not usually take into account the effect of the medium on the fluorescence intensity when determining the concentration of <em>phytoplankton</em>. This article describes the use of a fibre-optic spectrometer developed by the authors to identify the relationship between the fluorescence of the chlorophyll-a <em>in phytoplankton cells and under</em> environmental conditions, such as temperature and illumination. A mathematical model is used to calculate the chlorophyll-a concentration based on fluorescence measurements and takes the temperature and amount of light into account. <em>Using the resulting proportionality coefficient</em> can reduce the error in the chlorophyll-a concentration determined using fluorescence methods by a factor of two. <em>In this article the, authors</em> describe the results of applying the method they developed to performance monitoring in the waters of the Gulf of Peter the Great in September and October 2013.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.11.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77395976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1016/j.psra.2015.12.006
Asit Dey, Madhumangal Pal
The aim of this paper is to introduce the concept of generalised multi-fuzzy soft set. We also define several generalised multi-fuzzy soft set operations and study their properties, and applications of generalised multi-fuzzy soft sets in decision making problem were presented.
{"title":"Generalised multi-fuzzy soft set and its application in decision making","authors":"Asit Dey, Madhumangal Pal","doi":"10.1016/j.psra.2015.12.006","DOIUrl":"10.1016/j.psra.2015.12.006","url":null,"abstract":"<div><p>The aim of this paper is to introduce the concept of generalised multi-fuzzy soft set. We also define several generalised multi-fuzzy soft set operations and study their properties, and applications of generalised multi-fuzzy soft sets in decision making problem were presented.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.12.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90688480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1016/j.psra.2015.11.008
Oleg T. Kamenev , Vladislav A. Kolchinskiy , Yuri S. Petrov , Roman V. Romashko , Yuri N. Kulchin , Leonid P. Yatsenko , Vladimir M. Khodakovskyy
An adaptive fibre-optic interferomety system based on a dynamic hologram recorded in a bismuth titanium oxide crystal is developed and studied. The system possesses a low cutoff frequency (4 mHz), making possible the adaptive detection of ultra-slow physical signals with an amplitude equivalent to fibre elongation of 5 nm.
{"title":"An adaptive fibre-optic interferometer with low cutoff frequency","authors":"Oleg T. Kamenev , Vladislav A. Kolchinskiy , Yuri S. Petrov , Roman V. Romashko , Yuri N. Kulchin , Leonid P. Yatsenko , Vladimir M. Khodakovskyy","doi":"10.1016/j.psra.2015.11.008","DOIUrl":"10.1016/j.psra.2015.11.008","url":null,"abstract":"<div><p>An adaptive fibre-optic interferomety system based on a dynamic hologram recorded in a bismuth titanium oxide crystal is developed and studied. The system possesses a low cutoff frequency (4 mHz), making possible the adaptive detection of ultra-slow physical signals with an amplitude equivalent to fibre elongation of 5 nm.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.11.008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91443942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.1016/j.psra.2015.12.001
Ganesh Ghorai, Madhumangal Pal
The theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed m-polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on m-polar fuzzy graphs. It is proved that any of the products of m-polar fuzzy graphs are again an m-polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete m-polar fuzzy graphs is complete. If any of the products of two m-polar fuzzy graphs G1 and G2 are strong, then at least G1 or G2 must be strong. Moreover, the density of an m-polar fuzzy graph is defined, the notion of balanced m-polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two m-polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product m-polar fuzzy graph is introduced, and it is shown that every product m-polar fuzzy graph is an m-polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product m-polar fuzzy graphs.
{"title":"On some operations and density of m-polar fuzzy graphs","authors":"Ganesh Ghorai, Madhumangal Pal","doi":"10.1016/j.psra.2015.12.001","DOIUrl":"10.1016/j.psra.2015.12.001","url":null,"abstract":"<div><p>The theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed <em>m</em>-polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on <em>m</em>-polar fuzzy graphs. It is proved that any of the products of <em>m</em>-polar fuzzy graphs are again an <em>m</em>-polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete <em>m</em>-polar fuzzy graphs is complete. If any of the products of two <em>m</em>-polar fuzzy graphs <em>G</em><sub>1</sub> and <em>G</em><sub>2</sub> are strong, then at least <em>G</em><sub>1</sub> or <em>G</em><sub>2</sub> must be strong. Moreover, the density of an <em>m</em>-polar fuzzy graph is defined, the notion of balanced <em>m</em>-polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two <em>m</em>-polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product <em>m</em>-polar fuzzy graph is introduced, and it is shown that every product <em>m</em>-polar fuzzy graph is an <em>m</em>-polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product <em>m</em>-polar fuzzy graphs.</p></div>","PeriodicalId":100999,"journal":{"name":"Pacific Science Review A: Natural Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.psra.2015.12.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73452033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}