International Journal Of Nonlinear Analysis And Applications
Volume:14 Issue: 12, Dec 2023

In this research article, we study the existence, uniqueness and Ulam-Hyers stability of solutions in connection to the generalized Caputo Langevin fractional differential equations in Banach Space. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the technique of measure of noncompactness combined with the Monch fixed point theorem, the implementation Banach contraction principle fixed point theorem.  Moreover,  the Ulam--Hyers stability is discussed by utilizing the Urs's. Lastly, we deliver an example to check the efficiency and accuracy of the proposed methods.

In this paper, we examine the perturbed absolute value variational inequalities (PAVVI), a new class of variational inequalities. For the (PAVVI), some new merit functions are established. We develop the error bounds for (PAVVI) using these merit functions. The results presented here recapture a number of previously established findings in the relevant fields because (PAVVI) include variational inequalities, the absolute value complementarity problem, and systems of absolute value equations as special cases.

The automotive industry is one of the most important industries in the economy of countries due to its extensive relationship with other industries; High production and employment rates play a significant role in the sustainable development of countries. Therefore, the improvement of brand equity integration strategies in this industry is significant because it is related to the level of economic sustainability of countries. This study aims to analyze the integration matrix of the process of creating sustainable value in the automotive industry. This research is a development / mixed methodology that aims to symmetrically combine the relationship between the components of sustainable brand equity integration through Mick Mac matrix analysis to identify the most effective drivers of the research subject in the Iranian automotive industry. Therefore, in this study, first, in the qualitative part, meta-synthesis analysis and Delphi analysis were used to identify the thematic components of the integration of the process of creating sustainable value and to determine the theoretical adequacy of the components. Then, in a small part, an attempt was made to explain the approved components, based on the symmetric matrix analysis in the Mic Mac diagram, in the automotive industry to determine more stimulus for integrating the sustainable brand equity process, with the participation of 16 automotive executives. Based on the results in the qualitative section, 8 thematic components were identified to evaluate the integration of the sustainable brand equity process, and after Delphi's approval, these components were approved in terms of theoretical adequacy. The results in the quantitative part based on matrix analysis showed that the most motivating component in integrating the process of creating sustainable value in the automotive industry is the development of innovative ideas. To create integration in creating sustainable value, it is necessary to create a positive impact of creative ideas in the three components of balancing performance with the changing needs of K3 customers, the dynamics of communication with K8 suppliers, and reducing the diversity of materials used in K5 production.

This study presents a convex formulation for generation-transmission expansion planning in the presence of phase shifter transformers and aims at maximizing social welfare. By changing the voltage angle, the phase shifter transformer can control the transmission power of the line. Therefore, by installing a phase shifter transformer, one can reduce the investment cost of new lines and use the nominal capacity of available transmission lines. Accordingly, the planning of the generation-transmission expansion in this paper is formulated with the assumption that there is a pool electricity market. The problem is formulated in the form of mixed integer programming and the CPLEX solver is used to solve it in the YALMIP Toolbox environment. In the proposed method, the location, capacity and year of installation of generators, transmission lines and new phase shifter transformers will be determined simultaneously. In order to validate the proposed planning, the expansion planning of the IEEE 24-bus system has been simulated in MATLAB software. Simulation results show the efficiency of the proposed method.

In this note, we study bounded linear operators associated with unitary representations which commute with certain module actions.

The study aims to know the role of environmental vigilance in the sustainability of environmental and social performance, so as a result of wars and infections from factories, hospitals, natural disasters and the spread of viruses, we have not found any interest in the Ministry of Health and Environment. The role of the department is to investigate the level of environmental vigilance in the sustainability of environmental and social performance. Therefore, the results of the study indicate a link between environmental vigilance and sustainability of environmental performance, despite the high gap between them and the sustainability of environmental performance in the ministry. Especially in the technical department, which emphasizes the importance of the dimensions of environmental vigilance and its impact on improving the performance of the department in particular and the ministry in general.

The purpose of this research is the design The Organizational Aesthetics Pattern with Grounded Theory. Current research is exploratory-applied research in terms of purpose, deductive in terms of method, descriptive survey and it is qualitative research. First, 11 experts were interviewed using the theoretical sampling method. Then, the interviews were analyzed by using Grounded Theory, and 189 items were identified as primary concepts from the context of the interview by open coding, and they are categorized as 16 organizer themes, 50 basic themes, and five categories. In the quantitative part of the research, a questionnaire was distributed based on the statistical society of 412 and it was analyzed by data analysis in SPSS software. In the qualitative part of the research, the dimensions of causal condition (2 organizer themes and 8 basic themes), intervening condition (2 organizer themes and 4 basic themes), contextual condition (2 organizer themes and 9 basic themes), strategic condition (3 organizer themes and 9 basic themes) and consequential condition (5 organizer themes and 16 basic themes) were determined and the process of activity and the pattern were created in the following. Also, it can be concluded according to the derived results, the composed model has acceptable reliability and validity and it can be used as a trustful model to design the organizational aesthetics pattern.

In this study, it is attempted to analyze sensitivity and reliability in order to evaluate the liquefaction potential in soil layers in Tabriz. 62 boreholes that had possible conditions for liquefaction were selected. Seismic mapping was simulated using the finite fault method and then the effect of soil layers on PGA was estimated. In continuation, the liquefaction potential index was estimated and the zoning map of liquefaction risk was presented. In final, through sensitivity and reliability analysis of the Monte Carlo method, the rate of density function against the safety factor of the soil layers versus liquefaction was determined.

In [24], Khan et al. established some fixed point theorems in complete and compact metric spaces by using altering distance functions. In [16] Gordji et al. described the notion of orthogonal set and orthogonal metric spaces. In [18] Gungor et al. established fixed point theorems on orthogonal metric spaces via altering distance functions. In [25] Lotfy et al introduced the notion of $\alpha_{*}$-$\psi$-common rational type mappings on generalized metric spaces with application to fractional integral equations. In [28] K. Royy et al. described the notion of Branciari $S_b$-metric space and related fixed point theorems with an application. In this paper, we introduce the notion of the common fixed point ($\alpha_*$-$\psi$-$\beta_{i}$)-contractive set-valued mappings on orthogonal Branciari $S_{b}$-metric space with the application of the existence of a unique solution to an initial value problem.

The purpose of this study is to investigate the impact of environmental indicators on the traditional financial performance of manufacturing companies admitted on the Tehran Stock Exchange. Today, many companies are facing environmental issues and are looking for a suitable way to report and disclose information to the public to assure the shareholders of the company's compliance with environmental issues and environmental protection. This research measures environmental indicators from the components of pollution control, prevention of environmental damage, research and development, conservation of natural resources and environmental policy, as well as the variables of return on equity, return on sales, and return on assets. Book market value, residual profit and return on investment were used to measure the financial performance of companies. Using the website of the stock exchange, accompanying notes and activity reports of the board of directors to the assembly of 108 manufacturing companies admitted to the Tehran Stock Exchange during the period from 2013 to 2020, the required data was collected and using the method Multivariate regression was analyzed using the F test of Limer, Hausman, Brosch-Godfrey and Brosch-Pagan with the help of R software. The results of the hypothesis test showed that there is a positive and significant relationship between environmental indicators and traditional financial criteria. The results of this research will help managers to identify the environmental indicators that affect environmental performance in their companies and use them to increase the company's value and improve the company's financial performance.

In this paper, the modified matrix exponential method (MME), under the zero-order hold (ZOH) assumption, is applied to solve the Abel equation of the second kind. The modified exponential matrix method is iterative, and by increasing the iteration, we can get a better approximation with fewer errors. We use the MME to turn an Abel differential equation into a system of nonlinear equations and determine the solution. By using the MME, the Abel differential equations approximate well. Using the numerical results, we can conclude that this method is effective, and in comparison with well-known techniques, the MME is highly accurate.

Today, several businesses across all industries strive to increase performance at a level suited to their activities to effectively operate their operations under the current competitive conditions. The examination of organizational entrepreneurship's key components and the discussion of it are two elements that might have an impact on an organization's success. Recent changes in the insurance business, including privatization, tariff liberalization in some insurance sectors, and allowing foreign insurance firms to participate in the nation, have made competition one of the primary foundations of the insurance market. As a result, insurance firms can no longer conduct business as usual in this industry, and they will fail if they do not work to establish a long-term competitive edge for themselves. Organizational entrepreneurship is a method for acquiring a competitive edge in the modern day. So, by considering the function of mediating customer happiness, this research has established an efficient organizational entrepreneurship model on financial performance. This study has a practical goal and qualitatively analyzes data. Based on the theme analysis, four major entrepreneurial factors—innovation, risk-taking, pioneering, and investment—were found. The investigated community includes Parsian Insurance Company offices in Tehran. The final conceptual model was created using the theme analysis technique, and experts accepted it based on Lawshe's validity assessment.

The issue of increasing tax revenues and possible ways for this increase is an attractive issue for governments. Especially in a single product economy like Iran, whose main source of income is volatile and unpredictable oil income. Today, tax revenues play an important role in financing governments so that tax is considered as a legitimizing factor for a government. After introducing the presented models and classifying them, this research aims to investigate and identify the effective factors in increasing tax revenues and evaluating public trust and participation in the field of tax with a meta- synthesis approach. The main components of this dynamic model include economic, cultural factors and political factors. Then, in order to better understand the variables affecting this relationship and understand the existing dynamics, a model has been presented for evaluating trust and public participation in the field of tax using the approach of system dynamics modeling and drawing causal-loop diagrams (CLD). Finally, the simulation has been done by Vensim software. Three basic scenarios for increasing the main components and one scenario for simultaneous increase of all the main components were analyzed as levers of the model. The simulation results indicate the positive effect of economic factors on trust and public participation in the field of tax. The point is that the effect of economic factors is greater when all simultaneous components are applied.

The present era is marked by rapid improvement and advances in technology. Nowadays inefficient traffic light management systems can make long delays and waste energy improving the efficiency of such complex systems to save energy and reduce air pollution in future smart cities. In this paper, we propose to take real-time traffic information from the surrounding environment. Such a process, which is called profilization constantly gathers and analyses information for vehicles and pedestrians throughout smart cities in order to fairly predict their actions and behaviours. We develop an efficient multi-level traffic light control system to schedule traffic signals’ duration based on a distributed profile database, which is generated by embedding sensors in streets, Vehicles and everywhere. We deploy pervasive deep learning models from the cloud to users (vehicles, bikes and pedestrians) to learn and control the traffic lights. In the cloud-level learning model, the maximum waiting time of different vehicles and pedestrians is calculated based on their profiles. The profilization process is a constant learning process throughout the whole city at the user level. Each vehicle deploys a separate learning model (decision-making) based on its average and maximum speed in a different area, waiting times at the intersections and possible trips and destinations. Such a multi-level deep learning model in the level of intersection and cloud aims to locally schedule the traffic with deadlines toward their destinations within a certain period. The results show that the proposed multi-level traffic light system can significantly improve the efficiency of the traffic system in future smart cities.

In this paper, we present a numerical simulation for integrating active load control using corona discharge-based plasma actuators on the trailing edge of a wind turbine blade. Eulerian simulation is done on a 660 kW wind turbine blade with NACA 0012 profile. The electrohydrodynamic incompressible flow created between two electrodes using the combination of the EHDFoam solver with the BoyantPimpleFoam solver is carried out in the free and open-access OpenFOAM software. The results have been validated using numerical and experimental work. The effects of environmental parameters such as temperature, relative humidity and environmental pressure on the corona discharge process have been investigated. The results of this research showed that with the increase in temperature, humidity and pressure, the discharge process is decreased. The results show a 62% and 35% decrease in the average transfer momentum with an increase in relative humidity and temperature, respectively.

Water is now an important issue in the world, and the effective development of water resources and optimal management of industrial projects are essential for sustainable growth. Limitations and crises of water and wastewater companies in the supply and optimal exploitation of water resources and wastewater disposal require strategic planning and management, thereby increasing the competitive advantages of human societies. Given the importance of optimal management of water and wastewater industry projects, the present research sought to detect and introduce indices and criteria, which affected the optimal management of this industry based on certain models (Porter Diamond Model, Porter's Five Forces, and PESTEL), by examining and analyzing political, economic, and socio-cultural trends and using the results of interpretation and analysis of trends. To this end, the experts in the water and wastewater industry, as well as the managers working in this industry were surveyed. Based on experts' opinions, the results of the certain criteria after screening were finally converted into 22 out of 95 criteria using the fuzzy Delphi technique, and then the 22 criteria selected by the experts were reviewed and any of them with the potential to be quantified and their trends could be examined, were selected and quantified. Finally, the results introduced 12 indices in three categories: economic indices (similar in all industries), specialized indices of water and wastewater, and cultural-educational indices. The Gross Domestic Product (GDP), the complexity of the supply chain of the water and wastewater industry, and cultural infrastructures (Intellectual maturity, management attitude, education, corruption, and population) were respectively representatives of the indices.

Despite the widespread and successful use of FRP sheets in improving the seismic behavior of structures, the effect of FRP sheets on the strength of structural members under lateral load (such as concrete columns), especially at high temperatures, has received less attention. Therefore, in this study, while making sure the accuracy of numerical simulations, then, by numerical modeling of three-dimensional finite element columns of reinforced concrete columns in both non-reinforced and reinforced conditions with CFRP sheets and thermal coupling-displacement analysis of this model during cyclic lateral loading at different fire temperatures, the effect of reinforcement of reinforced concrete columns with FRP sheets on the cyclic lateral behavior of these columns at different fire temperatures has been investigated. From the results of these studies, It has been observed that following the increase of fire temperature from 250 to 1000 ° C in both reinforced concrete columns and reinforced with FRP sheets, on the amount of lateral force, anchorage and energy of these columns during lateral loading of the cycle, the amount of lateral force, anchorage and energy of these columns during cyclic lateral bearing has been increased, which this increase (as the result of the increase in fire temperature) of the mentioned responses in the columns is more significant than the temperature of 500 ° C and especially in the reinforced concrete columns reinforced with FRP sheets.

in the theoretical dimension, the current article focuses on the analytical function of the concept of political awareness in domestic scientific articles and reflects the ways of using this concept in the theoretical models of previous studies. In the experimental dimension, the article sought to discover the generalizable experimental dimensions of political awareness in Iranian society and to draw a scatter map of the study of components connected with this phenomenon in order to know the points of emptiness and accumulation. With this description, two questions have been raised: "What are the methods of conceptualization and theoretical explanation of the phenomenon of political awareness in Persian language scientific articles?" and "To what extent is there synergy between empirical findings on various aspects of political awareness in Iranian society?" 21 articles (quantitative and qualitative) were selected for a systematic review of the analytical features of articles in the field of political awareness, of which only 16 quantitative articles were present in the process of collecting experimental data and meta-analysis studies. The findings of the article show that the trend of political awareness studies in Persian articles is towards the theoretical analysis of this concept as a dependent variable. The most synergy between the empirical results of the studies in this field refers to the confirmation of the effect of the "media" variable on increasing political awareness, and the confirmation of the effect of "demographic characteristics" and the rejection of the effect of "social class" on political awareness is in the next rank.

One of the important applications of data envelopment analysis is to determine the progress and regress of the units under evaluation at two different times, which has been addressed in many papers. Also, one of the distinctions of data coverage analysis technique with other methods is the introduction of achievable and flexible benchmarks. In the present paper, we intend to study the progress and regress of Iranian regional electricity companies during two consecutive years of 2015 and 2016. Since some of the evaluated indicators are semi-positive and semi-negative indicators, in this study we will develop Emrooznejad et al.  [7] to determine the productivity index of Malmquist for semi-positive and semi-negative indicators. Finally, for further explanation, we have used the proposed models to determine the progress and regression of 16 regional electricity companies in Iran with 3 semi-positive and semi-negative indices in the presence of the limitation on the benchmark, an undesirable index and 11 completely positive indices in the nature of input with constant scale returns as a black box.

The present study is based on presenting a model of factors affecting financial health and the life cycle of listed banks on the Tehran Stock Exchange. For this purpose, at the beginning and after interviews with 48 experts in the fields of accounting and financial management; Factors affecting financial health in the life cycle of banks were identified and, consequently, research hypotheses were developed. In the next step, the theoretical foundations of research are collected by referring to databases, dissertations, and related articles, and in the data analysis section; Financial data of 11 banks for a period of 10 years (2012-2021) were collected, research variables were measured and default regression tests were performed. In the next step; Through multivariate linear regression; Research hypotheses, tests and finally, through nonlinear power regression and artificial neural network algorithms; A model of factors affecting financial health was presented. The findings of the study explained that regardless of the life cycle of banks; financial reporting quality, corporate governance and investment efficiency on banks' financial health; have a positive and significant effect and financial leverage has a negative and significant effect on the financial health of banks. But statistically; The effect of financial reporting quality, corporate governance, financial leverage and investment efficiency on banks' financial health; was not achieved at any stage of their life cycle. Other findings also stated that banks' financial sound forecasts; The firefly algorithm performed better than the backup machine and decision tree algorithms, and the decision tree algorithm performed better than the backup machine algorithm.

In this work, we establish the existence of at least two positive solutions for a coupled system of $p$-Laplacian fractional-order boundary value problems. Establishing the existence of positive solutions to the problem is challenging for a variety of reasons, the most important of which is a lack of compatibility with the kernel. To address these issues, we have included the necessary conditions for overcoming certain methodological hurdles on the kernel as well as adapting to the problem's nature of positivity. The method is based on the AH functional fixed point theorem.

The current research was conducted with the aim of validating the implementation model of the fourth generation of the industry in order to achieve the goals of sustainable development in Iran Khodro Company. For this purpose, the initial model of the implementation of the fourth-generation industry was designed to achieve the goals of sustainable development in Iran Khodro Company, and then the designed model was validated. This research is applied-developmental in terms of purpose, and in terms of data collection method, it is non-experimental (descriptive) with a cross-sectional survey approach, and in terms of the nature of the data, it is mixed (qualitative-quantitative). The statistical population in the qualitative section included 8 senior managers of Iran Khodro Company and the targeted sampling method. The statistical population in the quantitative part included 384 experts with experience in Iran Khodro company and a simple random sampling method. The data collection tools in the qualitative part were questionnaires and semi-structured interviews, and in the quantitative part, the structural-interpretive modelling (ISM) questionnaire and a questionnaire with a 5-point Likert scale. In the qualitative part of the research, the content analysis technique and software (MAXQDA) were used to analyze the expert interviews and extract the main and secondary components. In the quantitative part of the research, the structural-interpretive modelling technique and software (MICMAC) were used to identify the causal relationships between the main components of the research and provide the initial model, and the partial least squares technique and software (SMART PLS) were used to validate the initial model. The final model included 10 main components and the results of the partial least squares technique fully confirmed the validity of the model.

The purpose of this study was to provide a profit forecasting model based on the behavioral tax of companies listed on the Tehran Stock Exchange; Research method in terms of purpose, basic-applied in terms of data type, quantitative; Depending on the time of data collection, it was a combination (time series and cross-sectional) and according to the method of data collection or the nature and method of research, survey and library. The statistical population of the first part of the study included all companies listed on the Tehran Stock Exchange. To determine the samples of this part of the research, a systematic sampling method was used, which was finally selected as a sample by applying the desired filters to 120 companies. The second group of the statistical population of this study included all investors in the Tehran Stock Exchange who were selected using the cluster random sampling method and the Cochran Orkut formula of 385 people as a sample. Modern Rahdavard and Tadbiardazar database software and the distribution of researcher-made questionnaires based on standard questionnaires were used to collect the data. In the inferential and quantitative sections, we used two models of data panel regression and structural equations to answer the research questions. The results showed that behavioral variables such as management overconfidence, stock price information efficiency, stock price synchronization, information efficiency, reluctant effect, mass effect, emotional bias, cognitive bias and exponential bias Corporate profits are effective Also, indicators of economic confidence and information reliability affect the interaction between behavioral decisions and corporate profits.

High-precision prediction of financial prices is still a deemed long-term challenge that constantly calls for state-of-the-art approaches. Thus, the purpose of the current study was to examine the efficacy of optimal stopping and use its connection with branching processes to predict several financial markets. For this purpose, the S&P 500 index and dollar, gold, oil and bitcoin markets are predicted at 5-, 10-, 30-, 50-, and 100-day forecast horizons, for each of which the optimal buying and selling point was determined. Closing price data for at least 2200 trading days during the period 2013-2021 was used for the purposes of this study. Moreover, given that any prediction and decision in the financial markets is highly based on probability, and hence risk, two strategies are devised for examination, namely (1) high risk (success rate of at least 50%) and (2) low risk (success rate of at least 70%). The findings indicated that the estimations on all the indices and prices were relevant for the high-risk scenario (that is a success rate of at least 50%), while only those on the S&P 500 index and price of gold were relevant for the low-risk scenario (success rate of at least 70%).

In this paper, we study the spread of COVID-19 and its effect on a population through mathematical models. We propose a Caputo time-fractional compartmental model (SEIR) comprising the susceptible, exposed, infected and recovered population for the dynamics of the COVID-19 pandemic. The proposed nonlinear fractional model is an extension of a formulated integer-order COVID-19 mathematical model. The existence of a unique solution for the proposed model was shown by using basic concepts such as continuity and Banach's fixed-point theorem. The uniqueness and boundedness of the solutions of the proposed model are investigated. We calculate a central quantity in epidemiology called the basic reproduction number, $R_{0}$ by the concept of the next-generation matrices approach. The equilibrium points of the model are calculated and the local asymptotic stability for the derived disease-free equilibrium point is discussed.

The purpose of this research is to quantify the unknown factors of corporate governance caused by the tax gap and to determine its mediating effect on the relationship between the tax gap and the cost of equity. The research sample includes 149 companies accepted in the Tehran Stock Exchange covering a period of seven years from March 2013 to March 2020. The results show that there is a significant relationship between the unknown factors of corporate governance and the tax gap. Therefore, the first hypothesis is confirmed and the results of the second hypothesis test show that the tax gap variable (independent variable) is not significant on the cost of equity variable in the fourth regression related to the second hypothesis, so the variable of the unknown factors of corporate governance plays a complete mediating role. In other words, the tax gap variable can only estimate the cost of equity mediated by the unknown factors of corporate governance. First, it is expected that the results of the research can develop the theoretical foundations of previous research on the tax domain. Second, the current research can provide useful information for capital market and tax legislators. Third, it can create new ideas for conducting future research in the tax field.

This research aims to identify the impact of customer perception of innovation and customer involvement on the customers' perceived value and behavioral tendencies through the creation of shared value in the statistical community of tire sales agents in the country with an applied purpose and correlational research method. The evidence was collected using a closed-ended questionnaire from 650 samples using the stratified random sampling method, and validity with construct indices and validity with the internal consistency method were investigated and supported. Descriptive analysis using central tendency and dispersion indices and inferential analysis using structural equation modeling has been done. The fit indices of the model have supported the compatibility of the conceptual model with the supporting theoretical model and the structural part of the model from the twelve hypotheses of the research in a positive and meaningful way. The results indicate that increasing customer perception of innovation and involvement leads to increased perceived value, customer behavioral tendencies, cooperative behaviors, and customer citizenship. Participatory and citizenship behaviors of customers also increase the customers' perceived value and behavioral tendencies. Also, the indirect effect of customer perception of innovation and customer involvement on the customers' perceived value and behavioral tendencies through cooperative behaviors and customer citizenship has been supported. Therefore, tire manufacturers can provide a competitive advantage and success in the tire industry by planning to improve model structures.

The work is devoted to the characteristic properties analysis of the sea surface image on video stream frames, which makes it possible to make a decision about the detection of object images on them in the absence of a priori information about objects, which is important in the development of navigation systems, security and surveillance systems. In this paper, it is proposes to analyze the values of the normalized cross-correlation coefficients of a given image fragment with higher dimension fragments on sequential video stream frames to identify the distinctive properties of the agitated sea surface and floating objects images. The computational experiments were carried out and have shown that the analysis of the results of calculating the frame fragments cross-correlations allows us to estimate the amount of displacement and distortion of a given image fragment. The results of computational experiments demonstrate the presence of differences in the values of the corresponding cross-correlation coefficients for the sea surface images with different agitation degrees, containing and not containing an image of the object. Based on the analysis of the proposed correlation properties of the sea surface images, a decisive rule for selecting fragments of frames containing an image of an object is formulated, the use of which, in many cases, allows to detection of fragments of object images correctly.

In 2000, exponential trapezoidal fuzzy numbers were defined for the first time by Chen and Lie [3] without investigating the definition and properties of fuzzy numbers for them.  Therefore, in this paper first, some necessary definitions and the difference between fuzzy numbers and fuzzy quantities are presented. Then, the correctness of the definition of exponential trapezoidal fuzzy numbers is investigated. It is concluded that exponential trapezoidal fuzzy numbers do not satisfy general conditions of fuzzy numbers such as bounded amplitude and continuity. In fact, these are fuzzy quantities not fuzzy numbers. As a result, a ranking method is proposed for such quantities to be examined using common tools and test platforms that exist for ranking fuzzy quantities. Moreover, the strength and weaknesses of the method are reported.

The study of the Nevanlinna theory for difference operators was introduced independently by Halburd & Korhonen and Chiang & Feng in the years 2006 and 2008 respectively. Halburd and Korhonen proved the uniqueness theorem for meromorphic functions associated with c-separated pairs. In this paper, we have generalised the result by introducing c-separated pairs of multiplicity p and their counting functions. We have deduced some analogues of certain unique results of classical Nevanlinna theory due to Chen, Chen & Tsai; Gopalakrishna & Bhoosnurmath; and Lahiri & Pal. Thereafter, we have also discussed certain implications of the deduced results.