Mathematics and Statistics
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Item A new method for intuitionistic fuzzy multi-objective linear fractional optimization problem and its application in agricultural land allocation problem(Elsevier, 2023) Moges, Demmelash Mollalign; Mushi, Allen R.; Wordofa, Berhanu GutaThis paper presents a new method for solving an intuitionistic fuzzy multi-objective linear fractional optimization (IFMOLFO) problem with crisp and intuitionistic fuzzy constraints. Here, all uncertain parameters are represented as triangular intuitionistic fuzzy numbers. We used an accuracy ranking function and variable transformation in the proposed method to convert an IFMOLFO problem into a crisp multi-objective linear optimization problem. Then, we formulated the first phase of the weighted intuitionistic fuzzy goal programming (WIFGP) model to obtain an intuitionistic fuzzy non-dominant (IFND) solution for the IFMOLFO problem. Several strategies for obtaining an IFND solution to the IFMOLFO problem have been proposed in the literature. However, in addition to constructing the phase-I WIFGP model, this study shows that the IFND solution may not be Pareto-optimal when some of the under-deviation variables are zero. As a result, the second phase of the WIFGP model is applied to address this issue. The benefits of both models are merged to provide a novel method, unlike any other method in the literature, for producing optimal solutions that satisfy both IFND and Pareto-optimal requirements. The suggested algorithm’s efficiency and reliability are demonstrated by addressing a real-life case study of an agricultural production planning problem and followed by solving a numerical example from literature.Item Solving multi-objective multilevel programming problems using two-phase intuitionistic fuzzy goal programming method(Elsevier, 2022) Mollalign, Demmelash; Mushi, Allen R.; Guta, BerhanuThis paper presents a two-phase intuitionistic fuzzy goal programming (two-phase IFGP) algorithm to solve Multi-Objective Multilevel Programming (MO-MLP) problems. The coefficient of each objective and constraint function is assumed to be triangular intuitionistic fuzzy parameters and the crisp MO-MLP problems are obtained using the accuracy function method. To avoid decision lock, the top levels set tolerance limits for decision variables to control the lower levels. The problem is modeled in the intuitionistic fuzzy environment using membership and non-membership functions for each objective function at all levels and decision variables controlled by the top levels. Then, we proposed an IFGP algorithm to achieve the highest degree of each membership and non-membership goal by minimizing unwanted deviational variables and generating compensatory solutions for all decision-makers at all levels. Moreover, in the proposed approach, two-phase IFGP is modeled to yield a compromise solution that satisfies both the MN-Pareto optimal solution and the Pareto optimal solution at each level. Also, verification of the proposed method is discussed with numerical examples.Item Solving the University course timetabling problem using bat inspired algorithm(Tanzania Journal of Science, 2021) Limota, Ushindi; Mujuni, Egbert; Mushi, Allen R.Many mathematical optimization problems from real-life applications are NP-hard, and hence no algorithm that solves them to optimality within a reasonable time is known. For this reason, metaheuristic methods are mostly preferred when their size is big. Many meta-heuristic methods have been proposed to solve various combinatorial optimization problems. One of the newly introduced metaheuristic methods is a bat-inspired algorithm, which is based on the echolocation behaviour of microbats. Bat algorithm (BA) and its variants have been used successfully to solve several optimization problems. However, from the No-free Lunch Theorem, it is known that there is no universal metaheuristic method that can solve efficiently all optimization problems. Thus, this study work focused on investigating the usefulness of BA in solving an optimization problem called Course Teaching Problem (CTP). Since BA was originally designed to solve continuous problems, and CTP is a combinatorial optimization problem, a discrete version of BA for CPT has been proposed and tested using real-life data from the Dar es Salaam University College of Education (DUCE). The algorithm has produced promising results, as in each execution test, it generated a timetable in which all hard constraints were met and soft constraints were significantly satisfied within a few iterations.Item Aretrospective evaluation of the intellectual structure of private agricultural and food standards research in global trade(International Trade, Politics and Development, 2023) Lwesya, Francis; Mbukwa, Justine N.Purpose The aim of this article was to present a retrospective assessment of the intellectual structure of private agricultural and food standards research in global trade. This study was motivated by the increasing role of standards and certifications in governing global agricultural and food trade. Design/methodology/approach The current investigation was carried out with bibliometric methods using VOSviewer software. Techniques such as citation, co-citation, keyword co-occurrence, keyword evolution and co-authorship analyses were performed to tackle the research questions. Articles were extracted from Scopus database for the period 1998–2022 (30th August 2022) with selected keywords (“Private food standard*” OR “food standard*” OR “agri-food standard*” AND “agri*” OR “agro*” OR “farm*” OR “food*” AND “international trade” OR “global trade” OR “international business”) along certain filters (subject – Economics and Business management: language – English: Document – article and review articles and source – journals). Findings The results show that the intellectual structure of private agricultural and food standards research in global trade has evolved around five clusters, namely: (1) the political economy of food standards, (2) food standards and their challenges in global trade, (3) food standards and integration into value chains, (4) food standards and market access and (5) food standards and exports from developing countries. However, the authors found the research gaps in each of the thematic clusters. Research limitations/implications The main limitation of this study is that the authors focused their attention on certain aspects of bibliometric review, such as the intellectual structure of the field, the citation analysis and the collaboration network. Future research could attempt to explore new field development through bibliographic coupling and deepening of conceptual structure using content analysis by incorporating the research methods used in the respective studies. Practical implications The emerging research areas in private agricultural and food standards in global trade are related to topics on food quality, sustainable development, genetically modified organisms, World Trade Organization, tariff structure, trade agreements, food industry and European Union. However, there is less research and little collaboration between Africa and developed countries. For example, Africa's total publications were (15), while the US had (46), China (15), Belgium (23), Germany (27), Italy (32) and the UK (24). Originality/value There are limited studies that have conducted a retrospective evaluation of the intellectual structure of private agricultural and food standards research in the global trade using bibliometric analysis. The present investigation is novel in identifying the thematic research clusters, emerging issues and future research directions. This is more important to developing countries as their agricultural produce face challenges to access markets of the developed world.Item Effect of Statistics on Collaboration for Enhancing Institutional Sustainability: A Case of Mzumbe University-Tanzania(Springer Nature Switzerland, 2024) Mbukwa, Justine N.; Mbegalo, Tukae; Lwaho, JosephThe article discusses the effects of statistics on collaboration and its potential in spearheading sustainable industrial development. In this regard, three days’ workshop were conducted by Mzumbe University Laboratory for Interdisciplinary Analysis (MULISA) in collaboration with the Ifakara health institute. These activities are statistical literacy, scientific writing and winning the research grants. The objective was to create a smooth environment for the sustainability of the statistical laboratory through knowledge. The participants in the workshop were students and lecturers at Mzumbe University, and researchers and interns from Ifakara Research Institute (IHI). The majority of the participants in all three days of workshop were males. The results revealed that the workshop has increased the research and publication activities among MULISA collaborators after the workshop compared to before the workshop. This noted benefit derived from the sharing the skills and collaboration during the workshop. Therefore, the collaborative workshops and training are the engineering tool for sustainability because it allows sharing of new knowledge. The collaboration in writing enhances thoughts, ideas, and knowledge transferability to the next generation.Item Climate change, food security, and diarrhoea prevalence nexus in Tanzania(humanities and social sciences communications, 2024) Kitole, Felician A.; Mbukwa, Justine N.; Tibamanya, Felister Y.; Sesabo, Jennifer K.The impact of climate change on food security and public health has hindered poverty reduction efforts in developing nations, including Tanzania, resulting in the impoverishment of millions and compromising both health and food production. To unravel these complex interactions, rigorous scientific research is indispensable. Leveraging three waves of the Agriculture Sample Census (2002/03, 2007/08, 2019/20), this study meticulously examines the interplay between climate change, food security, and diarrhoea prevalence in Tanzania. Employing Instrumental Variable Probit and Control Function Approach models to address endogeneity and heterogeneity, temperature anomalies serve as instrumental variables. The findings reveal a substantial impact of climate change on both food security (−0.331142, p < 0.01) and diarrhoea incidence (0.214602, p < 0.01). These results signify that climate change places significant stress on food security, rendering households more susceptible to insecurities, and heightens health concerns through increased diarrhoea prevalence. This underscores the urgency of prioritizing public health and well-being through an agricultural lens in climate change mitigation. A comprehensive strategy is imperative, entailing a synergy of sustainable agricultural practices, robust public health interventions, and targeted policies to fortify the adaptive capacity of communities. Special emphasis should be placed on cultivating climate-resilient agricultural systems, ensuring food security, and implementing health programs tailored to address the unique challenges posed by climate-induced factors. Moreover, community engagement and awareness initiatives play a pivotal role in fostering a collective understanding and commitment to sustainable practices, contributing to the overall resilience of societies amidst the challenges of climate change.Item Bayesian multilevel modelling of the association between socio-economic status and stunting among under-five-year children in Tanzania(Journal of Health, Population and Nutrition, 2023) Musheiguza, Edwin; Mbegalo, Tukae; Mbukwa, Justine N.Background: Stunting is associated with socioeconomic status (SES) which is multidimensional. This study aimed to compare different SES indices in predicting stunting. Methods: This was the secondary data analysis using Tanzania Demographics and Health Surveys (TDHS). The study used 7492, 6668, and 8790 under-five-year children from TDHS 2004/5, 2010, and 2015/16, respectively. The Household Wealth Index (HWI); Water and Sanitation, Assets, Maternal education and Income (WAMI); Wealth Assets, Education, and Occupation (WEO); and the Multidimensional Poverty Index (MPI) indices were compared. The summated scores, principal component analysis (PCA), and random forest (RF) approaches were used to construct indices. The Bayesian and maximum likelihood multilevel generalized linear mixed models (MGLMM) were constructed to determine the association between each SES index and stunting. Results: The study revealed that 42.3%, 38.4%, and 32.4% of the studied under-five-year children were stunted in 2004/5, 2010, and 2015/16, respectively. Compared to other indicators of SES, the MPI had a better prediction of stunting for the TDHS 2004/5 and 2015/16, while the WAMI had a better prediction in 2010. For each score increase in WAMI, the odds of stunting were 64% [BPOR = 0.36; 95% CCI 0.3, 0.4] lower in 2010, while for each score increase in MPI there was 1 [BPOR = 1.1; 95% CCI 1.1, 1.2] times higher odds of stunting in 2015/16. Conclusion: The MPI and WAMI under PCA were the best measures of SES that predict stunting. Because MPI was the best predictor of stunting for two surveys (TDHS 2004/5 and 2015/16), studies dealing with stunting should use MPI as a proxy measure of SES. Use of BE-MGLMM in modelling stunting is encouraged. Strengthened availability of items forming MPI is inevitable for child growth potentials. Further studies should investigate the determinants of stunting using Bayesian spatial models to take into account spatial heterogeneity.Item Spatial Distribution and Pattern Analysis of Women Sexual Violence in Tanzania(Springer, Cham, 2023) Mbukwa, Justine N.; Mbegalo, Tukae; Levira, FrancisIn sub-Saharan Africa, sexual violence is very common among married women. This has a negative effect on health and wellbeing. This problem has not been well documented geographically, particularly in Tanzania. The main objective of this chapter was to describe the geographical distribution of women sexual violence in Tanzania. We used data from the Tanzanian demographic and health survey (2015/2016), comprising a random sample of 10,333 women aged 15–49 years. The study used ArcMap software version 10.8, for understanding the spatial pattern of sexual violence and Chi-square to find out the drivers of high women sexual prevalence rate across the regions. Findings show sexual violence was more prevalent in the Lake and Central zones. Wealth index, marital status, partner’s education, drinking habit and occupation were the main drivers.Item Utilization of non-financial business support services to aid development of Micro, Small and Medium Enterprises (MSMEs) in Tanzania(AECA (Asociación Española de Contabilidad y Administración de Empresas) Universidad Politécnica de Cartagena, 2021) Lwesya, Francis; Mwakalobo, Adam Beni Swebe; Mbukwa, Justine N.A variety of factors inhibit the development of MSMEs in African countries, which in turn affects entrepreneurship, job creation and economic transformation. Using cross-sectional data from 250 MSMEs in the Dar es Salaam region, we find in most of the examined variables the positive relationship between the use of non-financial business support services (BDS) and the development of MSMEs in the Dar es Salaam region. However, contrary to expectations, building business linkages and mentoring programs recorded negative relationships with MSMEs development. This is related to restricted capacities stemming from the size of MSMEs compared to large companies and deficiencies in the content of mentoring programs. In addition, the discrepancy between BDS demand and supply as well as the low adoption rate of BDS are associated with the inadequate adaptation of BDS to the needs of MSMEs, high service costs and a lack of qualified service providers. Thus, we argue that the provision of BDS to MSMEs should be demand-driven and that institutions should build on the pre-eminent characteristics of MSMEs when designing business support programs. On the other hand, Government efforts to nurture the development of MSMEs through policies and programs should extend to promoting business linkages between MSMEs and large enterprises.Item Unfolding the potential of the ARIMA model in forecasting maize production in Tanzania(Business Analyst Journal (Emerald Publishing Limited ), 2023) Lwaho, Joseph; Ilembo, BahatiPurpose – This paper was set to develop a model for forecasting maize production in Tanzania using the autoregressive integrated moving average (ARIMA) approach. The aim is to forecast future production of maize for the next 10 years to help identify the population at risk of food insecurity and quantify the anticipatedmaize shortage. Design/methodology/approach – Annual historical data on maize production (hg/ha) from 1961 to 2021 obtained from the FAOSTAT database were used. The ARIMA method is a robust framework for forecasting time-series data with non-seasonal components. The model was selected based on the Akaike Information Criteria corrected (AICc) minimum values and maximum log-likelihood. Model adequacy was checked using plots of residuals and the Ljung-Box test. Findings – The results suggest that ARIMA (1,1,1) is the most suitable model to forecast maize production in Tanzania. The selected model proved efficient in forecasting maize production in the coming years and is recommended for application. Originality/value – The study used partially processed secondary data to fit for Time series analysis using ARIMA (1,1,1) and hence reliable and conclusive results