The Max-Mean Dispersion Problem comprises selecting a subset of elements from a set while maximising the average of a measure of dispersion. We usually compute this measure of dispersion based on some distance metric between the elements of the candidate set. However, in real-world applications, this measure of dispersion could be ill-defined or vague. For example, consider the problem of building a team to execute some kinds of project. We can see the dispersion between the members of the team as the team chemistry, so the coach is interested in maximising this chemistry. In this example, it would be very difficult to compute exactly a dispersion measure for each candidate. This is due to the lack of information about how well the candidates worked together in the past. To cope with imprecise or vague information, in this paper, we propose three mixed integer linear programming models based on possibility, necessity, and credibility measures. To the best of our knowledge, this is the first approach which explicitly considers this type of uncertainty in this optimisation problem.

Portfolio selection is one of the most important financial and investment issues. Portfolio selection seeks to allocate a predetermined capital (wealth) over one or multiple time periods between assets and stocks in a such way that the wealth of investor (portfolio owner) is maximized the risks are minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount Sharpe ratios of portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust POSSIBILISTIC programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model has been tested on 27 companies active in the Tehran stock market. At the end, the results of the model demonestrate the good performance of the robust POSSIBILISTIC programming model.

one of the most important financial and investment issues is Portfolio selection, that seeks to allocate a predetermined capital (wealth) over one or multiple periods between assets and stocks in such a way that the wealth of investor (portfolio owner) is maximized and, Simultaneously, its risk minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount of Sharpe ratios of the portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust POSSIBILISTIC programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model was tested on 27 companies active in the Tehran stock market. In the end, the results of the model demonstrated the good performance of the robust POSSIBILISTIC programming model.

ABSTRACTDuring the last century, ports of Persian Gulf become the most important storage, refining and transportation of crude oil, oil derivation, petrochemical products and also, business activities. Nowadays, due to functional diversity between ports, the impact of port activities on the development of urban spaces will be different, and this issue leads to structural differences of port cities. The purpose of this research is to identify the key VARIABLES affecting the relations and spatial structure of port-city in Dubai as the most thriving and successful port-city in the Persian Gulf. This research is based on deductive reasoning and carried out by analysis of cross effects with secondary data (results of other prominent articles) and also primary data (questionnaire). sampling method is based on purposive sampling and Micmac software was used to analyze the data. Output of Micmac software shows the position of the instability of the system. Therefore, the position of each VARIABLES in the conceptual model can be categorized to driver, linkage, dependent, and autonomous factors. The research findings indicate 4 VARIABLES (like as “income, cost and investmnets in port-city”) can be introduced as a driver factor, 5 VARIABLES (like as “advanced multimodal transportation in the port”) can be introduced as a linkage factor, 6 VARIABLES (like as “quality of living environment and desirable city”) can be introduced as a dependent factor, 3 VARIABLES (like as “environmental protection and sustainable development of the city-port”) can be introduced as an autonomous factor. The rapid development of Dubai can be explained by the purposeful distribution of revenues from trade and tourismExtended AbstractIntroductionDuring the last century, ports of Persian Gulf become the most important storage, refining and transportation of crude oil, oil derivation, petrochemical products and also, business activities. The global increase in oil demand since the 1950s led to the creation of discovery of new oil wells and large industrial areas. With the construction of new oil or gas facilities in the port areas, increasing oil revenues contributed to the countries of the Persian Gulf region and form a new geographical relationship between ports and coastal cities which had an impact on the spatial structure and relation of them. Nowadays, due to functional diversity between ports, the impact of port activities on the development of urban spaces will be different, and this issue leads to structural differences of port cities. In the 1950s, Containerization (container loading technology) was based in some of the world's ports and created a huge transformation in the shipping industry, which had a significant impact on the development of ports. Although the ports of the Persian Gulf have made a significant contribution to the economic growth and physical development of other ports in the world, but few researches have been done on the VARIABLES and factors affecting the development of the spatial structure of the important ports of the Persian Gulf. This region, due to its unique geographical location, has always been considered as a most important corridor in the field of economic and transportation throughout history. Some of the most important energy and commercial ports in this region are: Dubai, Manama, Kuwait, Dammam, Doha, Bushehr, Bandar-Abbas and Assaluyeh. In this regard, the purpose of this research is to identify the key VARIABLES affecting the relations and spatial structure of port-city in Dubai as the most thriving and successful port-city in the Persian Gulf. MethodologyThis research is based on deductive reasoning and carried out by analysis of cross effects with secondary data (results of other prominent articles) and also primary data (questionnaire). The method used in this research is quantitative and the sampling method is based on purposive sampling. the VARIABLES affecting the spatial structure of port-city relations were identified in the form of a review of 31 prominent articles. 25 experts (who had comprehensive knowledge and information about the development process of the city-port of Dubai) participated to determine the effectiveness or influence of VARIABLES. Finally, the output of data analysis was done by the Micmac software. Results and discussionOutput of Micmac software shows the position of the VARIABLES in the diagram that it indicates their status in the system and their role in the dynamics and changes of the system. The method of distribution and dispersion of the VARIABLES in the spatial structure of port-city relations indicates the instability of the system. Therefore, based on the output of the system, the position of each VARIABLES in the conceptual model can be identified in five categories (driver, linkage, dependent, autonomous and regulatory VARIABLES). According to the results, some VARIABLES such as “the changes in the strategic positions” and “geopolitics of port-city”, “the modification of the management method” and “regional planning of the ports”, “the promotion of local governance in the relations between port-city” and “the way of national and international management of ports have been introduced as driver VARIABLES. On the other hand, five VARIABLES consist of “advanced multimodal transportation in the port” and “income, cost and investment in the port-city”, “the contrast and physical integration of the port - city space”, “the development of various industrial and production activities in the ports and their local hinterland” and “their qualities Financial and commercial policies of ports” have been introduced as linkage VARIABLES. Findings of research also shows that some VARIABLES consist of “quality of living environment and desirable city”, “quantity and quality of transit corridors (rail, road and air) to hinterland”, “construction and launching the new port (sea port or dry port)”, “terminal facilities and infrastructure and warehousing”, “conflict or convergence between the city and the port” and “increase in population growth rate and migration to the port - city” categorized as dependent VARIABLES. Three VARIABLES including “cultural and historical background of ports”, “use of cheaper energy, Less-polluted, clean and renewable energies in the city-port” and “environmental protection and sustainable development of the city-port” categorized as autonomous VARIABLES. Finally, a variable with the title of “improvement in management and information technology and development in loading, unloading and storage of commodities” have been introduced as regulatory VARIABLES. The findings of this research have a remarkable similarity with other researches carried out in the field of city-port relation and clearly emphasize the direct impact of the "investment in port-city" in the development of them. For example, Grossmann (2008) emphasized that city-port of Hamburg has become one of the largest ports in Northern Europe during the last few decades due to huge domestic and foreign investment. ConclusionThis research carried out in order to introduce and explain the key VARIABLES affecting the development of the spatial structure of the port-city of Dubai. On this basis, 21 VARIABLES have been extracted by systematic reviews of prominent articles. In the following, 25 experts were selected with the purposive sampling method. Among the 21 VARIABLES extracted, 4 VARIABLES (like as “geopolitics of port-city”) introduced as a driver factor, 5 VARIABLES (like as “advanced multimodal transportation in the port”) introduced as a linkage factor, 6 VARIABLES (like as “quality of living environment and desirable city”) introduced as a dependent factor, 3 VARIABLES (like as “environmental protection and sustainable development of the city-port”) introduced as an autonomous factor. The rapid development of Dubai can be explained by the purposeful distribution of revenues from trade and tourism. A part of these revenues has been directed towards investment in important transportation infrastructures such as airports and ports of this city. These strategies have a wide impact on improving the economic growth of the city and the development of the port in order to adapt with the global trade and advanced technologies. FundingThere is no funding support. Authors’ ContributionAuthors contributed equally to the conceptualization and writing of the article. All of the authors approved the content of the manuscript and agreed on all aspects of the work declaration of competing interest none. Conflict of InterestAuthors declared no conflict of interest. Acknowledgments We are grateful to all the scientific consultants of this paper.

In this paper, a multi- objective quadratic programming (Poss- MOQP) problem with POSSIBILISTIC VARIABLES coefficients matrix in the objective functions is studied. Through the use of b-level sets the Poss- MOQP problem is converted into the corresponding deterministic multi- objective quadratic programming (b-MOQP) problem and hence into the single parametric quadratic programming problem using the weighting method. An extended b-possibly efficient solution is specified. A necessary and sufficient condition for finding such a solution is established. A relationship between the solutions of POSSIBILISTIC levels is constructed. Numerical example is given to clarify the obtained results.

In some complicated datasets, due to the existence of noisy data points and outliers, cluster validity indices can yield con icting results in terms of determining the optimal number of clusters. This paper presents a new validity index for fuzzy-POSSIBILISTIC C-means clustering called Fuzzy-POSSIBILISTIC (FP) index, which works well in the presence of clusters that vary in shape and density. Moreover, like most of the clustering algorithms, Fuzzy-POSSIBILISTIC C-Means (FPCM) is susceptible to some initial parameters. In this regard, in addition to the number of clusters, FPCM requires a priori selection of the degree of fuzziness (m) and the degree of typicality ( ). Therefore, an e cient procedure was presented for determining optimal values of m and  . The proposed approach is evaluated using several synthetic and real-world datasets. Final computational results demonstrate the capabilities and reliability of the proposed approach compared with several well-known fuzzy validity indices in the literature. Furthermore, to clarify the ability of the proposed method in real applications, the proposed method is implemented in microarray gene expression data clustering and medical image segmentation.

Image segmentation is an essential issue in image description and classification. Currently, in many real applications, segmentation is still mainly manual or strongly supervised by a human expert, which makes it irreproducible and deteriorating. Moreover, there are many uncertainties and vagueness in images, which crisp clustering and even Type-1 fuzzy clustering could not handle. Hence, Type-2 fuzzy clustering is the most preferred method. In recent years, neurology and neuroscience have been significantly advanced by imaging tools, which typically involve vast amount of data and many uncertainties. Therefore, Type-2 fuzzy clustering methods could process these images more efficient and could provide better performance. The focus of this paper is to segment the brain Magnetic Resonance Imaging (MRI) in to essential clusters based on Type-2 POSSIBILISTIC C-Mean (PCM) method. The results show that using Type-2 PCM method provides better results.

Disaster relief logistics is one of the major activities in disaster management. The significance of accounting for uncertainty in such context stimulates an interest to develop appropriate decision making tools to cope with uncertain and imprecise parameters in relief logistics system design problems. This paper proposes a multi-objective POSSIBILISTIC non-linear programming model (MOPNLP) to deal with such issues. Our multi-objective model contains: (i) the minimization of the sum of setup cost, transportation costs and shortage costs of commodity in affected area, (ii) the maximization customer satisfaction. The model includes the imprecise nature of some critical parameters such as demands for various types of relief commodities, cost coefficients and capacity levels. To solve the proposed model, a two-phase interactive fuzzy solution approach is developed. Numerical experiments demonstrate the significance and applicability of the developed POSSIBILISTIC model as well as the usefulness of the proposed solution approach for actual decision making problem.

In this paper, a novel risk-based, two-objective (technical and economical) optimal reactive power dispatch method in a wind-integrated power system is proposed which is more consistent with operational criteria.  The technical objective includes the minimization of the new voltage instability risk index. The economical objective includes cost minimization of reactive power generation and active power loss. The proposed voltage instability risk employs a hybrid POSSIBILISTIC (Delphi-Fuzzy)-probabilistic approach that takes into consideration the operator’s experience, the wind speed and demand forecast uncertainties when quantifying the risk index. The decision VARIABLES are the reactive power resources of the system. To solve the problem, the modified multi-objective particle swarm optimization algorithm with sine and cosine acceleration coefficients is utilized. The method is implemented on the modified IEEE 30-bus system. The proposed method is compared with those in the previously published literature, and the results confirm that the proposed risk index is better at estimating the voltage instability risk of the system, especially in cases with severe impact and low probability. In addition, according to the simulation results compared to typical security-based planning, the proposed risk-based planning may increase the security and economy of the system due to better utilization of system resources.