Necessity Measures Research Articles

A Necessity-Based Optimization Approach for Closed-Loop Logistics Considering Carbon Emission Penalties and Rewards under Uncertainty

The recycling of waste products can bring enormous economic and environmental benefits to supply chain participants. Under the government’s reward and punishment system, the manufacturing industry is facing unfolded pressure to minimize carbon emissions. However, various factors related to the design of closed-loop logistics networks are uncertain in nature, including demand, facility capacity, transportation cost per unit of product per kilometer, landfill cost, unit carbon penalty cost, and carbon reward amount. As such, this study proposes a new fuzzy programming model for closed-loop supply chain network design which directly relies on fuzzy methods based on the necessity measure. The objective of the proposed optimization model is to minimize the total cost of the network and the sum of carbon rewards and penalties when selecting facility locations and transportation routes between network nodes. Based on the characteristics of the problem, a genetic algorithm based on variant priority encoding is proposed as a solution. This new solution encoding method can make up for the shortcomings of the four traditional encoding methods (i.e., Prüfer number-based encoding, spanning tree-based encoding, forest data structure-based encoding, and priority-based encoding) to speed up the computational time of the solution algorithm. Several alternative solution approaches were considered to evaluate the proposed algorithm including the precision optimization method (CPLEX) and priority-based encoding genetic algorithm. The results of numerous experiments indicated that even for large-scale numerical examples, the proposed algorithm can create optimal and high-quality solutions within acceptable computational time. The applicability of the model was demonstrated through a sensitivity analysis which was conducted by changing the parameters of the model and providing some important management insights. When external parameters change, the solution of the model maintains a certain level of satisfaction conservatism. At the same time, the changes in the penalty cost and reward amount per unit of carbon emissions have a significant impact on the carbon penalty revenue and total cost. The results of this study are expected to provide scientific support to relevant supply chain enterprises and stakeholders.

An elementary belief function logic

ABSTRACT Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and plausibility functions as well as between upper and lower probabilities extend the duality between possibility and necessity modalities to the graded environment. It has been shown that the all-or-nothing version of possibility theory can be exactly captured by a minimal epistemic logic (MEL) that uses a very small fragment of the KD modal logic, without resorting to relational semantics. Independently, a belief function logic has been obtained by extending the modal logic S5 to probabilistic graded modalities using Łukasiewicz logic, albeit using relational semantics. This paper shows that a simpler belief function logic can be devised by adding Łukasiewicz logic on top of MEL. It allows for a more natural semantics in terms of Shafer basic probability assignments.

A new fuzzy DEA network based on possibility and necessity measures for agile supply chain performance evaluation: A case study

With respect to the necessity (Nec) measure, suggesting by Dubois and Prade, there is a dearth of any procedure or formula to deal with equality chance constraints. Therefore, this study attempted to introduce (Nec) and possibility (Pos) equality constraints in a real-case network non-oriented slack based model problem via agile supply chain (ASC) theory. The efficiency of different levels of agility of a dairy supply chain (SC), using a new fuzzy network Date Envelopment Analysis slack based model (FNDEA-SBM) on the basis of (Pos)/(Nec) measures, has been measured in this paper. The measurement took place in a multi-stage process. Since the agility features were rather qualitative in nature, the measures were likely to be delineated subjectively using linguistic expressions and fuzzy data. The application of (Pos)/(Nec) measures and different confidence levels made decision makers capable of getting information of all efficiency and sub efficiency scores through optimistic-pessimistic lenses and taking appropriate decisions on the basis of different optimistic-pessimistic points of view and confidence levels. The validity of the suggested approach was demonstrated through a real-life case study related to Iranian top twenty dairy firms. The results indicated the success of the suggested approach and computations were straightforward.

Improving semantic information retrieval by combining possibilistic networks, vector space model and pseudo-relevance feedback

To improve the performance of information retrieval systems (IRSs), we propose in this article a novel approach that enriches the user’s queries with new concepts. Indeed, query expansion is one of the best methods that plays an important role in improving searches for a better semantic information retrieval. The proposed approach in this study combines possibilistic networks (PNs), the vector space model (VSM) and pseudo-relevance feedback (PRF) to evaluate and add relevant concepts to the initial index of the user’s query. First, query expansion is performed using PN, VSM and domain knowledge. PRF is then exploited to enrich, in a second round, the user’s query by applying the same approach used in the first expansion step. To evaluate the performance of the developed system, denoted conceptual information retrieval model (CIRM), several experiments of query expansion are performed. The experiments carried out on the OHSUMED and Clinical Trials corpora showed that using the two measures of possibility and necessity combined the cosinus similarity and PRF improves the query expansion process. Indeed, the improvement rate of our approach compared with the baseline is +28, 49% in terms of P@5.

The First Evidence of Microplastics Occurrence in Greater Pipefish (Syngnathus acus Linnaetabus, 1758) in the Black Sea

Microplastics (MPs) occurrence in greater pipefish Syngnathus acus was assessed in the Black Sea for the first time. MPs were found in 21 % of total pipefish examined. MPs were mainly fibres in shape (89 %), black in colour (52 %) and 0.2- 1 mm (52 %) in size. The mean MP concentration was 0.30 mp. fish-1 (considering all the fish analysed) and was 1.38 mp. fish-1 (considering the fish that ingested them). The frequency of MP occurrence in male pipefish was higher (23.5 %) compared to females (20.7%) and immatures (16.7 %). 91.7 % of the polymers found were synthetic with the polyethylene terephthalate (PET) (29%) being the most common polymers. FTIR spectroscopy also confirmed the presence of the plastic-related compounds, butyl stearate (BS) and glyceraldehyde unnatural form (GA) in the analysed samples. Our results show that S. acus, which is an ecologically important demersal fish, is contaminated by MPs in the Black Sea and that there is an urgent assessment to better understand the environmental fate of MPs in the Black Sea and taking necessity measures to reduce the amount of plastics entering this basin.

Designing an integrated humanitarian logistics network for the preparedness and response phases under uncertainty

In the current paper, a model of possibilistic location-allocation is proposed for designing a multi-period bi-objective humanitarian logistics network that pursues a reduction in the total cost and maximizes the total network coverage. The model considers the inventory management of perishable relief items and the flow of affected and wounded people in pre-disaster and post-disaster phases, simultaneously. Moreover, wounded people are categorized according to the injury severity. The uncertainty associated with key parameters is also addressed. To handle the uncertainty, a fuzzy chance-constrained programming method originated in the Me measure is used. The purpose of this measure is to prevent the extreme attitudes of the decision maker by considering the combination of possibility and necessity measures and using the optimistic-pessimistic parameter. This paper presents a solution procedure derived from a fuzzy interactive programming approach and two meta-heuristic algorithms, imperialist competitive algorithm and invasive weed optimization, so as to solve the study model. As for the validation of the proposed model and solution procedures, a number of test problems have been generated. A real-life case study is also implemented to instantiate whether the proposed model is applicable or not.

An Extended Necessity Measure Maximisation Incorporating the Trade-Off between Robustness and Satisfaction in Fuzzy LP Problems

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker’s requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach.

On some bridges to complex evidence theory

Complex evidence theory, an extension of Dempster–Shafer evidence theory, is a generalized evidence theory based on complex values, which has been widely used to solve decision making of uncertainty information. In order to make a step development based on previous researches, we set out to make a connection between CET and other uncertainty theories like possibility theory, modal logic, fuzzy set theory and probability theory. With a restricted condition of a special generalized consonant belief function, it is found that possibility and necessity measure can be regarded as generalized plausibility measure and belief measure in possibility theory, and the standard interpretation of fuzzy sets in complex evidence theory is obtained by summing up the experience of predecessors and modifying the upper bound of fuzzy sets in this paper. In addition, we established the relationship between generalized plausibility, belief function and modal logic, and elaborate how to explain the complex basic belief distribution with the general semantics of modern modal logic. Finally, the transformation algorithm between complex basic belief assignment and probability distribution is proposed by using the transformation of uncertainty invariance principle, and some properties of them are derived.

Multi-objective quasi oppositional Jaya algorithm to solve multi-objective solid travelling salesman problem with different aspiration level

Multi-Objective Travelling Salesman Problem (MOTSP) is one of the most crucial problems in realistic scenarios and is difficult to solve by classical methods. However, it can be solved by evolutionary methods. This paper presents an Aspiration Level based Multi-Objective Quasi Oppositional Jaya (AL-based MOQO-Jaya) Algorithm for solving the Multi-Objective Solid Travelling Salesman Problem (MOSTSP). Furthermore, fuzzy judgment was characterised by utilizing the possibility and necessity measures to allow the decision-maker (DM) for optimising different scenarios of the Fuzzy Multi-Objective Solid Travelling Salesman Problem (FMOSTSP). A numerical illustration is provided for 10, 80, 100 and 120 cities, and sensitivity analysis is performed with different shape parameters and aspiration levels. Further the results are compared by CPLEX optimizer and Hybrid GA. The results obtained by AL-based MOQO Jaya are more efficient, the run time of AL-based MOQO is 5.8667, 40.9115, 58.4789 and 60.6882 seconds for 10, 80,100 and 120 cities for FMOSTSP which is quite less as compared to CPLEX and Hybrid GA. To access the performance of the proposed method coverage and hypervolume are calculated. This paper concludes that developed approach has solved MOSTSP and FMOSTSP efficiently with an effective output and provides alternative solutions for decision-making to DM.

Qualitative capacities: Basic notions and potential applications

Qualitative capacities are set functions valued on a finite chain, increasing in the wide sense with respect to set inclusion. This paper exploits formal analogies between qualitative capacities and numerical capacities: we first recall qualitative counterparts to Möbius transforms, game-theoretic core, and conjugate set functions. However, in the qualitative setting, possibility measures play the same role as probability measures in the quantitative setting. Then possibility and necessity measures sometimes do not convey the same type of information. This situation creates difficulties to interpret qualitative capacities and related notions inspired from the quantitative setting. In particular, we propose three different ways of using qualitative capacities: either as bounds on ill-known possibility or necessity measures, or as tools to express the decision maker attitude in qualitative criteria under uncertainty, or yet qualitative counterparts of belief functions that handle both incompleteness and inconsistency of pieces of information stemming from several sources. In the latter framework possibility and necessity measures do not represent the same type of information. We define order relations between capacities with a view to compare them in terms of informational contents. We also study a counterpart of Dempster rule of combination in the qualitative setting. We compare several capacity combination rules in the framework of an information fusion problem. Finally, we address the problem of eliciting qualitative capacities based on human-originated information.

ALLOCATION OF CAPITAL INVESTMENTS OF AN OIL COMPANY BASED ON INDEPENDENT OPPORTUNITY INFORMATION

To solve the problem of investment allocation with optimization of the total level of return on investment for projects under conditions of risk associated with uncertainty of project income, a linear combination with non-negative coefficients of two loss-making models was used: the model of the usual minimax loss-making and the model of the minimax loss-making level. The problem of probabilistic programming obtained as a result of this combination, provided that the probabilistic variables characterizing the profitability of investments in projects are independent (unrelated), is reduced to a linear programming problem. The solution of this problem by the simplex method gives a vector of the equity distribution of investments that determine the total return of investments by the criterion of the minimum of the loss function. On the basis of the proposed approach to the optimal solution of the problem of investment allocation, an algorithm for project investment planning has been developed using a database of invested and returned funds for projects in previous planning periods, according to which distributions of possible investment returns are modeled. The numerical implementation of the algorithm is illustrated by the example of investment planning in an oil company for oil and gas production projects. Keywords: probability programming, investments, investment portfolio, minimax criterion, loss-making function, return on investment, income, concentrated distribution, probability distribution, measure of opportunity, measure of necessity, fractile model, probability variable, fuzzy variable membership function.

Distributionally robust possibilistic optimization problems

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is used to model imprecise probabilities. In one of interpretation, a possibility distribution (a membership function of a fuzzy set) in the set of coefficient realizations induces a necessity measure, which in turn defines a family of probability distributions in this set. The distributionally robust approach is then used to transform the imprecise constraints into deterministic counterparts. Namely, the uncertain left-hand side of each constraint is replaced with the expected value with respect to the worst probability distribution that can occur. It is shown how to represent the resulting problem by using linear or second-order cone constraints. This leads to problems which are computationally tractable for a wide class of optimization models, in particular for linear programming.

Sustainable agricultural water management incorporating inexact programming and salinization-related grey water footprint

In arid and semi-arid regions, improper irrigation activities not only exacerbate water shortages, but also lead to environmental pollution such as soil salinization that hinders crop growth and agricultural sustainability. There has been a lack of agricultural water management tools that could support agricultural water management with salinization-related grey water footprints being considered and associated uncertainties being addressed. In this study, salinization-related grey water footprints were measured through accounting for relationships among irrigation, soil salinity, evapotranspiration and crop yield, and then incorporated into an agricultural water management model for supporting environmentally sound irrigation decisions. Such an agricultural water management model was also characterized by a newly proposed generalized fuzzy interval fractional programming (GFIFP) method that could address ratio problems of two objectives and dual uncertainties. The developed methodology coupling the GFIFP method and grey water footprints was applied to an irrigation region in northwestern China where water scarcity and soil salinization hindered local development. Five credibility levels corresponding to decision makers' varied satisfactory degrees over water availability, and nine weight coefficients of possibility and necessity measures were considered. Results showed that, in order to reduce negative environmental impacts while increasing economic benefits, more irrigation water should be allocated to wheat and sunflower rather than corn. When the credibility level is 0.5 and weight coefficient is 0.9, the system efficiency would be the highest. Compared to the benchmark year of 2018, this scenario would generate [0.330, 6.647] billion yuan more benefits and [16.0, 133.9] million m3 less grey water footprints. Compared to three conventional approaches, GFIFP could provide decisions with more flexibility and less environmental impacts. The developed approach could also be applied to agricultural water management problems in other areas aiming at reducing grey water footprints and enhancing environmental benefits under uncertainty.

Fuzzy Random Bimatrix Games Based on Possibility and Necessity Measures

In this study, we formulate bimatrix games with fuzzy random payoffs, and introduce equilibrium solution concepts based on possibility and necessity measures. It is assumed that each player has linear fuzzy goals for his/her payoff. To obtain equilibrium solutions based on the possibility and necessity measures, we propose two algorithms in which quadratic programming problems are solved repeatedly until equilibrium conditions are satisfied.

Designing of higher order information granules through clustering heterogeneous granular data

This study is devoted to the generalization of information granules by forming higher order, namely, order-2 information granules. Information granules are semantically meaningful entities, which play a central role in knowledge representation and system modeling in the framework of Granular Computing. The encountered information granules could exhibit significant heterogeneity because of the diversified formal formalisms. To facilitate an effective generalization of heterogeneous granular data when using clustering algorithms, an efficient scheme has been proposed to form a unified representation of various types of granular data by using Possibility–necessity measures. Once the clustering process has been completed in the possibility–necessity feature space, the higher order information granules come as results of decoding by involving the possibility–necessity metrics and fuzzy relational calculus. The extent to which the higher order information granules are supported by the granular data present at a lower level of hierarchy is quantified in terms of the membership degrees obtained in the clustering process. Experimental studies concerning a series of publicly available datasets coming from UCI and KEEL machine learning repositories are carried out in this study.

Fuzzy multiple objective fractional optimization in rough approximation and its aptness to the fixed-charge transportation problem

This article presents a multiple objective fractional fixed-charge transportation problem (MFFTP) in a rough decision-making framework. A transformation procedure is modified to convert non-linear multi-objective transportation problem to its linear version. The parameters of the designed model are considered to be fuzzy. We employ separate kinds of fuzzy scale, i.e., possibility, credibility and necessity measures, to deal with the fuzzy parameters. Using the fuzzy chance-constrained rough approximation (FCRA) technique, we extract the more preferable optimal solution from our suggested MFFTP. The initial result is compared with that of the robust ranking (RR) technique. We also use the theory of rough sets for expanding as well as dividing the feasible domain of the MFFTP to accommodate more information by considering two approximations. Employing these approximations, we introduce two variants, namely, the lower approximation (LA) and the upper approximation (UA), of the suggested MFFTP. Finally, by using these models, we provide the optimal solutions for our proposedproblem. We also associate our MFFTP with a real-world example to showcase its applicability as well as performance. Our core concept of this article is that it tackles an MFFTP using two separate kinds of uncertainty and expands its feasible domain for optimal solutions. Optimal solutions of the designed model (obtained from FCRA technique) belong to two separate regions, namely, “surely region” and “possible region”. The optimal solution which belongs to the “surely region” is better (as these are minimum values) than the one in the “possible region” and other cases. An interpretation of our approach along with offers about the intended future research work are provided at last.

A novel model for multi-criteria assessment based on BWM and possibilistic chance-constrained programming

The best-worst method (BWM) is one of the most important methods for determining the weights of criteria or options in multi-criteria decision-making (MCDM) and has attracted the attention of many researchers due to its advantages such as fewer numbers of comparisons and higher consistency rate. Given that real-world decision making is often associated with uncertainty, in this study several fuzzy linear programming models have been developed using trapezoidal fuzzy numbers for BWM that can calculate the optimal weights of criteria. The proposed models are based on three measures of possibility, necessity, and credibility, which are parts of possibilistic chance-constrained programming (PCCP). Development of BWM based on possibilistic distribution allows the decision-maker (DM) to take into account uncertainties in the calculation of weights as well as include his optimistic, pessimistic, and intermediate attitudes in determining the weight of decision criteria. The possibility approach reflects the DM's optimistic view of the issue. The necessity approach is used in situations where the DM prefers a pessimistic view, and the credibility approach indicates that DM has an intermediate view between optimistic and pessimistic views, or in other words, considers an intermediate approach between possibility and necessity approaches. Finally, the feasibility and effectiveness of the proposed approaches were tested using two numerical examples and the sensitivity of the results was analyzed for different values of uncertainty (alpha parameter). Also, by analyzing the coefficient of variation, it was found that the results of the proposed models had very little dispersion for different values of uncertainty, and this confirmed the validity of the results. Examining the results of the proposed models revealed that the possibility approach provides more robust results than other approaches when the levels of confidence of the decision-makers are changed.

Некоторые вопросы категории «обязанность» в трудовом праве

Responsibility is an essential element of the development and functioning of society and human beings as an integral part of society. Therefore, a comprehensive scientific study of the category «duty» is of particular importance in the study of the fundamental rights and freedoms of the individual. The article discusses the various approaches of representatives of different branches of law to the definition of the concept of duty as a legal category, its essence and content. The multiplicity of theoretical views on the study of this category of law is usually reduced to two understandings of the definition of duty through a measure of due conduct and a measure of necessity. It is important to note that traditionally the category of duty was considered and studied by researchers, together with a theoretical and practical analysis of human rights and freedoms. «Duty» as a category of labour law has its own distinctive characteristics and characteristics.

Research on Intelligent Supply Chain Management Under Unconventional Emergencies

The harm of unconventional emergencies is increasingly prominent, which seriously restricts the sustainable development of society. Therefore, how to effectively deal with all kinds of unconventional emergencies and improve the ability of emergency management in the face of unconventional emergencies has attracted extensive attention from all walks of life. Therefore, the establishment of a sound emergency intelligent supply chain system is an important means to speed up the development of China’s emergency industry and enhance the emergency support capacity of government. This paper mainly analyzes the problems existing in China’s logistics system under unconventional emergencies, and puts forward the necessity and specific measures of introducing intelligent supply chain under unconventional emergencies.

Success of Orientation and Mobility of Person’s With Visual Impairment in University of Calabar, Cross River State

The paper is on success of orientation and mobility of persons with visual impairment in university of Calabar, Cross River State. This paper discussed about how Orientation and Mobility (OM) is a course that concerns instructing individuals who are visually impaired for safe and effective travel through their environment. The meaning of Orientation and Mobility (OM) was also explained and the important as the ability to move safely, efficiently, and effectively from one place to another regardless of age or existence of the problem. Different types of mobility skills were outlined as a self-protective measure to safely explore any unfamiliar space. The paper advised that it is important for person with visual impairment to learn how to move safely in both familiar and unfamiliar environments. And the paper concludes that Orientation and Mobility (OM) is a necessity measure to enable graceful movement.