Fuzzy Linear Programming with Interval Type-2 fuzzy constraints

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A STOCHASTIC SIMULATION-BASED HYBRID INTERVAL FUZZY PROGRAMMING APPROACH FOR OPTIMIZING THE TREATMENT OF RECOVERED OILY WATER

In this paper, a stochastic simulation-based hybrid interval fuzzy programming (SHIFP) approach is developed to aid the decision-making process by solving fuzzy linear optimization problems. Fuzzy set theory, probability theory, and interval analysis are integrated to take into account the effect of imprecise information, subjective judgment, and variable environmental conditions. A case study related to oily water treatment during offshore oil spill clean-up operations is conducted to demonstrate the applicability of the proposed approach. The results suggest that producing a random sequence of triangular fuzzy numbers in a given interval is equivalent to a normal distribution when using the centroid defuzzification method. It also shows that the defuzzified optimal solutions follow the normal distribution and range from 3,000-3,700 tons, given the budget constraint (CAD 110,000-150,000). The normality seems to be able to propagate throughout the optimization process, yet this interesting finding deserves more in-depth study and needs more rigorous mathematical proof to validate its applicability and feasibility. In addition, the optimal decision variables can be categorized into several groups with different probability such that decision makers can wisely allocate limited resources with higher confidence in a short period of time. This study is expected to advise the industries and authorities on how to distribute resources and maximize the treatment efficiency of oily water in a short period of time, particularly in the context of harsh environments

Comparaison d'intervalles flous pour la programmation multi-objectifs dans l'incertain

Depuis plusieurs années, on considère que les deux sources d'incertitude principales sont le manque d'informations et la variabilité des phénomènes. On modélise alors les informations soit par des distributions de probabilité (informations aléatoires) soit par des ensembles flous (informations incomplètes). Dans pas mal de situations, les deux sources d'incertitude peuvent se trouver combinées. Les variables aléatoires floues proposent un bon formalisme pour cette combinaison. Ces dernières années, des travaux ont été réalisés dans la prise en compte simultanée du flou et de l'aléa en programmation mathématique. Ce travail s'évertue à faire avancer l'état de l'art dans ce domaine en proposant des résultats concernant les variables aléatoires floues dans le but de développer des approches pour la résolution d'un programme linéaire multi-objectif s en présence de ces dernières. On a alors, en premier lieu, étendu aux variables aléatoires floues, deux concepts connus en théorie de la décision, à savoir la dominance stochastique et la préférence statistique en les combinant avec des méthodes de comparaison d'intervalles flous, ces dernières généralisant les ordres d'intervalles. On a envisagé trois façons de comparer les intervalles flous : vus comme des distributions de possibilité ordinales, comme intervalles graduels ou comme intervalles aléatoires consonants. On a, en second lieu, généralisé conjointement, aux variables aléatoires floues, les deux variantes du "chance constrained programming", l'une avec des coefficients flous due à Dubois, l'autre avec des coefficients aléatoires due à Charnes et Cooper selon trois versions : (i) en combinant probabilité et possibilité, ou probabilité et nécessité (version 1) ; (ii) en combinant probabilité et indices scalaires de comparaison de quantités floues (version 2) ; et (iii) en combinant "chance-constrained programming" et comparaisons d'intervalles aléatoires (un intervalle flou peut être vu comme un intervalle aléatoire) (version 3). Dans le cas où les coefficients des contraintes sont purement flous ou purement aléatoires, se réduit à "chance constrained programming" avec des coefficients flous ou "chance constrained programming" avec des coefficients aléatoires. Cette généralisation permet de développer des approches pour la programmation linéaire multi-objectifs en présence de variables aléatoires floues normales au sens de Shapiro, discrètes, normales de type L-R ou discrètes de type L-R. On a, ensuite, établi les conditions de convexité des ensembles des solutions admissibles résultant de l'application de cette méthode à des contraintes floues stochastiques. C'est en quelque sorte une extension aux variables floues des conditions de convexité des ensembles des solutions admissibles résultant de l'application de "chance constrained programming" due à Charnes et Cooper en programmation linéaire stochastique. Et en fiin on a considéré des programmes linéaires multi-objectifs en présence de variables aléatoires floues discrètes, normales au sens de Shapiro, discrètes de type L-R ou normales de type L-R, on distingue quatre cas, selon que les coefficients des objectifs sont déterministes, flous, aléatoires ou flous aléatoires. Pour la résolution, on peut appliquer pour tous les cas, "chance constrained programming" avec des coefficients flous aléatoires. Ou combiner selon le cas considéré, les techniques de la programmation linéaire multi-objectifs déterministe, floue ou stochastique entre elles ou avec "chance constrained programming" avec des coefficients flous aléatoires.In the recent years, it has been acknowledged that the two principal sources of uncertainty are the lack of information and the variability of phenomena. Then, one represents the information by probability distributions (random information ) or by fuzzy sets (incomplete information). In quite a lot of situations, both sources of uncertainty can be combined. Fuzzy random variables propose a good formalism for this combination. These last years, works were realized in the simultaneous consideration of the fuzziness and the randomness in mathematical programming. This work makes every effort to advance the state of the art in this domain by proposing results concerning the comparison of fuzzy random variables with the aim in developing approaches for the resolution of multiobjective linear programming problem in the presence of fuzzy random variables. Then, firstly, one extends to fuzzy random variables two concepts known in decision theory, namely stochastic dominance and statistical preference, by combining them with methods of comparison of fuzzy intervals which generalize interval orders. One has envisaged three manners to compare fuzzy intervals : viewed as ordinal possibilty distributions, as gradual intervals or as consonant random intervals. One has, secondly, generalized jointly, to fuzzy random variables, the two variants of chance constrained programming, the one with fuzzy coefficients due to Dubois, the other with random coefficients due to Charnes and Cooper, according to three versions :(i) bycombining probability and possibility, or probability and necessity (version 1) ; (ii) by combining probability and scalar indices for comparing fuzzy quantities (version 2) ; and (iii) by combining chance-constrained programming and random interval comparisons (a fuzzy interval can be viewed as a random interval) (version 3). In the case where the coefficients of constraints are purely fuzzy or purely random, chance constrained programming with fuzzy random coefficients reduces to chance constrained programming with fuzzy coefficients or to chance constrained programming with random coefficients. This generalization allows to develop approaches for solving multiobjective linear programming problem in presence of fuzzy random variables, which can be normal as defined by Shapiro, discrete, normal of type L-R, or discrete of type L-R. One has, thereafter, established the conditions of convexity of the set of feasible solutions resulting from the application of this method to fuzzy stochastic constraints. It is in a way, an extension, to fuzzy random variables, of the conditions of convexity of the set of feasible solutions resulting from the application of chance constrained programming due to Charnes and Cooper in stochastic linear programming. Finally, one has proposed multiobjective linear programming problem in presence of fuzzy random variables which can be discrete, normal as defined by Shapiro, discrete of type L-R or normal of type L-R. One distinguishes four cases, as the coefficients of objectives are determinist, fuzzy, random or fuzzy random. To solve these problems, one can apply to all the cases, chance constrained programming with fuzzy random coefficients, or combine the techniques of deterministic, fuzzy or stochastic multiobjective linear programming between them, or with chance constrained programming with fuzzy random coefficients

A robust fuzzy possibilistic AHP approach for partner selection in international strategic alliance

The international strategic alliance is an inevitable solution for making competitive advantage and reducing the risk in today’s business environment. Partner selection is an important part in success of partnerships, and meanwhile it is a complicated decision because of various dimensions of the problem and inherent conflicts of stockholders. The purpose of this paper is to provide a practical approach to the problem of partner selection in international strategic alliances, which fulfills the gap between theories of inter-organizational relationships and quantitative models. Thus, a novel Robust Fuzzy Possibilistic AHP approach is proposed for combining the benefits of two complementary theories of inter-organizational relationships named, (1) Resource-based view, and (2) Transaction-cost theory and considering Fit theory as the perquisite of alliance success. The Robust Fuzzy Possibilistic AHP approach is a noveldevelopment of Interval-AHP technique employing robust formulation; aimed at handling the ambiguity of the problem and let the use of intervals as pairwise judgments. The proposed approach was compared with existing approaches, and the results show that it provides the best quality solutions in terms of minimum error degree. Moreover, the framework implemented in a case study and its applicability were discussed