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| | If you are definitely severe about becoming a chef then you will will need to make positive that you are fully ready to do so. This indicates that you will need all of the equipment and clothing needed to work in a fully functioning kitchen. The cost of this serrated knife is about the very same as any other superior high quality kitchen knives in the marketplace, but what tends to make this serrated bread knife stand out from the rest for me is its razor sharp blade , good balance, funky modern day appears, overall durability and the dimple impact handle is simple to keep clean and presents wonderful grip. Chef Knives are truly a multi-purpose kitchen knife that can be made use of and utilized for many different tasks in the kitchen.<br><br><br><br>When you loved this article and you wish to receive much more information with regards to [http://www.thebestkitchenknivesreviews.com/best-steak-knives-reviews/ mundial steak knives review] i implore you to visit the webpage. In particular if you are new to pumpkin carving this is the tool set you require and I whole heartedly agree with what was said on the net about them: if you purchased them seperately every of them would price $30 and now you can have the complete set for that cost. What's far more this set will not sit in your draw forgotten for the rest of the year, you can use them all the time. If you have a set like this and you consider I've missed the mark, take your set by an estate silver shop or old line jeweler.<br><br>With so numerous choices out there, we can assist you figure out the best knife for you! I don't mind this at all, but he took my big, heavy chef's knife amongst other folks, and I am fond of it both for its high-quality and for sentimental worth. I appear forward to getting in a position to use the ideal knife in town when it arrives, just after I have stressed to my [http://Www.Ehow.com/search.html?s=husband husband] that as substantially as he might study to appreciate it, it should remain property.<br><br>Even believed the pocket knives are quite easy and swift to open none of them fit the definition of a switchblade defined by the U.S. Switch Blade Knife Act of 1958. Columbia River Knife & Tool make great pocket knives, hunting knives and knives for the military. This attractive knife block set is the crowning glory of the modern day Stellar FM range. Test out some knives at a knife or hobby shop or shop.<br><br>In his manual, Chad Ward implies that if you are going to invest in a knife established from a retailer with very a lot of open up stock, they could be willing to swap in knives from the incredibly exact same brand. Wusthof Knife Sets (Simple) Prior to we get commenced, it can be worthy of examining some kitchen knife record. Rather a few men and women now are unaware of the great upheaval that the kitchen region knife marketplace has undergone in the final ten years.<br><br>If you happen to be not into tracking down the ideal individual knives and just want decent cutting energy, a set can unquestionably be a nice way to go. Despite the fact that you could spend thousands on a knife set, in my investigation I identified it really is not worth dropping additional than $350 to $400. In reality, in their overview of knife sets, America's Test Kitchentwo a la carte sets comprised of distinct brands. Rates of most popular knife sets are really [http://Www.answers.com/topic/expensive expensive].<br><br>For the price tag, we never consider you can beat the Victorinox Rosewood Straight Edge Steak Knife Set That said, if you want a heavier, additional luxurious knife Shun Steak Knives Review set, we'd go with the Wusthof Classic Ikon Steak Knives ($290 for four). Forged in Solingen, Germany, these high-carbon stainless steel knives have lovely contoured handles and have been the finest balanced of all the knives we tested. We tested 4 serrated knives, and 1 micro-serrated knife (at front). |
| The '''preference ranking organization method for enrichment of evaluations''' and its descriptive complement '''geometrical analysis for interactive aid''' are better known as the '''Promethee and Gaia'''<ref name="Figueria">{{Cite book|title=Multiple Criteria Decision Analysis: State of the Art Surveys|author=J. Figueira, S. Greco, and M. Ehrgott|year=2005|publisher=Springer Verlag }}</ref> methods.
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| Based on mathematics and sociology, the Promethee and Gaia method was developed at the beginning of the 1980s and has been extensively studied and refined since then.
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| It has particular application in decision making, and is used around the world in a wide variety of decision scenarios, in fields such as business, governmental institutions, transportation, healthcare and education.
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| Rather than pointing out a "right" decision, the Promethee and Gaia method helps decision makers find the alternative that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, identifying and quantifying its conflicts and synergies, clusters of actions, and highlight the main alternatives and the structured reasoning behind.
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| == History==
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| The basic elements of the Promethee method have been first introduced by Professor Jean-Pierre Brans (CSOO, VUB Vrije Universiteit Brussel) in 1982.<ref name="Brans">{{Cite news|author=J.P. Brans|title=L’ingénierie de la décision: élaboration d’instruments d’aide à la décision. La méthode PROMETHEE.|year=1982|publisher=Presses de l’Université Laval}}</ref> It was later developed and implemented by Professor Jean-Pierre Brans and Professor Bertrand Mareschal (Solvay Brussels School of Economics and Management, ULB Université Libre de Bruxelles), including extensions such as GAIA.
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| The descriptive approach, named Gaia,<ref name="Gaia">{{Cite news|title=Geometrical representations for MCDA. the GAIA module|author=B. Mareschal, J.P. Brans|year=1988|publisher=European Journal of Operational Research}}</ref> allows the decision maker to visualize the main features of a decision problem: he/she is able to easily identify conflicts or synergies between criteria, to identify clusters of actions and to highlight remarkable performances.
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| The prescriptive approach, named Promethee,<ref name="Promethee">{{Cite news|title=A preference ranking organisation method: The PROMETHEE method for MCDM|author=J.P. Brans and P. Vincke|publisher=Management Science|year=1985}}</ref> provides the decision maker with both complete and partial rankings of the actions.
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| Promethee has successfully been used in many decision making contexts worldwide. A non-exhaustive list of scientific publications about extensions, applications and discussions related to the Promethee methods<ref name="applications">{{Cite news|author=M. Behzadian, R.B. Kazemzadeh, A. Albadvi and M. Aghdasi|title=PROMETHEE: A comprehensive literature review on methodologies and applications|year=2010|publisher=European Journal of Operational Research}}</ref> was published in 2010.
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| == Uses and applications ==
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| While it can be used by individuals working on straightforward decisions, the Promethee & Gaia is most useful where groups of people are working on complex problems, especially those with several multi-criteria, involving a lot of human perceptions and judgments, whose decisions have long-term impact. It has unique advantages when important elements of the decision are difficult to quantify or compare, or where collaboration among departments or team members are constrained by their different specializations or perspectives.
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| Decision situations to which the Promethee and Gaia can be applied include:
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| * [[Choice]] – The selection of one alternative from a given set of alternatives, usually where there are multiple decision criteria involved.
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| * [[Prioritization]] – Determining the relative merit of members of a set of alternatives, as opposed to selecting a single one or merely ranking them.
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| * [[Resource allocation]] – Allocating resources among a set of alternatives
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| * [[Ranking]] – Putting a set of alternatives in order from most to least preferred
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| * [[Conflict resolution]] – Settling disputes between parties with apparently incompatible objectives
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| <br>
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| The applications of Promethee and Gaia to complex multi-criteria decision scenarios have numbered in the thousands, and have produced extensive results in problems involving planning, resource allocation, priority setting, and selection among alternatives. Other areas have included forecasting, talent selection, and tender analysis.
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| <br> | |
| Some uses of Promethee and Gaia have become case-studies. Recently these have included:
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| * Deciding which resources are the best with the available budget to meet SPS quality standards (STDF – [[WTO]]) [See more in External Links]
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| * Selecting new route for train performance ([[Italferr]])[See more in External Links]
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| == The mathematical model ==
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| === Assumptions ===
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| Let <math>A=\{a_1 ,..,a_n\}</math> be a set of n actions and let <math>F=\{f_1 ,..,f_q\}</math> be a consistent family of q criteria. Without loss of generality, we will assume that these criteria have to be maximized.
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| The basic data related to such a problem can be written in a table containing <math>n\times q</math> evaluations. Each line corresponds to an action and each column corresponds to a criterion.
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| <math>
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| \begin{array}{|c|c|c|c|c|c|c|} \hline
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| & f_{1}(.) & f_{2}(.) & ... & f_{j}(.) & ... & f_{q}(.) \\ \hline
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| a_{1} & f_{1}(_a{1}) & f_{2}(a_{1}) & ... & f_{j}(a_{1}) & ... & f_{q}(a_{1}) \\
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| \hline
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| a_{2} & f_{1}(a_{2}) & f_{2}(a_{2}) & ... & f_{j}(a_{2}) & ... & f_{q}(a_{2}) \\ \hline
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| ... & ... &... & ... & ... & ... & ... \\ \hline
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| a_{i} & f_{1}(a_{i}) & f_{2}(a_{i}) & ... & f_{j}(a_{i}) & ... & f_{q}(a_{i}) \\ \hline
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| ... & ... & ... & ...& ... & ... & ... \\ \hline
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| a_{n} & f_{1}(a_{n}) & f_{2}(a_{n}) & ...& f_{j}(a_{i}) & ...&
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| f_{q}(a_{n})
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| \\ \hline
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| \end{array}
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| </math>
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| === Pairwise comparisons ===
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| At first, [[pairwise comparisons]] will be made between all the actions for each criterion:
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| :<math>d_k(a_i,a_j)=f_k(a_i)-f_k(a_j)</math>
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| <math>d_k(a_i,a_j)</math> is the difference between the evaluations of two actions for criterion <math>f_k</math>. Of course, these differences depend on the measurement scales used and are not always easy to compare for the decision maker.
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| === Preference Degree ===
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| As a consequence the notion of preference function is introduced to translate the difference into a unicriterion preference degree as follows:
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| :<math>\pi_k(a_i,a_j)=P_k[d_k(a_i,a_j)]</math>
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| where <math>P_k:\R\rightarrow[0,1]</math> is a positive non-decreasing preference function such that <math>P_j(0)=0</math>. Six different types of preference function are proposed in the original Promethee definition. Among them, the linear unicriterion preference function is often used in practice for quantitative criteria:
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| :<math>P_k(x) \begin{cases} 0, & \text{if } x\le q_k \\ \frac{x-q_k}{p_k-q_k}, & \text{if } q_k<x\le p_k \\ 1, & \text{if } x>p_k \end{cases}</math>
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| where <math>q_j</math> and <math>p_j</math> are respectively the indifference and preference thresholds. The meaning of these parameters is the following: when the difference is smaller than the indifference threshold it is considered as negligible by the decision maker. Therefore the corresponding unicriterion preference degree is equal to zero. If the difference exceeds the preference threshold it is considered to be significant. Therefore the unicriterion preference degree is equal to one (the maximum value). When the difference is between the two thresholds, an intermediate value is computed for the preference degree using a linear interpolation.
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| | |
| === Multicriteria preference degree ===
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| When a preference function has been associated to each criterion by the decision maker, all comparisons between all pairs of actions can be done for all the criteria. A multicriteria preference degree is then computed to globally compare every couple of actions:
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| :<math>\pi(a,b)=\displaystyle\sum_{k=1}^qP_{k}(a,b).w_{k}</math>
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| Where <math>w_k</math> represents the weight of criterion <math>f_k</math>. It is assumed that <math>w_k\ge 0</math> and <math>\sum_{k=1}^q w_{k}=1</math>. As a direct consequence, we have:
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| :<math>\pi(a_i,a_j)\ge 0</math>
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| :<math>\pi(a_i,a_j)+\pi(a_j,a_i)\le 1</math>
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| === Multicriteria preference flows ===
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| In order to position every action a with respect to all the other actions, two scores are computed:
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| :<math>\phi^{+}(a)=\frac{1}{n-1}\displaystyle\sum_{x \in A}\pi(a,x)</math>
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| :<math>\phi^{-}(a)=\frac{1}{n-1}\displaystyle\sum_{x \in A}\pi(x,a)</math>
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| The positive preference flow <math>\phi^{+}(a_i)</math> quantifies how a given action <math>a_i</math> is globally preferred to all the other actions while the negative preference flow <math>\phi^{-}(a_i)</math> quantifies how a given action <math>a_i</math> is being globally preferred by all the other actions. An ideal action would have a positive preference flow equal to 1 and a negative preference flow equal to 0. The two preference flows induce two generally different complete rankings on the set of actions. The first one is obtained by ranking the actions according to the decreasing values of their positive flow scores. The second one is obtained by ranking the actions according to the increasing values of their negative flow scores. The Promethee I partial ranking is defined as the intersection of these two rankings. As a consequence, an action <math>a_i</math> will be as good as another action <math>a_j</math> if <math> \phi^{-}(a_i) \ge \phi^{-}(a_j)</math> and <math>\phi^{-}(a_i)\le \phi^{-}(a_j)</math>
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| The positive and negative preference flows are aggregated into the net preference flow:
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| :<math>\phi(a)=\phi^{+}(a)-\phi^{-}(a)</math>
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| Direct consequences of the previous formula are:
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| :<math>\phi(a_i) \in [-1;1]</math>
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| :<math>\sum_{a_i \in A} \phi(a_i)=0</math>
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| The Promethee II complete ranking is obtained by ordering the actions according to the decreasing values of the net flow scores.
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| === Unicriterion net flows ===
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| According to the definition of the multicriteria preference degree, the multicriteria net flow can be disaggregated as follows:
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| :<math>\phi(a_i)=\displaystyle\sum_{k=1}^q\phi_{k}(a_i).w_{k}</math>
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| Where:
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| :<math>\phi_{k}(a_i)=\frac{1}{n-1}\displaystyle\sum_{a_j
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| \in
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| A}\{P_{k}(a_i,a_j)-P_{k}(a_j,a_i)\}</math>.
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| The unicriterion net flow, denoted <math>\phi_{k}(a_i)\in[-1;1]</math>, has the same interpretation as the multicriteria net flow <math>\phi(a_i)</math> but is limited to one single criterion. Any action <math>a_i</math> can be characterized by a vector <math>\vec \phi(a_i) =[\phi_1(a_i),...,\phi_k(a_i),\phi_q(a_i)]</math> in a <math>q</math> dimensional space. The GAIA plane is the principal plane obtained by applying a principal components analysis to the set of actions in this space.
| |
| | |
| === Promethee preference functions ===
| |
| *Usual
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| :<math>\begin{array}{cc} P_{j}(d_{j})=\left\{
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| \begin{array}{lll}
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| 0 & \text{if} & d_{j}\leq 0 \\
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| \\
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| 1 & \text{if} & d_{j}>0\\
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| \end{array}
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| \right.
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| \end{array}</math>
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| | |
| *U-Shape
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| | |
| :<math>\begin{array}{cc} P_{j}(d_{j})=\left\{
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| \begin{array}{lll}
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| 0 & \text{if} & |d_{j}| \leq q_{j} \\
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| \\
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| 1 & \text{if} & |d_{j}| > q_{j}\\
| |
| \end{array}
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| \right.
| |
| \end{array}</math>
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| | |
| *V-Shape
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| | |
| :<math>\begin{array}{cc} P_{j}(d_{j})=\left\{
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| \begin{array}{lll}
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| \frac{|d_{j}|}{p_{j}} & \text{if} & |d_{j}| \leq p_{j} \\
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| \\
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| 1 & \text{if} & |d_{j}| > p_{j}\\
| |
| \end{array}
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| \right.
| |
| \end{array}</math>
| |
| | |
| *Level
| |
| | |
| :<math>\begin{array}{cc} P_{j}(d_{j})=\left\{
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| \begin{array}{lll}
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| 0 & \text{if} & |d_{j}| \leq q_{j} \\
| |
| \\
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| \frac{1}{2} & \text{if} & q_{j}<|d_{j}| \leq p_{j} \\
| |
| \\
| |
| 1 & \text{if} & |d_{j}| > p_{j}\\
| |
| \end{array}
| |
| \right.
| |
| \end{array}
| |
| </math>
| |
| | |
| *Linear
| |
| | |
| :<math>\begin{array}{cc} P_{j}(d_{j})=\left\{
| |
| \begin{array}{lll}
| |
| 0 & \text{if} & |d_{j}| \leq q_{j} \\
| |
| \\
| |
| \frac{|d_{j}|-q_{j}}{p_{j}-q_{j}} & \text{if} & q_{j}<|d_{j}| \leq p_{j} \\
| |
| \\
| |
| 1 & \text{if} & |d_{j}| > p_{j}\\
| |
| \end{array}
| |
| \right.
| |
| \end{array}</math>
| |
| | |
| *Gaussian
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| | |
| :<math>P_{j}(d_{j})=1-e^{-\frac{d_{j}^{2}}{2s_{j}^{2}}}</math>
| |
| | |
| == Promethee rankings ==
| |
| | |
| ===Promethee I===
| |
| Promethee I is a partial ranking of the actions. It is based on the positive and negative flows. It includes preferences, indifferences and incomparabilities (partial preorder).
| |
| | |
| ===Promethee II===
| |
| Promethee II is a complete ranking of the actions. It is based on the multicriteria net flow. It includes preferences and indifferences (preorder).
| |
| | |
| ==See also==
| |
| * [[Decision making]]
| |
| * [[Decision-making software]]
| |
| * [[D-Sight]]
| |
| * [[Multi-criteria decision analysis]]
| |
| * [[Pairwise comparison]]
| |
| * [[Preference]]
| |
| | |
| ==References==
| |
| {{Reflist|2}}
| |
| | |
| ==External links==
| |
| * [http://www.standardsfacility.org/en/TAEcoAnalysis.htm STDF Case Study]
| |
| * [http://www.d-sight.com/sites/default/files/documents/news/d-sight_case_study_italferr.pdf Italferr Case Study]
| |
| * [http://www.d-sight.com D-Sight: PROMETHEE based software]
| |
| * [http://code.ulb.ac.be/promethee-gaia/ CoDE: PROMETHEE & GAIA Literature]
| |
| * [http://www.promethee-gaia.net PROMETHEE & GAIA web site]
| |
| | |
| {{DEFAULTSORT:Promethee}}
| |
| [[Category:Decision theory]]
| |
| [[Category:Operations research]]
| |
If you are definitely severe about becoming a chef then you will will need to make positive that you are fully ready to do so. This indicates that you will need all of the equipment and clothing needed to work in a fully functioning kitchen. The cost of this serrated knife is about the very same as any other superior high quality kitchen knives in the marketplace, but what tends to make this serrated bread knife stand out from the rest for me is its razor sharp blade , good balance, funky modern day appears, overall durability and the dimple impact handle is simple to keep clean and presents wonderful grip. Chef Knives are truly a multi-purpose kitchen knife that can be made use of and utilized for many different tasks in the kitchen.
When you loved this article and you wish to receive much more information with regards to mundial steak knives review i implore you to visit the webpage. In particular if you are new to pumpkin carving this is the tool set you require and I whole heartedly agree with what was said on the net about them: if you purchased them seperately every of them would price $30 and now you can have the complete set for that cost. What's far more this set will not sit in your draw forgotten for the rest of the year, you can use them all the time. If you have a set like this and you consider I've missed the mark, take your set by an estate silver shop or old line jeweler.
With so numerous choices out there, we can assist you figure out the best knife for you! I don't mind this at all, but he took my big, heavy chef's knife amongst other folks, and I am fond of it both for its high-quality and for sentimental worth. I appear forward to getting in a position to use the ideal knife in town when it arrives, just after I have stressed to my husband that as substantially as he might study to appreciate it, it should remain property.
Even believed the pocket knives are quite easy and swift to open none of them fit the definition of a switchblade defined by the U.S. Switch Blade Knife Act of 1958. Columbia River Knife & Tool make great pocket knives, hunting knives and knives for the military. This attractive knife block set is the crowning glory of the modern day Stellar FM range. Test out some knives at a knife or hobby shop or shop.
In his manual, Chad Ward implies that if you are going to invest in a knife established from a retailer with very a lot of open up stock, they could be willing to swap in knives from the incredibly exact same brand. Wusthof Knife Sets (Simple) Prior to we get commenced, it can be worthy of examining some kitchen knife record. Rather a few men and women now are unaware of the great upheaval that the kitchen region knife marketplace has undergone in the final ten years.
If you happen to be not into tracking down the ideal individual knives and just want decent cutting energy, a set can unquestionably be a nice way to go. Despite the fact that you could spend thousands on a knife set, in my investigation I identified it really is not worth dropping additional than $350 to $400. In reality, in their overview of knife sets, America's Test Kitchentwo a la carte sets comprised of distinct brands. Rates of most popular knife sets are really expensive.
For the price tag, we never consider you can beat the Victorinox Rosewood Straight Edge Steak Knife Set That said, if you want a heavier, additional luxurious knife Shun Steak Knives Review set, we'd go with the Wusthof Classic Ikon Steak Knives ($290 for four). Forged in Solingen, Germany, these high-carbon stainless steel knives have lovely contoured handles and have been the finest balanced of all the knives we tested. We tested 4 serrated knives, and 1 micro-serrated knife (at front).