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The '''weighted product model''' ('''WPM''') is a popular [[multi-criteria decision analysis]] (MCDA)&nbsp;/&nbsp;[[multi-criteria decision making]] (MCDM) method.  It is similar to the [[weighted sum model]] (WSM). The main difference is that instead of addition in the main mathematical operation now there is multiplication.  As with all MCDA&nbsp;/&nbsp;MCDM methods, given is a finite set of decision alternatives described in terms of a number of decision criteria. Each decision alternative is compared with the others by multiplying a number of ratios, one for each decision criterion.  Each ratio is raised to the power equivalent to the relative weight of the corresponding criterion. Some of the first references to this method are due to Bridgman<ref>{{cite book | last = Bridgman | first = P.W. | authorlink = | title = Dimensional Analysis | publisher = Yale University Press | year = 1922 | location = New Haven, CT, U.S.A. | pages = | url = | doi = | id = | isbn = }}</ref> and Miller and Starr.<ref>{{cite book | last = Miller | first = D.W. | authorlink = | coauthors = and M.K. Starr | title = Executive Decisions and Operations Research | publisher = Prentice-Hall, Inc. | year = 1969 | location = Englewood Cliffs, NJ, U.S.A. | pages = | url = | doi = | id = | isbn = }}</ref>
Now the ready hearth pile was't virtually as neat, and I experienced 1 a lot more hearth starter to test. I sort of roughly bundled it up once again and pulled out one more cotton ball. I pulled out the Blast Match created by Greatest Survival Technologies for a single handed use, which could be really practical if you located yourself in a survival circumstance, wounded, with only one particular usable hand. This a single is assembled in the US from foreign components, but the 1 handed procedure characteristic is just too difficult to move on. We chose the black model of the Blast Match as pictured. It is also obtainable in orange.<br>To pick the ideal Gerber Folding Knife you 1st want to request yourself what you require in a knife If you need to have a tactical folding knife you could want to go with a tanto blade. Do you want an edge that is simple or serrated? What variety of handle do you require? All extremely excellent inquiries. The background [http://www.thebestpocketknifereviews.com/best-swiss-army-knife-choosing-the-best-models/ Best swiss army knife] of [http://Wiki.Ippk.ru/index.php/Best_Swiss_Army_Knife_For_Camping pocket knives] dates again to the early several years of the existence of gentleman. For the duration of that time, guy utilized pocket knives for looking animals for food. These days, pocket knives are different, and are one particular of the most beneficial instrument and unsafe weapons at the exact same time.<br>The blade is partly serrated, I know that a whole lot of folks do not like serrations nevertheless the Les [http://Dev.Jibo.ro/author/sujenner/ Stroud Supreme] Survival knife is made so that the serrations only take up about a half inch of the four/3/four inch blade. When i examined this knife the serrations did not get in the way of chopping and whittling so I have to give props to Les for the design. When it comes to the file folders, they are impeccably sturdy and best business identification growth equipment for your businesses. For that explanation, company provides you low cost file folder printing options in the globe today.<br>I would recommend putting a contact of lubricant on any joints that shift if you use a folding knife. Also, put a minor bit on to a rag and wipe it into the blade truly effectively. This will stop oxidation and corrosion of your blade and preserve it like new. That must get your knife serviceable again. It is always great to have a knife steel useful to freshen up the blade each and every now and then. 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The huge hole in the blade tends to make it simple for any person to open this knife-a considerably far better opening approach than those little, shallow slits found on several pocket knives. The blade itself is extremely thin and about as sharp as is attainable. The blade is only 3 inches, which could be needed in some places with rigorous blade size rules, but is type of undersized in my view. When open, the entire knife [http://Www.collegiatepins.com/blog/view/129531/swiss-army-knife-tools measures] in at seven inches. When locked in spot, the blade feels solid and unbreakable.<br>The take care of by itself is a tiny smoother than I like in a knife. It has enough grit to make it graspable, but is clean enough that a slippery palm might lead to the knife to slip, not ideal with a blade this sharp. All round, it is dependent on grip, hand size, and moisture. The deal with is definitely not unpleasant, and total makes the Lachesis a quite comfortable folding knife. When you buy your folding knives and tactical knives from our site, the commitment and consumer support we offer will make you a repeat client over and in excess of again. We offer you totally free delivery for U.S. orders above $a hundred and fifty and your pleasure is confirmed.<br>Lavinia has authored many books and CD applications. He book, What Are You Afraid Of? A Entire body/Head Guidebook to Courageous Residing has been printed in six languages. She teaches the Feldenkrais Approach and The Imaginative Human body in NC, the place she is the director of Asheville Movement Heart. Lavinia conducts workshops internationally and operates with many corporations on entire body/thoughts and interaction topics. www.laviniaplonka.com A leather-based jacket can be utilised for many a long time, nevertheless, a rip, tear or holes on the jacket is a widespread prevalence. As they say, a stitch in time will save 9, fixing the jacket in the nick of time is sure to make it very last for a whilst.<br>Users of the Intense Ops folding knife are also cautioned in the directions not to use the reducing blade as a "can opener, chisel, pry bar, screw driver, or for any weighty function for which your knife was not made." Smith & Wesson also isn't going to want users to use the again of the knife handle as a hammer. In other phrases, you aren't meant to do anything at all too severe with your Excessive Ops Folding Knife. This Chinese-made knife may possibly be a great deal more like Walter Mitty than it's intense paint job may reveal. In fairness, there are greater finish Smith & Wesson knives that might in shape the monthly bill.<br>Use desk toppers. Desk toppers are related to overlays, but protect the whole table top and dangle more than the desk edge a number of inches on all sides. They are typically employed more for colour plan or branding. Using table skirts and equipment at your next event can support to make your function search more prestigious or expert. Use the ideas over to aid make your following celebration the best it can be. Soon after a long working day in which my residence was ultimately "Feng Shui'ed" I understood I graduated from a junk drawer to a junk room which at minimum experienced nothing at all below the [https://Projects.Boblycat.org/blimp/ticket/55708 mattress]! Hey, I am a witch. Not ideal!
 
More details on this method are given in the MCDM book by Triantaphyllou.<ref name='MCDMbook'>{{cite book | last = Triantaphyllou | first = E. | authorlink = http://www.csc.lsu.edu/trianta | title = Multi-Criteria Decision Making:  A Comparative Study | publisher = Kluwer Academic Publishers (now Springer) | year = 2000 | location = Dordrecht, The Netherlands | pages = 320 | url = http://www.csc.lsu.edu/trianta/Books/DecisionMaking1/Book1.htm | doi = | id = | isbn = 0-7923-6607-7 }}</ref>
 
Suppose that a given [[MCDA]] problem is defined on ''m'' alternatives and ''n'' decision criteria. Furthermore, let us assume that all the criteria are benefit criteria, that is, the higher the values are, the better it is. Next suppose that ''w<sub>j</sub>'' denotes the relative weight of importance of the criterion ''C<sub>j</sub>'' and ''a<sub>ij</sub>'' is the performance value of alternative ''A<sub>i</sub>'' when it is evaluated in terms of criterion ''C<sub>j</sub>''. Then, if one wishes to compare the two alternatives ''A<sub>K</sub>'' and ''A<sub>L</sub>'' (where ''m''&nbsp;≥&nbsp;''K'',&nbsp;''L''&nbsp;≥&nbsp;1) then, the following product has to be calculated:<ref name = 'MCDMbook' />
 
::<math>P( A_K / A_L ) = \prod_{j=1}^n ( a_{Kj} / a_{Lj} ) ^{w_j},  \text{ for }K, L = 1, 2, 3,\dots, m. </math>
 
If the ratio ''P''(''A''<sub>''K''</sub>/''A''<sub>''L''</sub>) is greater than or equal to the value&nbsp;1, then it indicates that alternative ''A<sub>K</sub>'' is more desirable than alternative ''A<sub>L</sub>'' (in the maximization case).  If we are interested in determining the best alternative, then the best alternative is the one that is better than or at least equal to all other alternatives.
 
The WPM is often called '''dimensionless analysis''' because its mathematical structure eliminates any units of measure.<ref name = 'MCDMbook' /><ref name='PARADOX'>{{cite journal | title = An Examination of the Effectiveness of  Multi-Dimensional Decision-Making Methods: A Decision-Making Paradox  | journal = International Journal of Decision Support Systems | year=1989 | first = E. | last = Triantaphyllou | authorlink = http://www.csc.lsu.edu/trianta | coauthors =  and S.H. Mann | volume = | issue = 5 | pages = 303–312 | id =  | url = http://www.csc.lsu.edu/trianta/Journal_PAPERS1/PARADX1.htm | accessdate = 2010-06-25 }}</ref>
 
Therefore, the WPM can be used in single- and multi-dimensional [[MCDA]]&nbsp;/&nbsp;[[MCDM]] problems. That is, on decision problems where the alternatives are described in terms that use different units of measurement. An advantage of this method is that instead of the actual values it can use relative ones.
 
The following is a simple numerical example which illustrates how the calculations for this method can be carried out. As data we use the same numerical values as in the numerical example described for the [[weighted sum model]]. These numerical data are repeated next for easier reference.  
 
==Example==
 
This simple decision problem is based on three alternatives denoted as ''A''<sub>1</sub>, ''A''<sub>2</sub>, and ''A''<sub>3</sub> each described in terms of four criteria ''C''<sub>1</sub>, ''C''<sub>2</sub>, ''C''<sub>3</sub> and ''C''<sub>4</sub>. Next, let the numerical data for this problem be as in the following decision matrix:
 
{| class="wikitable"
|-
!  !! ''C''<sub>1</sub> !! ''C''<sub>2</sub> !! ''C''<sub>3</sub> !! ''C''<sub>4</sub>
|-
| '''Alts. ''' || 0.20 || 0.15 || 0.40 || 0.25
|-
| ''A''<sub>1</sub> || 25 || 20 || 15 || 30
|-
| ''A''<sub>2</sub> || 10 || 30 || 20 || 30
|-
| ''A''<sub>3</sub> || 30 || 10 || 30 || 10
|}
From the above data we can easily see that the relative weight of the first criterion is equal to 0.20, the relative weight for the second criterion is 0.15 and so on. Similarly, the value of the first alternative (i.e., ''A''<sub>1</sub>) in terms of the first criterion is equal to 25, the value of the same alternative in terms of the second criterion is equal to 20 and so on.   However, now the restriction to express all criteria in terms of the same measurement unit is not needed. That is, the numbers under each criterion may be expressed in different units.
 
When the WPM is applied on the previous data, then the following values are derived:
 
::<math> P( A_1 / A_2 ) =  (25/10) ^{0.20} \times (20/30) ^{0.15} \times (15/20) ^{0.40} \times (30/30) ^{0.25}  = 1.007 > 1.  </math>
 
Similarly, we also get:
::<math>P( A_1 / A_3) =  1.067 > 1,\text{ and } P( A_2 / A_3) =  1.059 > 1. \, </math>
 
Therefore, the best alternative is ''A''<sub>1</sub>, since it is superior to all the other alternatives. Furthermore, the following ranking of all three alternatives is as follows: ''A''<sub>1</sub>&nbsp;>&nbsp;''A''<sub>2</sub>&nbsp;>&nbsp;''A''<sub>3</sub>  (where the symbol&nbsp;">" stands for "better than").
 
An alternative approach with the WPM method is for the decision maker to use only products without the previous ratios.<ref name = 'MCDMbook' /><ref name = 'PARADOX' />
That is, to use the following variant of main formula given earlier: 
 
::<math>P( A_K ) = \prod_{j=1}^n ( a_{Kj} ) ^{w_j}, \text{ for } K = 1, 2, 3, \dots , m. </math>
 
In the previous expression the term ''P''(''A''<sub>''K''</sub>) denotes the total performance value (i.e., not a relative one) of alternative ''A''<sub>''K''</sub> when all the criteria are considered simultaneously under the WPM model. Then, when the previous data are used, exactly the same ranking is derived. Some interesting properties of this method are discussed in the 2000 book by Triantaphyllou on [[MCDA]]&nbsp;/&nbsp;[[MCDM]].<ref name = 'MCDMbook' />
 
==See also==
* [[Weighted sum model]]
 
== References ==
<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags which will then appear here automatically -->
{{Reflist}}
 
[[Category:Decision theory]]

Latest revision as of 19:47, 22 July 2014

Now the ready hearth pile was't virtually as neat, and I experienced 1 a lot more hearth starter to test. I sort of roughly bundled it up once again and pulled out one more cotton ball. I pulled out the Blast Match created by Greatest Survival Technologies for a single handed use, which could be really practical if you located yourself in a survival circumstance, wounded, with only one particular usable hand. This a single is assembled in the US from foreign components, but the 1 handed procedure characteristic is just too difficult to move on. We chose the black model of the Blast Match as pictured. It is also obtainable in orange.
To pick the ideal Gerber Folding Knife you 1st want to request yourself what you require in a knife If you need to have a tactical folding knife you could want to go with a tanto blade. Do you want an edge that is simple or serrated? What variety of handle do you require? All extremely excellent inquiries. The background Best swiss army knife of pocket knives dates again to the early several years of the existence of gentleman. For the duration of that time, guy utilized pocket knives for looking animals for food. These days, pocket knives are different, and are one particular of the most beneficial instrument and unsafe weapons at the exact same time.
The blade is partly serrated, I know that a whole lot of folks do not like serrations nevertheless the Les Stroud Supreme Survival knife is made so that the serrations only take up about a half inch of the four/3/four inch blade. When i examined this knife the serrations did not get in the way of chopping and whittling so I have to give props to Les for the design. When it comes to the file folders, they are impeccably sturdy and best business identification growth equipment for your businesses. For that explanation, company provides you low cost file folder printing options in the globe today.
I would recommend putting a contact of lubricant on any joints that shift if you use a folding knife. Also, put a minor bit on to a rag and wipe it into the blade truly effectively. This will stop oxidation and corrosion of your blade and preserve it like new. That must get your knife serviceable again. It is always great to have a knife steel useful to freshen up the blade each and every now and then. Maintain working towards and you will be a expert in no time. For all your knife needs go to us at A Excellent Knife.
Right now most folding knives, equally big and modest, lock open. This is accomplished for safety causes when the knife is set to hard use. At first most all knives employed a design and style called the lock-again. In this style the knife backbone in the centre of the manage Best Swiss Army Knives is made to pivot. When the knife blade is pulled open up it raises the backbone at the pivot conclude. When the knife blade is entirely open up, the spine falls again into spot and locks the knife in the open place. When the knife is totally closed the spine returns to its standard placement.
The blade on the Calypso three is a ZDP-189 laminate, which is manufactured of 420j2 brushed stainless steel. The huge hole in the blade tends to make it simple for any person to open this knife-a considerably far better opening approach than those little, shallow slits found on several pocket knives. The blade itself is extremely thin and about as sharp as is attainable. The blade is only 3 inches, which could be needed in some places with rigorous blade size rules, but is type of undersized in my view. When open, the entire knife measures in at seven inches. When locked in spot, the blade feels solid and unbreakable.
The take care of by itself is a tiny smoother than I like in a knife. It has enough grit to make it graspable, but is clean enough that a slippery palm might lead to the knife to slip, not ideal with a blade this sharp. All round, it is dependent on grip, hand size, and moisture. The deal with is definitely not unpleasant, and total makes the Lachesis a quite comfortable folding knife. When you buy your folding knives and tactical knives from our site, the commitment and consumer support we offer will make you a repeat client over and in excess of again. We offer you totally free delivery for U.S. orders above $a hundred and fifty and your pleasure is confirmed.
Lavinia has authored many books and CD applications. He book, What Are You Afraid Of? A Entire body/Head Guidebook to Courageous Residing has been printed in six languages. She teaches the Feldenkrais Approach and The Imaginative Human body in NC, the place she is the director of Asheville Movement Heart. Lavinia conducts workshops internationally and operates with many corporations on entire body/thoughts and interaction topics. www.laviniaplonka.com A leather-based jacket can be utilised for many a long time, nevertheless, a rip, tear or holes on the jacket is a widespread prevalence. As they say, a stitch in time will save 9, fixing the jacket in the nick of time is sure to make it very last for a whilst.
Users of the Intense Ops folding knife are also cautioned in the directions not to use the reducing blade as a "can opener, chisel, pry bar, screw driver, or for any weighty function for which your knife was not made." Smith & Wesson also isn't going to want users to use the again of the knife handle as a hammer. In other phrases, you aren't meant to do anything at all too severe with your Excessive Ops Folding Knife. This Chinese-made knife may possibly be a great deal more like Walter Mitty than it's intense paint job may reveal. In fairness, there are greater finish Smith & Wesson knives that might in shape the monthly bill.
Use desk toppers. Desk toppers are related to overlays, but protect the whole table top and dangle more than the desk edge a number of inches on all sides. They are typically employed more for colour plan or branding. Using table skirts and equipment at your next event can support to make your function search more prestigious or expert. Use the ideas over to aid make your following celebration the best it can be. Soon after a long working day in which my residence was ultimately "Feng Shui'ed" I understood I graduated from a junk drawer to a junk room which at minimum experienced nothing at all below the mattress! Hey, I am a witch. Not ideal!