Kodak Strategy Essay Example for Free

Kodak Strategy Essay The first Kodak camera led to the creation of their first slogan: â€Å"You press the button – we do the rest†. He named the brand of camera Kodak because it was short, it would not be mispronounced, and the name was unique in the business. (Gartrell, n. d. ) By the late 19th century and early 1900’s, advertising played a major role in Kodak’s marketing and promotion strategy. As a result, Kodak became a household word. Today, the Kodak name has become entrenched in home town America. It is known for being very American since its photo spots can be seen at iconic patriotic hot spots like Disneyland. In addition â€Å"Kodak Moments† help make it a household name for photography and imaging. (Wikinvest, 2007) Kodak has always dominated the â€Å"holy trinity of film†; film, paper and chemicals. (Upbin, 2000, para #8) Kodak’s big concern is to remain competitive in the market place. The Eastman Kodak company had to take on some strong competition, such as Polaroid, who is famous for instant photography. Kodak began to sell their version of the instant camera in June 1976 to expand its market. The camera was called the Pronto which spit out a picture card which formed into a picture before the photographers eyes. The idea was successful and although Kodak’s ten picture pack of film was more expensive than Polaroid’s, several Japanese companies made cameras that used the new Kodak Film. (Time Magazine, 1976) Soon after, the disposable camera became popular. According to statistics, U. S. sales of disposable cameras grew 30% a year. Kodak sells more than anyone else, allowing Kodak to have sufficient cash flow to invest in a digital future. In the mid 1990’s Kodak’s innovators began to dabble with digital photography. In fact, they invented the first digital camera and realized that digital technology would transform their business. By the year 2000, Kodak had sunk more than $5 billion into digital investments during the 1990s, but received only $20 million in digital earnings in 1999 to show for it. Daniel Carp, the latest Chief Executive at Eastman Kodak stated that â€Å"digital can generate half of revenue and quarter of profits by 2005†. (Upbin, 2000, para. #3) So why wasn’t Kodak getting a return on their investment? One of the main issues that plagued the Eastman Kodak Company was not their innovation, but their timing in their marketing strategy and their assessment of the adaptability of its consumers. Kodak missed out on several holiday seasons where digital camera growth was high and failed to get a leg up on the competition back in 1996. The company was unable to â€Å"wean itself† from traditional film business. They have three major customer bases. The first is the Photofinishing Group which makes up almost 1/3 of sales. This group is made up of Kodak’s traditional film products and services that the average customer uses, plus products used by the film industry to reproduce and distribute motion pictures. The second group, not formed until 2003, is the Graphic Communications Group (GCG). It’s Kodak’s largest division which includes document imaging and digital printing services for businesses. The third group relates to healthcare services and is called the Health Group. This group specializes in healthcare imaging products such as x-ray devices and specialized films. To catch up to their competition, Kodak created a fourth group, the Consumer Digital Group, to change their main product line from traditional film to digital products. They turned their focus to digital cameras and printers, photo kiosks (like at CVS and Wal-Mart) and online photo sharing. Wikinvest, 2007) The problem was they did not react to the market until almost 2 years after their fierce competitors, such as Hewlett Packard, Canon, and Sony began to overtake the business. The irony is that although Kodak created many digital products that were ahead of their time, such as the Photo CD and high-end digital cameras, Kodak continued to focus their marketing strategy on the investor rat her than the customer. It is unfortunate because many of the digital imaging products that Kodak introduced, and that we still use today, did not get the commitment they deserved from their creators. Because of their own corporate reluctance to replace their main base of income (traditional film), many investors questioned whether it was too late for Kodak to join the digital age. (Nikondigital. org, 2007, para. #2) Timing was not the only problem. Kodak had digital competition from the evolution of the internet, the Sony Corporation, Hewlett Packard, and Canon, to name a few. Despite the invention of the digital camera, Kodak fell behind in efficiency profit margins and sheer sales. The company failed to market other media devices leaving Hewlett Packard and Lexmark to dominate the printer industry. Kodak is now trying to catch up in that area. Kodak needed to make several adjustments in their marketing strategy, develop their product line, promote their product, rethink their distribution efforts and develop a pricing strategy to steal market shares from industry leaders. With a new management philosophy and marketing strategy, Kodak realized the need to adjust its consumables. Most of Kodak’s traditional photography was based on their services, their paper and ink. With the addition of digital imagery, that had to change. Chemicals, to produce the photos were no longer needed for digital photography. How could Kodak compensate for the changing technology? Putting their innovators to the test, Kodak came up with the EasyShare family of cameras. It became one of Kodak’s biggest successes. Even today, it is still the â€Å"simplest way to get started in digital† photography. (Nikondigital. org, 2007, para. #7) Kodak developed this type of camera by studying how camera users take and print pictures and how it fits into their daily lives. Their research paid off. Kodak focused on low-priced, easy-to-use cameras that would appeal to women, who take the majority of snapshots. In 2004 the competition with Sony, the largest digital camera maker, paid off with a rise from a 5% market share in 2000 to a 19% share in 2004. (Hansell, 2004) In addition to the EasyShare system, category expansion has increased Kodak’s consumer base. One of the ways they accomplished this is by developing effective partnerships. To compete with some of the industry leaders, Kodak developed the â€Å"Kodak Gallery† an online photo sharing site which allows consumers to upload their photos and share them with friends and family. This competes with sites like Shutterfly and Photobucket. It recently partnered with Martha Stewart, Apple, Microsoft, and Amazon. com. (Wikinvest, 2007) Kodak has also planned investment in Lucky Film, Co. Ltd which will strengthen its position in Asia, and has increased its interest in medical markets. They have acquired PracticeWorks, a leader in digital dental imaging, and have improved their economic performance with Kodak Directview PACS System 5 for radiologists. (Eastman Kodak Company, 2004) To promote their products, Kodak has used the traditional advertising as well as some creative promotion techniques. Kodak wants to develop the customers of traditional cameras into future consumers of digital products. One of the ways they are doing this is donating 5,000 traditional cameras to those provinces in China that are not familiar with photography. As China’s rural areas become more economically independent, Kodak hopes to capture the market. This allows Kodak to continue its traditional (bread and butter) line of products to third world nations while focusing the digital sales to the United States, Canada and some European countries. (China Daily, 2004) One way to focus those sales in the U. S. is Kodak’s distribution to direct marketers who want to customize their flyers or retail changes that need variable posters. Digital technology makes it possible to economically print custom copies of anything and at almost any volume. They want to â€Å"elevate print and other visual communications for creativity and commerce†. (Sherburne, 2007, para. #3) Kodak is introducing the MarketMover Network, designed to focus on small business in a similar fashion that the Kodak Creative Network does, where the consumers create the photo books, calendars and flyers. Finally, Kodak’s pricing strategies had to be dramatic. One of the best things we hear about Kodak is the â€Å"quality of their service†. The problem is the competition is rapidly meeting Kodak’s quality standards. In 2007, Kodak developed KOS, the Kodak Operating System to streamline the production system and incorporate that into all aspects of Kodak’s operations. It changed their management philosophy. This had some effect on not only their marketing strategies, but their pricing strategies. In the past, companies were willing to sacrifice profits on the â€Å"durable† portion of their product – the printer, to make money on the â€Å"consumable† portion – printer cartridges. In February of that year, Kodak announced a new pricing strategy. It was a long term competitive dynamic disruption strategy. The strategy was aimed at reducing the cost of printing photos for the average consumer. Consumers will have to change their behavior to focus on printing costs instead of hardware costs. (Neff, 2007) In addition, the new printers will not have as many features as Hewlett-Packard printers currently have. This could corner an aging market that has not wanted to purchase â€Å"fancy† printers due to the challenge of technology. However, there is a growing share of private label recycled ink cartridges. Kodak will need to maintain their focus not only on the pricing of their ink cartridges, but they should reinforce the â€Å"quality† aspect of their product. During the past two decades, the Eastman Kodak has struggled with the advent of digital photography. What sets Kodak apart? Kodak is not a computer company, nor is Kodak a company which dabbles in several industries. They are focused on print products and photography.

Dual Trapezoidal Fuzzy Number and Its Applications

Dual Trapezoidal Fuzzy Number and Its Applications Jon Arockiaraj. J, Pathinathan.T, Revathy.S Abstract: In this paper, we introduce Convergence of ÃŽ ±-Cut. We define at which point the ÃŽ ±-Cut converges to the fuzzy numbers it will be illustrated by example using dual trapezoidal fuzzy number and Some elementary applications on mensuration are numerically illustrated with approximated values. KeyWords: Fuzzy number, ÃŽ ±-Cut, Dual trapezoidal fuzzy number, Defuzzification. Introduction: Fuzzy sets have been introduced by Lotfi. A. Zadeh (1965). Fuzzy numbers were first introduce by Zadeh in 1975.There after theory of fuzzy number was further studied and developed by Dubois and Prade, R.Yager Mizomoto, J.Buckly and Many others. Since then many workers studied the theory of fuzzy numbers and achieved fruitful results. The fuzziness can be represented by different ways one of the most useful representation is membership function. Also depending the nature and shape of the membership function the fuzzy number can be classified in different forms, such as triangular fuzzy number, trapezoidal fuzzy number etc. A fuzzy number is a quantity whose values are imprecise, rather than exact as is the case with single valued number. Fuzzy numbers are used in statistics computer programming, engineering and experimental science. So far fuzzy numbers like triangular fuzzy number, trapezoidal fuzzy numbers, pentagonal, hexagonal, octagonal pyramid and diamond fuzzy numbers have been introduced with its membership functions. These numbers have got many applications like non-linear equations, risk analysis and reliability. In this paper, we introduce Dual trapezoidal fuzzy numbers with its membership functions and its applications. Section one presents the introduction, section two presents the basic definition of fuzzy numbers section three presents Dual trapezoidal fuzzy numbers and its applications and in the final section we give conclusion. 2. Basic Definitions Definition 2.1: (Fuzzy set) A fuzzy set A in a universe of discourse X is defined as the following set of pairs A= {(x,  µA(x)): xX} Here  µA(x) : x is a mapping called the degree of membership function of the fuzzy set A and  µA(x) is called the membership value of xX in the fuzzy set These membership grades are often represented by real numbers ranging from [0, 1]. Definition 2.2: (Fuzzy Number) A fuzzy set A defined on the universal set of real number R is said to be a fuzzy number if its membership function has satisfy the following characteristics. ( i) ÃŽ ¼A (x) is a piecewise continuous (ii) A is convex, i.e.,  µA (ÃŽ ±x1 + (1-ÃŽ ±) x2) ≠¥ min ( µA(x1),  µA(x2)) É  x1 ,x2R É  ÃŽ ±[0,1] (iii) A is normal, i.e., there exist xo R such that  µA (xo)=1 Definition 2.3: (Trapezoidal Fuzzy Number) A trapezoidal fuzzy number represented with four points as A = (a b c d), Where all a, b, c, d are real numbers and its membership function is given below where a≠¤ b≠¤ c≠¤ d  µA(x)= 3. DUAL TRAPEZOIDAL FUZZY NUMBER Definition 3.1: (Dual Trapezoidal Fuzzy Number) A Dual Trapezoidal fuzzy number of a fuzzy set A is defined as ADT= {a, b, c, d (ÃŽ ±)} Where all a, b, c, d are real numbers and its membership function is given below where a≠¤b≠¤c≠¤d  µDT(x) = where ÃŽ ± is the base of the trapezoidal and also for the inverted reflection of the above trapezoidal namely a b c d Figure: Graphical Representation of Dual Trapezoidal fuzzy Number 3.2 DEFUZZIFICATION: Let ADT= (a, b, c, d, à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡) be a dual trapezoidal fuzzy number .The defuzzification value of ADT is an approximate real number. There are many method for defuzzification such as Centroid Method, Mean of Interval Method , Removal Area Method etc. In this Paper We have used Centroid area method for defuzzification . CENTROID OF AREA METHOED: Centroid of area method or centry of gravity method. It obtains the centre of area (X*) occupied by the fuzzy sets.It can be expressed as X* = Defuzzification Value for dual trapezoidal fuzzy number: Let ADT= {a, b, c, d (ÃŽ ±)} be a DTrFN with its membership function  µDT(x) = Using centroid area method +dx+++dx = + + + + + = = = ++ dx+++dx = = = c + d – a b Defuzzification = = = 3.3 APPLICATION In this section. We have discussed the convergence of à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut using the example of dual trapezoidal fuzzy number. CONVERGENCE OF ÃŽ ±-CUT : Let ADT = {a, b, c, d, (à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡) } be a dual trapezoidal fuzzy number whose membership function function is given as  µDT(x) = To find à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut of ADT .We first set à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ [0,1] to both left and right reference functions of ADT. Expressing X in terms of à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ which gives à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut of ADT. à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡= à ¢Ã¢â‚¬ ¡Ã‚ ¨ x l= a+ (b-a) à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡= à ¢Ã¢â‚¬ ¡Ã‚ ¨ x r =d-(d-c) à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ à ¢Ã¢â‚¬ ¡Ã‚ ¨ Aà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡DT= [a+ (b-a) à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡, d-(d-c) à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡] In ordinary to find à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut, we give à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ values as 0 or 0.5 or 1 in the interval [0, 1] .Instead of giving these values for à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡. we divide the interval [0,1] as many continuous subinterval. If we give very small values for à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡, the à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut converges to a fuzzy number [a, d] in the domain of X it will be illustrated by example as given below. Example: ADT = (-6,-4, 3, 6) and its membership function will be  µDT(x) = ÃŽ ±- cut of dual Trapezoidal fuzzy Number à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ = (x l + 6)/2 Xl = 2à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-6 à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ = (6 xr)/3 Xr = 6-3à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ 2à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-6, 6-3à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/10 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ = [-5. 8 , 5.7] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/102 then ADT =[-5.98 , 5.97] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/103 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ = [-5.998 , 5.997] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/104 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[-5.9998 , 5.9997] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/105 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[-5.99998 , 5.99997 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/106 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -5.999998 , 5.999997 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/107 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -5.9999998 , 5.9999997, ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/108 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -5.99999998 , 5.99999997 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/109 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -5.999999998 , 5.999999997] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/1010 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[-6 , 6] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/1011 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[-6 , 6] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/1012 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ =[-6 , 6] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/1013 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ =[-6 , 6 ] †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..etc When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=1/10n as n →∞ then the à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut converges to ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[-6, 6 ] Figure: Graphical Representation of convergence of à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/10 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡= [ -5.6,5.4 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/102 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡= [ -5.96,5.94 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/103 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -5.996,5.994 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/104 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ , -5.9996,5.9994 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/105 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ , -5.99996,5.99994 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/106 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ , -5.999996,5.999994 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/107 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[-5.9999996, 5.9999994 , ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/108 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ , -5.99999996,5.99999994 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/109 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ , -5.999999996,5.999999994 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/1010 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ , -6,6 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/1011 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -6,6 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/1012 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -6,6 ] When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/1013 then ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -6,6] †¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦etc When à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=2/10n as n →∞ then the à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡-cut converges to ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=[ -6,6 ] Simillarly, à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡=3/10n,4/10n,5/10n,6/10n,7/10n,8/10n,9/10n,10/10n upto these value n varies from 1to ∞ after 11/10n,12/10n†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦..100/10n as n varies from 2 to ∞ and101/10n,102/10n†¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦Ã¢â‚¬ ¦. as n varies from 3 to ∞ and the process is goes on like this if we give the value for à °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ it will converges to the dual trapezoidal fuzzy number[-6,6] From the above example we conclude that , In general we have { K/10n} if we give different values for K as n- varies upto to ∞ if we give as n tends to ∞ then the values of ADTà °Ã‚ Ã¢â‚¬ ºÃ¢â‚¬Å¡ converges to the fuzzy number[a,d] in the domain X. 3.4 APPLICATIONS In this section we have numerically solved some elementary problems of mensuration based on arithmetic operation using defuzzified centroid area method 1.Perimeter of Rectangle: Let the length and breadth of a rectangle are two positive dual trapezoidal fuzzy numbers ADT = (10cm, 11cm, 12cm,13cm) and BDT = (4cm, 5cm,6cm,7cm) then perimeter CDT of rectangle is 2[ADT+BDT] Therefore the perimeter of the rectangle is a dual trapezoidal fuzzy number CDT = (28cm, 32cm,36cm,40cm) and its membership functions  µDT(x) = The Perimeter of the rectangle is not less than 28 and not greater than 40 .The perimeter value takes between 32 to 36. Centroid area method: X* = = = = = 34 The approximate value of the perimeter of the rectangle is 34 cm. 2.Length of Rod: Let length of a rod is a positive DTrFN ADT = (10cm,11cm,12cm, 13cm). If the length BDT = (5cm, 6cm , 7cm, 8cm), a DTrFN is cut off from this rod then the remaining length of the rod CDT is [ADT(-)BDT] The remaining length of the rod is a DTrFN CDT = (2cm, 4cm, 6cm, 8cm) and its membership function  µDT(x) = The remaining length of the rod is not less than 2cm and not greater than 8cm.The length of the rod takes the value between 4cm and 6cm. Centroid area method: X* = = = = = 5 The approximate value of the remaining length of the rod is 5cm. 3.Length of a Rectangle: Let the area and breadth of a rectangle are two positive dual trapezoidal fuzzy numbers ADT=(36cm,40cm,44cm,48cm) and BDT=(3cm,4cm,5cm,6cm) then the length CDT of the rectangle is is ADT(:)BDT. Therefore the length of the rectangle is a dual trapezoidal fuzzy number CDT=(6cm,8cm,11cm,16cm) and its membership functions  µDT(x) = The length of the rectangle is not less than 6cm and not greater than 16cm .The length of the rectangle takes the value between 8cm and 11cm. Centroid area method: X * = = = = 10.38 The approximate value of the length of the rectangle is 10.38cm. 4. Area of the Rectangle: Let the length and breadth of a rectangle are two positive dual trapezoidal fuzzy numbers ADT=(3cm,4cm,5cm,6cm) and BDT=(8cm,9cm,10cm,11cm) then the area of rectangle is ADT(.) BDT Therefore the area of the rectangle is a dual trapezoidal fuzzy number CDT= (24cm, 36cm, 50cm, 66cm) and its membership functions  µDT(x) = The area of the rectangle not less than 24 and not greater than 66.The area of the reactangle takes the value between 36 and 50. Centroid area method: X * = = = = 44.167sq.cm 4.CONCLUSION: In this paper, we have worked on DTrFN .We have define the Convergence of ÃŽ ±-Cut to the fuzzy number. We have solved numerically some problems of mensuration based on operations using DTrFN and we have calculated the approximate values. Further DTrFN can be used in various problem of engineering and mathematical science. 5. References [1] Sanhita Banerjee, Tapan Kumar Roy Arithmetic Operations on Generalized Trapezoidal Fuzzy Number and its Applications TJFS: Turkish Journal of Fuzzy Systems (eISSN: 1309–1190) An Official Journal of Turkish Fuzzy Systems Association Vol.3, No.1, pp. 16-44, 2012. [2] Bansal. A., (2010), some non- linear arithmetic operations on triangular fuzzy number (m, ÃŽ ±, ÃŽ ²), Advances in Fuzzy Mathematics, 5,147-156. [3] G. J. Klir, Bo Yuan, Fuzzy Sets and Fuzzy logic, Prentice Hall of India Private Limited, (2005). [4] C. Parvathi, C. Malathi, Arithmetic operations on Symmetric Trapezoidal Intuitionistic Fuzzy Numbers, International Journal of Soft Computing and Engineering, 2 (2012) ISSN: 2231-2307. [5] T. Pathinathan, K. Ponnivalavan, Pentagonal fuzzy numbers, International journal of computing algorithm, 3 (2014) ISSN: 2278-2397. [6] Bansal Abhinav, Trapezoidal Fuzzy Numbers (a, b, c, d); Arithmetic Behavior, International Journal of Physical Mathematical Sciences, ISSN: 2010-1791. [7] T. Pathinathan, K. Ponnivalavan, Diamond fuzzy numbers, International scientific Publications and consulting services journal of fuzzy set valued analysis http://www.ispacs.com/journals/jfsva/2014/jfsva-00220 [8] D. Dubois, H. Prade, Operations on Fuzzy Numbers, International Journal of Systems Science, 9 (6) (1978) 613-626. http://dx.doi.org/10.1080/00207727808941724.

An Argument for the Existence of God Essay -- Argumentative Persuasive

An Argument for the Existence of God God can be defined as a being conceived as the perfect, omnipotent, omniscient originator and ruler of the universe, the principal object of faith and worship in monotheistic religions (1). There are many people that do not believe in any religion. People who do not believe in a religion have no reason for believing in a God. People who do not believe in a God and argue against the existence of God are proving something that is completely false. There is a God for numerous reasons. This paper's purpose is to prove the existence of God. There are ten main reasons that are presented in this paper that show the actuality of God. It also shows counter-arguments to the competing positions (the presence of evil). It also gives anticipatory responses to possible objections to the thesis.   Ã‚  Ã‚  Ã‚  Ã‚  The first reason focuses on the belief of faith. The following passage is taken from the Bible. It has excellent meaning because it shows that everyone has faith. Having faith is the first sign that shows everyone believes in a religion. There are two good definitions of religion. The first is belief in and reverence for a supernatural power or powers regarded as creator and governor of the universe. The second is a personal or institutionalized system grounded in such belief and worship. The passage shows that everyone has an institutionalized system that has belief. The passage is as follows, ?Everyone believes in something. No one can endure the stress and cares of life without faith in God. Atheists cannot prove there is no God. Pantheists cannot prove that everything is God. Pragmatists cannot prove that what will count for them in the future is what works for them now. Nor can agnostics prove that it is impossible to know one way or the other. Faith is unavo idable, even if we chose to believe only in ourselves. What is to be decided is what evidence we think is pertinent, how we are going to interpret that evidence, and who or what we are willing to believe in.? (Luke 16:16)(4) The passage is great proof that there is a God. It shows that everyone has faith. Faith is a big aspect in religion. With every religion, there is likely to be a single holy being, a god.   Ã‚  Ã‚  Ã‚  Ã‚  Many atheists have used science as a way to disapprove the existence of God. Science is not an accurate way of disapproving the existence of God(2). Scient... ...This is completely false because God made the ultimate sacrifice. Jesus sacrificed himself so he could redeem humanity and that all their sins would be forgiven. Making such a self sacrifice is good proof that God cares for humanity. The last reason that proves the existence of God is how we look at God. Most of humanity believes that God must look up to humanity, where as the truth is we must look up to God. The best argument that atheists have to disapprove the existence of God is the presence of evil. But their argument is shut down by the Augustinian theodicy. These reasons are great proof that shows the existence of God. Any atheist who reads all ten reasons and the Augustinian theodicy can never disapprove the existence of God. Bibliography   Ã‚  Ã‚  Ã‚  Ã‚  1) Oxford Readings in Philosophy. The Concept of God. New York: Oxford University press 1987   Ã‚  Ã‚  Ã‚  Ã‚  2) Gollwitzer, Helmut. The Existence of God: As Confessed By Faith. Philadelphia: The Westminister Press, 1965   Ã‚  Ã‚  Ã‚  Ã‚  3) The Summa Theologica of St. Thomas Aquinas. Whether God Exists? 1920. New Advent. http://www.newadvent.org/summa/100203.htm. K. Knight. 2003. 4) Holy Bible. New International Version. (New York). 1978.

Francois Rabelais’ Satire of Medieval and Renaissance Learning In Garga

Francois Rabelais’ Satire of Medieval and Renaissance Learning In Gargantua and Pantagruel In his book Gargantua and Pantagruel, Francois Rabelais uses satire to address the dislocation felt by Renaissance Humanists. By providing an exaggerated fable, comical in nature, Rabelais poses a serious introspection into the extremes of both the Medieval and the Renaissance man. More importantly, however, he brings into question his own ideals of Humanism. Through an analysis of Rabelais’ satirical technique and by examining his social parody of the Medieval and the Renaissance man, we are able to better understand Rabelais’ introspection into the ideals of his own generation and to accept his argument that learning is transitory and often a necessary, yet futile, attempt to understand our world. To understand the Gargantua and Pantagruel it is necessary to first understand Rabelais’ use of satire. As a man whose life spans the transition between the Medieval (Middle) Ages and the Renaissance, Rabelais, as most scholars of the time period, had to cope with a huge shift in thoughts and ideals. Between the changes in religion stemming from the Protestant Reformation, the changes in education stemming from the popularity of great philosophical thinkers, the move towards science and humanism, and the questioning of the universe arising from Copernicus’ discoveries, Rabelais felt the immense dislocation of his generation. He used satire, parody, and fantasy as a means to cope with this dislocation. Through the monstrous and grotesque comedy of Gargantua and Pantagruel, Rabelais is able to ridicule the institutions of his world without necessarily being offensive. He entices his readers to laugh at the events and human thoughts of ... ... of quenching the thirst for knowledge. He writes, â€Å"Every good drinker, every good and gouty one, if he is thirsty, let him come to this barrel of mine† (395). In the end, Rabelais suggests that, like the comical giants of his stories, we are characterized by the desire to know, sometimes beyond our ability to understand. In conclusion, through his depiction of the giant in his Gargantua and Pantagruel, Rabelais effectively satirizes two periods of thought, Medieval and Renaissance, and creates the argument that each, in its extreme, is limited. By comparing these two ages in the same satirical manner, Rabelais suggests that both schools of thought are transitory and that learning is often a necessary, yet futile, attempt to understand our world. Work Cited Putnam, Samuel, sel., transl., and ed. The Portable Rabelais. New York: Penguin Books, 1946.

Comparison Of 1984 And Animal Farm :: compare contrast

Comparison of 1984 and Animal Farm In George Orwell's 1984 and Animal Farm, reality is defined by what the leaders tell the commoners it is, and the idea of individuality and free thought are abolished in order to preserve that reality. 1984 demonstrated the concept of a perceived reality versus a true reality, and Animal Farm revealed that reality is in the beholder. The Outer Party members in 1984 were oblivious to the true reality of their lives and blindly accepted whatever was told to them. An excellent example of the Outer Party's ignorance to truth is when they are told that their chocolate rations have been increased, when actually the rations were just reduced a week earlier. Because of the Party's successful assault on the individuality of its members, people became cheerful when they heard of the news. This perceived reality is the truth to the Party members. The true reality in 1984 is shown only to the reader and some Inner Party members. O'Brien knows the real truth of things as shown by his torturing of Winston. He tells Winston that if the Party tells the people that 2+2=5, then it does. He also instructs Winston that if the Party informs its members that 2+2=3 or 4 or all at the same time, then it is so. Although this true reality is available to Inner Party members, they too do not have the freedom of thought or individuality... they are only just aware of its existence. Only the outside reader is able to think and understand the true nature of the reality established by the Party. In Animal Farm, Orwell unveiled that reality is a simple mental state that can be easily manipulated. Napoleon and the pigs proved this theory by repeatedly changing the Seven Commandments and reporting to the other animals that the 'laws' had always been in their changed condition when they were questioned. Napoleon uses the terror wielded by the dogs to rule the farm with

Contention about gay marriage Essay

Everyone has the right to get married, right, they should not be judged on who they are and what they believe. Everyone is equal and has equal rights I doesn’t matter what type of sex they are. Same-sex couples want to marry for all the same reasons as their opposite-sex counterparts. These reasons include: for legal security, to publicly celebrate their commitment, to provide greater legal protection for their children, or simply because they are in love. According to a national study by researchers at the University of Queensland, 54% of Australian same-sex partners would marry if they had the choice. 80% of Australians in same-sex relationships support marriage equality even if they do not wish to marry. First, we will look at the benefits that flow to same-sex couples who marry. This is followed by the wider social benefits that come from removing discrimination from the Marriage Act and ensuring equality for same-sex couples. Marriage has evolved throughout history, so it can change again. Different cultures have treated marriage differently. Some promoted arranged marriages. Others tied marriage to dowries. Still others saw marriage as a political relationship through which they could forge family alliances. But all these variations still embraced the fundamental, unchanging essence of marriage. They still saw it, in general, as a public, lifelong partnership between one man and one woman for the sake of generating and raising children. This understanding predates any government or religion. It’s a pre-political, pre-religious institution evident even in cultures that had no law or faith to promote it. Yet, even supposing the essence of marriage could change, would that mean it should? We know from other areas of life such as medical research and nuclear physics that just because you can do something doesn’t mean you ought. After all, such action may not be ethical or serve the common good. Even if this argument had historical basis, it would not necessarily be a good reason to change the meaning of  marriage.

What Is Nsa Device

NETWORK ATTACHMENT STORAGE Renika L. Whaley NT1110 Mr Dameon Hagler What is a NAS device? A NAS is hard disk storage that is set up with its own network address rather than being attached to the department computer that is serving applications to a network’s workstation. What is the speed of the network adapter available on a NAS DEVICE? The speed is typically one gigabit Ethernet connection but this can be changed to multiple gigabit, 10 gigabit, fiber optic by adding a PCI-e network card(s). Older parts can be used which may be limited to 10/100 megabit.If you need an exact answer for speed, simply look at the wiki on gigabit. What is the Capacity Range? The capacity range again varies; with port replication and add-on hard drive controller cards there is hardly a limit on size. A board with 6 SATA ports can be replicated (1 to 5 port) allowing for 30 drives to be attached. Is there any fault tolerance (such RAID) built into a NAS device? As fault tolerance, raid 50 is fairl y stable if set up correctly, raid 10 has been touted as one of the best setups since more drives can fail at one time without data loss.All of those features can be used on typical NAS devices. Are management features available? Yes Speculate on why a user would want to use a NAS. For example, what would be the advantage of all family photos and videos being stored on a NAS in a family where the parents and children all had their own computers? NAS is network allocated storage apart from any other systems attached to the network. There are a lot of considerations: 1. Power usage. All users may shutdown their computers. Some people build NAS from atom boards and other things for their low power characteristics. ) 2. Always on availability. As long as the network is up and the NAS is functioning, it is always available regardless of what computers are on/off the network. 3. Centralized Storage for backup. If a computer needs to be rebuilt or wiped, you can push files and backups and restore from the same location. 4. Cost effective. Installing a RAID 1 in each computer (Mirror drive) would cost more and use more storage than perhaps a RAID 5 in the NAS with multiple PC's.This may apply more to offices than for example a small home with 2-3 PC's. 5. Redundancy. Most personal computers operate a single drive (cost consideration) or on performance considerations (RAID 0 etc. ) more so than reliability. NAS are typically setup for redundancy in case of drive failure (RAID 1,5,6 and the various permutations. ) 6. Lower priority data. This doesn't always apply, but lower priority data can be moved to another location (for example, VM Images). They take up storage space, but a user may not want this to take up higher priority space.