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Considering that a manufacturer and its core part supplier make collaborative R&D on serial products of 3 grades, high-, mid-, and low-grade, and their core parts according to costumers' preference for the performance, or intrinsic value, of products, we propose a collaborative R&D model based on costumers' selection behavior to study the collaborative R&D policy and pricing policy of the supply chain. Then we establish a bargaining game model to study how they allocate the profit they earned. We obtain the optimal policies through theoretic and experimental analysis, and we use Apple iPhone case to illustrate the models and conclusions of this paper. It is found that if the aim of the supply chain is only to maximize its total profit, it should only develop the high-grade product and make its price half of its intrinsic value; if the aim of the supply chain is to maximizing profit while increasing the sales and market shares of the serial products, it should at least develop the high-grade and low-grade product; the ratio of price between the higher grade and the lower grade should be greater than the corresponding ratio of the intrinsic value, while the difference of price between higher grade and the lower grade should be less than the corresponding difference of the intrinsic value. [ABSTRACT FROM AUTHOR]

How satisfied is each of us with the fulfillment of his life? In this paper after a thorough search of the literature about satisfaction, 58 criteria and subcriteria related to satisfaction or fulfillment were identiffed and arranged in a hierarchic structure. A process of prioritization known as the Analytic Hierarchy Process is used with the structure, putting in judgments from knowledgeable people to derive priorities for the criteria and subcriteria. A template was then developed for the reader to rate his satisfaction on each of the subcriteria in the structure to obtain an overall measure of satisfaction with their life. Someone who feels they have a perfect life would get 100%. The template can be used by any individual to determine what grade they get in life satisfaction. [ABSTRACT FROM AUTHOR]

The nervous system uses its own kind of mathematical function patterns for both external and internal realities. The conscious part of the nervous system is there to respond to what happens outside by regulating externally received information signals from the senses and the skin and muscles of the body itself. To do that, it needs to communicate with its subconscious using the familiar language of neural firing. In this paper, we show that because reciprocal pairwise comparisons are performed at the neural level, the division algebra of the octonions, in which commutativity and associativity are not satisfied, provides the structure needed to represent mental processes and that these processes could be represented in G2-manifolds. [ABSTRACT FROM AUTHOR]

In this paper we consider many intangible criteria that influence the priorities and ranks of inventions as they contribute to human welfare, by using the Analytic Hierarchy Process. We apply the ideas to evaluate a number of modern inventions along with a few old ones. Both the categories of inventions and the effects they have on human well-being and human progress are considered in this weighting process. Different effects of similar types of inventions could have different properties. To our knowledge this work breaks new ground about the numerical prioritization of all kinds of inventions because of the effort spent in structuring the process in a comprehensive hierarchy. [ABSTRACT FROM AUTHOR]

One often assumes that comparisons are discrete and carried out in a matrix of numbers. However, our eyes and other senses perform comparisons in a continuous way by making many simultaneously. Here the mathematics of pairwise comparisons is generalized to the continuous case. It is more likely that in evolution, little creatures had and now still have a "feeling" about the environment in which they find themselves by sensing many things at once. Through evolution, sensing has been transformed to thinking and to discrete comparisons. This paper presents some material from other works written about continuous comparisons. [ABSTRACT FROM AUTHOR]

The rules of logic are nearly 2500 years old and date back to Plato and Aristotle who set down the three laws of thought: identity, non-contradiction, and excluded middle. The use of language and logic has been adequate for us to develop mathematics, prove theorems, and create scientific knowledge. However, the laws of thought are incomplete. We need to extend our logical system by adding to the very old laws of thought an essential yet poorly understood law. It is a necessary law of thought that resides in our biology even deeper than the other three laws. It is related to the rudiments of how we as living beings, and even nonliving things, respond to influences as stimuli. It helps us discriminate between being ourselves and sensing that there is something else that is not ourselves that even amoebas seem to know. It is the intrinsic ability to sense and distinguish. This fourth law is the law of comparisons. Although it has been missing from our logical deductions it underlies the other three laws of thought because without it we cannot know what is and what is not. [ABSTRACT FROM AUTHOR]

Abstract: Rank preservation and reversal, so fundamental in decision making, have been an unresolved issue in the field of economics and utility theory and came into focus when the Analytic Hierarchy Process was developed because it uses paired comparisons that inevitably make the priorities of the alternatives interdependent. This paper summarizes the important issues that can play a role in rank preservation and reversal with counterexamples to show that preserving rank in all situations is wrong. [Copyright &y& Elsevier]

Abstract: Because good decisions depend on the conditions of the future, and because conditions vary over time, to make a good decision requires judgments of what is more likely or more preferred over different time periods. There are at least three ways to deal with dynamic decisions. One is to include in the structure itself different factors that indicate change in time such as scenarios and different time periods and then carry out paired comparisons with respect to the time periods using the fundamental scale of the AHP. The second is to do paired comparisons as rates of relative change with respect to time. This is done at different points of time as representatives of intervals to which they belong. These intervals can have different lengths. For each representative point one needs to provide a pairwise judgment about the relative rate of change of one alternative over another and derive mathematical functions for that matrix of comparisons for one of the time periods. The third is to do what I proposed in my first book on the AHP and that is to use functions for the paired comparisons and derive functions from them. It is usually difficult to know what functions to use and what they mean. Ideas and examples are presented towards the development of a theory for dynamic decision making. [Copyright &y& Elsevier]

Abstract: The Analytic Hierarchy Process (AHP) provides a way to rank the alternatives of a problem by deriving priorities. A question that occurs in practice is: what is the best combination of alternatives that has the largest sum of priorities and satisfies given constraints? This leads one to consider the interface between the AHP and the combinatorial approach inherent in Linear Programming (LP). The priorities of the alternatives often serve as coefficients of the objective function of an LP problem. The constraints are determined from existing measurements, such as the range for the number of employees needed and the salaries required for various jobs. Another way to use the AHP might be to determine the coefficients of the constraints. This paper addresses the first half of the problem. Through various examples, we show how to apply the absolute measurement mode of the AHP together with LP to optimize human resource allocation problems. For example, one can determine which positions to fill, or which mix of candidates to hire. We also give an example of how to allocate resources to maximize the returns to a corporation of its training programs. Finally, we show that the combined AHP and LP model is capable of solving hiring problems involving synergy, such as when two persons with different complementary skills work as a team. [Copyright &y& Elsevier]

Abstract: Individuals, corporations and governments constantly face the extremely complex problem of ordering and prioritizing their numerous decisions according to urgency and importance. They need to sequence expenditures and allocate scarce resources to optimize the returns on their investments over time. Prioritization requires general and diverse economic, social, political, environmental, cultural and other criteria that reach beyond the familiar process of deciding on the best alternative in making a single decision. Decisions about decisions are more difficult as the best choice for each particular decision is often unknown requiring a large amount of time and resources to determine. There are three cases to consider: (1) the best alternative in each decision is known, (2) the best alternative in each decision is unknown, and (3) a combination of these two cases. What are the values and criteria that we need to use to prioritize the decisions themselves as the alternatives of a more general decision process? Decision-making often involves, among other things, generating alternatives, setting priorities, choosing a best alternative, allocating resources, determining requirements, predicting outcomes, designing systems, optimizing performance, insuring the stability of a system, planning, and resolving conflicts. Government decisions are even more complex than those of corporations: corporations do not have the issues with pressure from all sides that governments have, nor do they involve as much politics. And they are much more resource oriented than governments that tend to make their decisions easier with narrower constraints. [Copyright &y& Elsevier]

Abstract: Fuzzy set theory has serious difficulties in producing valid answers in decision-making by fuzzifying judgments. No theorems are available about its workability when it is applied indiscriminately as a number crunching approach to numerical measurements that represent judgments. When judgments are allowed to vary in choice over the values of a fundamental scale, as in the Analytic Hierarchy Process, these judgments are themselves already fuzzy. To make them fuzzier can make the validity of the outcome, when the actual outcome is known, worse, as shown by several examples in this paper. Also, improving the consistency of a judgment matrix does not necessarily improve the validity of the outcome. Validity is the goal in decision-making, not consistency, which can be successively improved by manipulating the judgments as the answer gets farther and farther from reality. An example of this is included. [Copyright &y& Elsevier]

Abstract: To achieve a decision with which the group is satisfied, the group members must accept the judgments, and ultimately the priorities. This requires that (a) the judgments be homogeneous, and (b) the priorities of the individual group members be compatible with the group priorities. There are three levels on which the homogeneity of group preference needs to be considered: (1) for a single paired comparison (monogeneity), (2) for an entire matrix of paired comparisons (multigeneity), and (3) for a hierarchy or network (omnigeneity). In this paper we study monogeneity and the impact it has on group priorities. [Copyright &y& Elsevier]

Abstract: This paper puts forth a framework for reshaping the group decision-making process. The proposed framework extends from the usual one-issue-at-a-time decision-making to one that involves several related issues simultaneously. Weaknesses of the traditional majority voting mechanism are first identified, and then a different voting method that takes each individual voter''s sentiment into account is discussed. Specifically, a decision-maker is asked to express his/her intensity of preference for the issues encountered. Three hierarchical structures—benefits, costs, and risks—are developed to evaluate the alternatives. Due to the nature of pairwise comparisons and synthesis, the proposed method is amenable to consensus building and has higher reliability and consistency. It can be used for candidate selection, e.g. governmental election, when a large population is involved. It is also effective for resource allocation and prioritization when a small group or business is concerned. We believe the proposed approach has potential for resolving deficiencies of the conventional voting mechanism, and can be applied to many real-world problems. Its implementation on the Internet is also discussed. [Copyright &y& Elsevier]

An intangible is an attribute that has no scale of measurement. Intangibles such as effort and skill arise in conjunction with resource allocation but are not usually included directly in a mathematical model because of the absence of a unit of measurement. However, intangibles can be quantified through relative measurement (priorities). Intangible resource allocation uses these priorities along with normalized measures of tangibles (when present) in a linear programming model with coefficients and variables measured in relative terms. The priorities of tangible resources from the optimal solution can then be used to assign monetary values to priorities of any intangible resources. [Copyright &y& Elsevier]

In this study, cultural, economic as well as certain crucial demo- graphic factors are considered as the determinants for projecting the average family size in rural India. We use the Analytic Hierarchy Process to analyze influences of the factors which enter implicitly in a rural couples decision-making to determine the number of children they want to have as time goes by. We did not attempt to make distinctions among the regional differences in rural India. The outcome projected in our analysis compares favor- ably with the results of other demographic studies. [ABSTRACT FROM AUTHOR]

Proposes an international center for conflict resolution. Functions of the center; Specific objectives of the proposed center; Activities of the center.

Abstract: This paper describes a forecast, performed in December 2008, of the time of the recovery of the U.S. economy from the contraction that began in December 2007. As in two earlier papers, the forecast uses an expert judgment approach, the Analytic Hierarchy Process (AHP), within the framework of decision theory, as well as its generalization to dependence and feedback in the form of the Analytic Network Process (ANP). The findings of this paper are that the economy would begin its recovery in July–August, 2010. While forecasting is always hazardous, our 2001 paper successfully forecast the date the recovery began. Since 1920 the validating authority for the turnaround dates has traditionally been the widely recognized National Bureau of Economic Research (NBER). The Bureau usually releases an official statement with their finding many months after the event (and of course after the forecasts had been done). Our results on the month in which the recovery began in 2001 were confirmed by the NBER in July 2003. We will again await the NBER determination of the time of recovery from the current recession. [Copyright &y& Elsevier]

This paper describes a forecast of the date for the resumption of growth of the US economy in 2001. It uses an expert judgment approach within the framework of decision theory, the Analytic Hierarchy Process, as well as its generalization to dependence and feedback, the Analytic Network Process.Note: We request the reader of this article to regard the following in considering our analysis and findings. The forecasting exercise described in this paper was conducted on April 7, 2001, while the final version of the manuscript was accepted for publication in August 2001. The authors clearly could not have taken into account the horrific acts of September 11, 2001 in New York, Washington, and Pennsylvania. As is now well known, the events of that day have significantly affected, in a negative manner, consumer and investor confidence both in the US and around the world. Further, they have moved the federal government to consider various budget deficit-exacerbating measures. These include massive financial assistance to the airline industry, emergency financial assistance for New York City, and the upgrading and enhancement (probably under federal control) of airline security systems. Importantly, all these measures come at a time when many analysts project a reduction in tax revenues associated with the economic decline in progress prior to September 11. Clearly, it will be many months before the net effects of these phenomena can be fully assessed in terms of the future course of the US economy.Note: We ask the reader of this article to consider the following in considering our analysis and findings: The forecasting exercise described in this paper was conducted on April 7, 2001, while the final version of the manuscript was accepted for publication in August 2001. The authors clearly could not have taken into account the horrific acts of September 11, 2001 in New York, Washington, and Pennsylvania. As is now well known, the events of that day have significantly affected, in a negative manner, consumer and investor confidence both in the U.S. and around the world. Further, they have moved the federal government to consider various budget deficit-exacerbating measures. These include massive financial assistance to the airline industry, emergency financial assistance for New York City, and the upgrading and enhancement (probably under federal control) of airline security systems. Importantly, all these measures come at a time when many analysts project a reduction in tax revenues associated with the economic decline in progress prior to September 11. Clearly, it will be many months before the net effects of these phenomena can be fully assessed in terms of the future course of the U.S. economy. [Copyright &y& Elsevier]