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Often big companies and governments fail to produce a successful plan of action in the post-data mining analysis and decision-making stage to face challenging situations, which results in billions of dollars loss. Indeed, this crucial stage is left to the decision makers (DMs) to make decisions based on their experience, available information, mindset and habits without any scientific and systematic approach. In this paper, we present a general formal model for decision-making and new knowledge generation that can be used in post-data mining analysis to derive better decisions. The proposed model is formulated in the framework of Habitual Domains theory. The concepts of optimization in changeable spaces and the related solution, the wonderful solution, are introduced in Part I of the paper. Further, ways on how to find wonderful solutions by expanding DMs Habitual Domains in post-data mining analysis and decision-making are presented with applications in Part II of the paper. The proposed model is a significant departure from the traditional decision models that are based on utility function. It can also be used to empower other sciences such as political sciences, medical sciences, management sciences and research activities in all areas.

In the Part I of this paper, we presented the main concept of the proposed comprehensive decision model based on Habitual Domains theory, the concept of wonderful solution for solving challenging decision problems that we called decision making in changeable spaces problem (DMCS). In this Part II of the paper, we complete the construction of the model and show that it is operational and effectively empowers DMs in facing challenges. For this purpose, we present the mental principles “7–8–9 principles” that can be used to restructure decision parameters so that new solutions or alternatives could emerge. Then we provide procedures for finding wonderful solutions as sequences of the 7–8–9 principles by solving optimization in changeable spaces (OCS) problems, a new paradigm in optimization. Finally, we present applications of the model to post data mining analysis and decision making. In fact, the proposed model can be used in any area involving decision making and knowledge discovery such as management, politics, health care, technology and research.

In the financial market, most available rating information is based on multi-criteria and published by myriad agents or companies. Given a multi-criteria rating report on a finite number of assets (e.g., stocks, bonds, mutual funds), we can construct sets of ordered classes. If ratings from a published report have useful and valid information value as claimed, the average performances of assets within classes are expected to show some monotonic property. A set of hypotheses and empirical tests based on Value Line Mutual Fund Survey are provided to illustrate our proposed method. Implications and future research opportunities are also discussed.

Investment in stock market involves many decision criteria and variables; hence investors are increasingly relying on the ratings provided by rating agencies to guide their stock selections. However, do these stock ratings have information value? Are these agencies' ratings valid? We establish the dominance cone principle and use the Value Line stock ratings to demonstrate the application of the dominance principle. Our results based upon limited data show that the Value Line rating does not support the notion that better rating results in better rate of return during 2006–2007.

In this chapter, we integrate the results of Chaps. 2– 5, to introduce and develop a tool for effective DMCS problem solving, the Optimisation in Changeable Spaces (OCS). The pair DMCS-OCS is a new paradigm in decision-making and optimisation. This paradigm is based on Habitual Domain, the model ( 3.3), the 7-8-9 principles, and the concept of competence set. In DMCS-OCS, new concepts of solutions are used, namely, the acceptable and wonderful solutions introduced in Chap. 1 and discussed in Sect. 3.5. Several OCS models are proposed for two large classes of DMCS problems, namely, the covering and discovering problems. Moreover, operational procedures for solving these two problems are developed in Sect. 6.6. The acceptable or wonderful solutions of DMCS problems are presented in the form of a sequence of 7-8-9 principles, called IG-operators. Two DMCS problems are solved to demonstrate the application potential of OCS.

In this chapter, we look at Innovation Dynamics as a DMCS problem. We analyse the process of Innovation Dynamics from Habitual Domains perspective using competence set and formulate it as a sequence of OCS problems. The elements of our Innovation Dynamics analysis are related to the involved fields of management. Illustrations are also provided.

This chapter completes Chap. 7 as it covers a different set of important human activity domains. We present DMCS problems and their solutions related to social phenomena, geopolitics, and discovery presented in Chap. 1, namely, Problems 1.3, 1.5, 1.6, 1.8 and 1.9, and Problem 2.2 (Alinsky airport strategy). We formulate them as OCS problems. For each of these OCS problems, a wonderful solution is found by the DM as an IG-operator from the set CM (see ( 6.1)).

In this chapter, we present the theory of Habitual Domain (HD) and the associated Human Behaviour Mechanism from which we derive a decision model that incorporates and integrates all the ten decision parameters analysed in Chap. 2, and their dynamics and interaction. We also show that this decision model is an adequate tool for formulating and solving DMCS problems. Moreover, we introduce the concepts of acceptable and wonderful solutions that we use as solutions to DMCS problems. Further, we present eight behavioural tendencies that can help solve DMCS problems.

In this book, we have presented a new general model for decision-making, the DMCS, focusing on DMCS dis/covering problems and the Optimisation in Changeable Spaces (OCS) as a tool for solving DMCS problems. The proposed model is a considerable departure from the traditional optimisation and decision theory framework for it incorporates human psychology and its dynamics and the possibility of restructuring the parameters of the decision problem. This aspect has never been taken into account in such a comprehensive way in traditional decision and optimisation models. Thus, the introduced models offer new possibilities to decision makers, managers and executives in solving real-world challenging decision problems effectively and efficiently. In this chapter, we sketch five potential areas for further research, development and application of the proposed model in five sections including management and game situations, artificial intelligence, knowledge extraction and competence set-related research problems.

In this chapter, we illustrate the application potential of OCS to real-world DMCS problems. We show how DMCS covering and discovering problems can be solved via OCS. For this purpose, we formulate some DMCS problems related to management and economics presented in Chap. 1, namely, Problems 1.1, 1.2, 1.4 and 1.7, and one new problem (wonderful solution to 1984 Olympic Games, converting potential big loss to big gains), as OCS problems using the models ( 6.3)–( 6.10) and construct their acceptable or wonderful solutions.

Our objective in this chapter is to present Competence Set Analysis with respect to decision-making. Competence set is a tool to evaluate the capacity of a decision-maker to solve a problem. Moreover, we formulate routine, mixed routine, fuzzy, and challenging decision-making problems (see Sect. 2.2, Chap. 2), including covering and discovering problems, in terms of competence set. This chapter will pave the way for Chap. 6, where we formulate and find acceptable or wonderful solutions to DMCS problems using the concept of competence set, HD theory and the 7-8-9 principles explained in Chap. 4.

In this chapter, our main objective is to analyse the decision process and point out its ten major parameters. We begin by briefly introducing these parameters before classifying non-trivial decision problems according to their difficulty. The most difficult problems are classified as challenging, while easy problems are classified as routine problems. We then present a comprehensive and detailed anatomy of the decision process. Finally, the decision process is summarised in a diagram and formulated as a mathematical model.

In this chapter, we present methods for HD expansion for solving challenging decision problems effectively. First, we discuss the types of HD expansion then present the 7-8-9 principles, twenty-four simple and powerful mental principles that DM can use to expand his HD to solve challenging decision problems. Then, we provide a procedure based on the 7-8-9 principles for solving DMCS problems with an illustration.

This paper proposes a new decision making/optimization paradigm, the decision making/optimization in changeable spaces (DM/OCS). The unique feature of DM/OCS is that it incorporates human psychology and its dynamics as part of the decision making process and allows the restructuring of the decision parameters. DM/OCS is based on Habitual Domain theory, the decision parameters, the concept of competence set, and the mental operators 7-8-9 principles of deep knowledge. The covering and discovering processes are formulated as DM/OCS problems. Some illustrative examples of challenging problems that cannot be solved by traditional decision making/optimization techniques are formulated as DM/OCS problems and solved. In addition, some directions of research related to innovation dynamics, management, artificial intelligence, artificial and e-economics, scientific discovery, and knowledge extraction are provided in the conclusion.

Challenging decision problems in changeable spaces are characterized by existence of complex decision parameters that are changing with time and situations, including criteria and alternatives. Some of these parameters may be critical for their effective solutions, but hidden in the depth of potential domains. In this rapidly changing world, including technology and attitude, without paying attention to the problems in changeable spaces, we could easily commit serious mistakes due to decision blinds, decision traps and/or decision shocks. The article starts with a brief description of the evolution of MCDM toward challenging problems in changeable spaces. Then it briefly sketches a dynamic human behavior mechanism and habitual domain theory which provide an effective list for us to search relevant decision parameters and pave the way for latter discussion. Competence set analysis, derived from habitual domain, is then introduced to exemplify decision blinds, decision traps and decision shocks in challenging decision problems. Checking lists and methods for discovering blinds and traps and for dealing with shocks are also provided. Innovation dynamics, a systematic network of thoughts, is introduced to further look out relevant key parameters in dynamic challenging problems. The related academic subjects in each link of the innovation dynamics are also explained, which allow us to see the complexity and interconnectivities among different challenging problems in changeable spaces. Finally we introduce three habitual domain tool boxes to empower ourselves to expand and enrich our thoughts into the depth of the potential domains of the challenging problems, which allows us to more effectively identify hidden parameters, problems and competence sets to reduce decision blinds, avoid decision traps and solve the problems, or dissolve the problems before they occur.

Challenging decision problems in changeable spaces are characterized by existence of complex decision parameters that are changing with time and situations, including criteria and alternatives. Some of these parameters may be critical for their effective solutions, but hidden in the depth of potential domains. In this rapidly changing world, including technology and attitude, without paying attention to the problems in changeable spaces, we could easily commit serious mistakes due to decision blinds, decision traps and/or decision shocks. The article starts with a brief description of the evolution of MCDM toward challenging problems in changeable spaces. Then it briefly sketches a dynamic human behavior mechanism and habitual domain theory which provide an effective list for us to search relevant decision parameters and pave the way for latter discussion. Competence set analysis, derived from habitual domain, is then introduced to exemplify decision blinds, decision traps and decision shocks in challenging decision problems. Checking lists and methods for discovering blinds and traps and for dealing with shocks are also provided. Innovation dynamics, a systematic network of thoughts, is introduced to further look out relevant key parameters in dynamic challenging problems. The related academic subjects in each link of the innovation dynamics are also explained, which allow us to see the complexity and interconnectivities among different challenging problems in changeable spaces. Finally we introduce three habitual domain tool boxes to empower ourselves to expand and enrich our thoughts into the depth of the potential domains of the challenging problems, which allows us to more effectively identify hidden parameters, problems and competence sets to reduce decision blinds, avoid decision traps and solve the problems, or dissolve the problems before they occur.

In this paper, we present a new approach to n-person games based on the Habitual domain theory. Unlike the traditional game theory models, the constructed model captures the fact that the underlying changes in the psychological aspects and mind states of the players over the arriving events are the key factors, which determine the dynamic process of coalition formation. We introduce two new concepts of solution for games: strategically stable mind profile and structurally stable mind profile. The theory introduced in this paper overcomes the dichotomy of non-cooperative/cooperative games, prevailing in the existing game theory, which makes game theory more applicable to real-world game situations.

In most challenging decision problems, relevant parameters are changing. Decision blinds, decision traps, and fuzziness, would unavoidably occur in the process of dealing with this kind of problems. To make effective decisions, it is important to be aware of the existence and changing nature of the potential parameters. In this article we first discuss a main cause of fuzziness and unknowns in decision making, and then introduce the relevant parameters including those in human behavioral systems and in decision processes. The concepts of habitual domains, decision blinds and decision traps are explored. The tools of habitual domains are proposed to enable decision makers to more effectively expand and enrich their visions and perceptions on the problems as to reduce decision blinds and fuzziness, and avoid decision traps. Consequentially, effective solutions for decision making in changeable spaces can be located.

Human behaviors involve dynamic, evolving, interactive and adaptive processes. Important decision makings usually are dynamic, involving multiple criteria in changeable spaces. This article introduces the behavior mechanism that integrates the findings of neural science, psychology, system science, optimization theory and multiple criteria decision making. It shows how our brain and mind operate and describes our behaviors and decision making as dynamic processes of multiple criteria decision making in changeable spaces. Unless extraordinary events occur or special effort exerted, the dynamic processes will be stabilized in certain domains, known as Habitual Domains. Habitual Domains, which play a vital role in upgrading the quality of our decision making and lives, will be explored. In addition, as important consequential derivatives, concepts of Competence Set Analysis and Innovation Dynamics will also be discussed. Note that these concepts involve transitions between dynamic and static states.

It is well known that human psychology determines his/her action and behavior. This fact has not been fully incorporated in game theory. This paper intends to incorporate human psychology in formulating games as people play them. In Part 1 of the paper, we formulate a two-person game by the habitual domain theory and the Markov chain theory. Using the habitual domains theory, we present a new model describing the evolution of the states of mind of players over time, the two-person second-order game. We introduce the concept of the focal mind profile as well as the solution concept of the win-win mind profile. In addition, we provide also a method to predict the average number of steps needed for a game to reach a focal or win-win mind profile. Then, in Part 2 of the paper, under some reasonable assumptions, we derive the possibility theorem stating that it is always possible to reach a win-win mind profile when suitable conditions are satisfied.

In Part 1 of the paper, using habitual domains theory and finite Markov chain theory, we have introduced a new model for describing the evolution of the states of mind of players over time, the two-person second-order game. The concepts of focal mind profile as well as the solution concept of win-win mind profile have been introduced as solution concepts for these games. In Part 2 of the paper, we address the problem of restructuring a game where the focal profile (1,1) is not reachable or is not a win-win profile into a game where the profile (1,1) is a reachable win-win profile. Precisely, under some reasonable assumptions, we derive the possibility theorem that it is always possible to reach a win-win mind profile in a two-person second-order game. Moreover, we provide practical operations for restructuring games for reaching a win-win profile.

Corporate competence sets can be expanded through capital investment and be dynamically changed overtime, which can explain the phenomenon of "taking loss at the ordering time and making profit at the time of delivery". Such phenomenon has existed in practice for a long time, but there are no mathematical model that can explain it adequately. This paper utilizes multiple criteria and multiple constraint levels linear programming (MC2LP) model and its extended techniques to explore the linear programming models with changeable parameters. The parameters include: unit profit, available resources, and input-output coefficients of production function. With those parameters changed with capital investment and/or time, we study how to find dynamic best solutions to make "taking loss at the ordering time and making profit at the time of delivery" feasible. For more general cases we also sketch a generalized mathematical programming model with changeable parameters and control variables.

We usually use a set of ideas, thinking paradigms and judgment rules, including alternatives, criteria, outcomes, preferences, to make decision. This set, known as actual domain (working knowledge) of habitual domain, will be stabilized over time unless extraordinary events occur. As such, our working knowledge cannot be broad and deep. Inevitably, we could get into decision traps, which lead us to making wrong decision or solving wrong problems. The actual domain is only a small part of our potential domain, the collection of all thoughts, ideas, thinking paradigms, etc. that have ever been encoded in our brain. In this paper, we will describe nine principles for deep knowledge, so that, we could expand and enrich our working knowledge by utilizing the potential domains of ourselves and other participants in the decision making. As a consequence, good ideas for solving challenging decision problems can be obtained or created. These principles are: The deep and down principle, the alternating principle, the contrasting and complementing principle, the revolving and cycling principle, the inner connection principle, the changing and transforming principle, the contradiction principle, the cracking and ripping principle, the void principle.

There are many parameters in challenging decision problems, including the alternatives, the criteria, resources, the perception of decision problems, decision makers and their psychological states, information inputs from the environment, and self-suggestion, etc. At any moment of time, some of these parameters can catch our attention, called alerted parameters; some cannot, called unalerted parameters. Some parameters are visible, some are invisible. In addition, the parameters themselves can vary over certain ranges or domains. All of these make challenging decision problems very complex. We call this kind of problems as decision problems with changeable spaces (parameters). We may focus on certain parameters with certain assumed values to find an "optimal" solution, which may lead to solve wrong problem with bad solution. Quite often, our focus may be just a small part of what we know, or just a part of what we are most familiar with. We may often neglect what we are not familiar with, and pay no attention to what we do not know. As a consequence, we may see just a small part of the problem domain (including all parameters and their possible variations over time). The portion (of the problem domain) that we cannot see is our decision blind. Suppose our alerted domain (those parameters and their variations that are currently under our consideration) to be fixed in only a small part of the problem domains. Then very likely we could end up with a serious mistake. This situation is known as decision trap. In this article, we will introduce a systematic scheme, based on habitual domain theory, to help us reduce decision blinds and avoid decision traps so that we could make decision with good quality. Then we will also introduce the concept of competence set analysis to help us cope with challenging decision problems. This including: (i) how to effectively expand our competence (resources, skill, know-how, information, ideas, effort, etc.) as to solve a given problem effectively; and (ii) given a set of competence, how to maximize its value by solving a set of value added problems. Furthermore, we will introduce innovation dynamics which describe the dynamics of how to solve a set of problems with our existent or acquired competence (to relieve the pains or frustrations of "certain customers or decision makers" at certain situations) as to create value, and how to distribute this created value so that we can continuously expand out competence set to solve more challenging problems and create more value.

In this article, we show that, in high-tech industries, there are significant differences in the Habitual Domains (HD) of technologists/researchers (T/R) and managers/leaders (M/L). The differences are measured specifically in the following: characteristics, attitudes toward career and life, perception of business problems, business competences and resources. We then describe how a T/R can effectively transform himself/herself into a successful M/L, by transforming his/her HD closer to that of a successful M/L.

In this paper, we discuss how information technology (IT) affects and influences people to make decisions. We first introduce human behavior mechanism and habitual domains — the software that drive the behaviors. Then we discuss the impacts of IT on decision elements and environment, and then IT's impacts on a variety of decision problems including routine problems, mixed routine problems, fuzzy problems and challenging problems. IT is useful in solving routine problems but not as obvious in solving fuzzy and challenging problems. To solve fuzzy and challenging problems, an effective concept and model of competence set analysis is introduced. Finally, we describe three types of competence set analysis and show how IT can help in these three types of problems.

In this paper, we consider the expansion processes of competence sets which have asymmetric cost functions, intermediate skills, and compound skills; among the skills, cyclic connections are possible. We introduce the concept of the stage expansion process (SEP) of the competence set, and provide mathematical programming methods to find a minimal cost SEP and the ordering of expansion.

This paper provides a method for finding the optimal expansion process of the competence set in generalized situations in which the cost functions are asymmetric and the directed graphs, which depict all possible expansion processes, have cycles and contain intermediate skills and compound nodes.

This chapter proposes a model of covering and discovering processes for solving non-trivial decision making problems in changeable spaces, which encompass most of the decision making problems that a person or a group of people encounter at individual, family, organization and society levels. The proposed framework fully incorporates two important aspects of the real-decision making process that are not fully considered in most of the traditional decision theories: the cognitive aspect and the psychological states of the decision makers and their dynamics. Moreover, the proposed model does not assume that the set of alternatives, criteria, outcomes, preferences, etc. are fixed or depend on some probabilistic and/or fuzzy parameter with known probability distribution and/or membership function. The model allows the creation of new ideas and restructuring of the decision parameters to solve problems. Therefore, it is called decision making/optimization in changeable spaces (DM/OCS). DM/OCS is based on Habitual Domain theory, the decision parameters, the concept of competence set and the mental operators 7-8-9 principles of deep knowledge. Some illustrative examples of challenging problems that cannot be solved by traditional decision making/optimization techniques are formulated as DM/OCS problems and solved. Finally, some directions of research are provided in conclusion.

This paper provides a method of finding the optimal expansion process and discusses the marginal analysis for expansion of the competence set when the cost functions are asymmetric. The concept of tree expansion process is introduced, and a method of finding the optimal tree expansion process is given. The paper also shows a way to identify the optimal competence set when both the expected return and cost are considered.

To select an optimal linear design means to select the best subset from a set of possible products or opportunities for commitment and to construct the corresponding optimal contingency plans for coping with the changes of decision parameters. Based on Lee, Shi and Yu, this paper discusses a method for generating generalized good designs from known potentially good designs. We describe how to use the multi-criteria and multi-constraint-level (MC 2 ) simplex method to identify the generalized optimal designs and their related optimal contingency plans. A procedure for effectively and systematically solving the problem of selecting linear designs is proposed.

Using a set covering concept we explore the possibility and flexibility of selecting a subset of all possible pairs of comparisons to assess priority weights of the decision criteria. Different techniques offer different priority weights with different properties. They are, however, interrelated when special subsets such as basic coverings, elementary cycles and complete covering are considered. This paper provides a framework for unifying existing assessment methods, and offers some fundamental theorems which reveal the intricate relationships among the methods over the subsets.

In many real world problems, we want to generate new designs (ideas) by taking unions of subsets of a given basic set of potentially good designs (primitives). This paper proposes a streamlined algorithm of finding distinct unions of subsets of the primitives. We show how to use the algorithm to eliminate a number of redundant unions of subsets of the primitives in the process of finding all distinct unions. Theoretical results are derived to justify the algorithm. Applications of the algorithm are also discussed.

Given a problem of multiple-criteria and multiple-constraint level (MC 2 ) linear programming, we can use the MC 2 -simplex method to effectively identify a set of potential solutions. These potential solutions maximize the MC 2 problem under some possible changes of resource availability levels and criterion coefficients. An opportunity that is not selected in any potential solutions is called a permanently dominated opportunity. This paper proposes techniques to recognize and eliminate permanently dominated opportunities from further consideration in the process of solving the given MC 2 problem. The elimination technique for multiple-criteria (MC) linear programming is also discussed.

A competence set is a collection of skills used to solve a problem. Based on deduction graph concepts, this paper proposes a method of finding an optimal process so as to expand a decision maker's competence set to enable him to solve his problem confidently. Using the concept of minimum spanning tree, Yu and Zhang addressed the problem of the optimal expansion of competence sets. In contrast, the method proposed here enjoys the following advantages: it can deal with more general problems involving intermediate skills and compound skills; it can find the optimal solution by utilizing a 0–1 integer program; and it can be directly extended to treat multilevel competence set problems, and thus is more practically useful.

Given a set of decision environments, we explore the selection of the optimal competence set so as to maximize the expected net return. Marginal analysis is used to formulate the concepts. An elegant theory and subsequent algorithms are derived for special classes of problems.

This chapter introduces the behavior mechanism that integrates the discoveries of neural science, psychology, system science, optimization theory and multiple criteria decision making. It shows how our brain and mind works and describes our behaviors and decision making as dynamic processes of multicriteria decision making in changeable spaces. Unless extraordinary events occur or special effort exerted, the dynamic processes will be stabilized in certain domains, known as habitual domains. Habitual domains and their expansion and enrichment, which play a vital role in upgrading the quality of our decision making and lives, will be explored. In addition, as important consequential derivatives, concepts of competence set analysis, innovation dynamics and effective decision making in changeable spaces will also be introduced.

To select an optimal linear production system means to select the best subset of products from the set of possible products for production and to prepare the necessary contingency plans that can be flexibly used to cope with changes of decision parameters, such as criterion coefficients and resource availability levels, in a given planning horizon. This paper describes mathematical models for selecting optimal production systems under multiple criteria environments by using the multiple criteria and multiple-constraints-level (MC 2 ) simplex method. An effective procedure is proposed for systematically identifying optimal linear production systems and constructing related contingency plans. A computer-aided support system to implement the procedure is also sketched.

In this paper, the concept of state-dependent weights is studied. This offers the flexibility to approximate the changing weights of the decision maker. The relationship between state-dependent weights and value functions is discussed.

It is difficult for a decision maker, confronted with a complex linear MCDM problem, to reach a final choice if he/she is presented with a large number of nondominated solutions. In general, the smaller the size of the nondominated set, the faster and easier the decision can be made. If the problem has only one nondominated solution, the solution will be chosen without hesitation. Using the concept of cone separation, we present fundamental theorems which guarantee a linear MCDM problem with a unique nondominated solution. As facilities for decision support, we investigate theorems and present methodologies for transforming and restructuring decision problems in order to obtain a unique nondominated point. Transformation and restructuring are done through altering the four decision elements: alternatives, criteria, outcomes, and preference structures. The issue is studied in the scope of problem structures. Example are given throughout to facilitate understanding.

In optimal design problems we try to select a subset from the opportunity set for commitment for a period of time. As the external parameters can vary with time, optimal contingency plans must be constructed to cope with the external conditions. We describe the formulation and methods for locating potentially good designs and their corresponding optimal contingency plans using a multiple-criteria and multiple-constraint level (MC2) simplex method to solve the optimal design problems which have been shown to become amenable to the techniques of decision making under uncertainty.

It always takes time for people to digest information and make judgments. The decision maker's preference is not always clear and stable when decision analysis and decision making are performed. In this paper, we introduce a generalized preference structure to cope with indefinite preferences. We describe its general properties, its implication on value function representation, its solution concepts, and methods for obtaining the solutions.