Ebook: Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making

In the literature of decision analysis it is traditional to rely on the tools provided by probability theory to deal with problems in which uncertainty plays a substantive role. In recent years, however, it has become increasingly clear that uncertainty is a mul­ tifaceted concept in which some of the important facets do not lend themselves to analysis by probability-based methods. One such facet is that of fuzzy imprecision, which is associated with the use of fuzzy predicates exemplified by small, large, fast, near, likely, etc. To be more specific, consider a proposition such as "It is very unlikely that the price of oil will decline sharply in the near future," in which the italicized words play the role of fuzzy predicates. The question is: How can one express the mean­ ing of this proposition through the use of probability-based methods? If this cannot be done effectively in a probabilistic framework, then how can one employ the information provided by the proposition in question to bear on a decision relating to an investment in a company engaged in exploration and marketing of oil? As another example, consider a collection of rules of the form "If X is Ai then Y is B,," j = 1, . . . , n, in which X and Yare real-valued variables and Ai and Bi are fuzzy numbers exemplified by small, large, not very small, close to 5, etc.

---

This volume brings together for the first time articles by well-known experts focusing on the topic of the joint occurrence of imprecision, dealt with in terms of fuzzy sets and possibility theory, and randomness, dealt with in terms of probability theory, in a wide spectrum of decision making problems. In the introductory section, some basic issues related to decision making under uncertainty and fuzziness are discussed in some survey-type papers. The second part is devoted to basic theoretical issues, including uncertainty measures, fuzzy measures, fuzzy random variables, fuzzy statistics and evaluation and aggregation of imprecise and uncertain evidence. The third part presents the concepts of a stochastic fuzzy set and a probabilistic set which are basically some fuzzy sets involving random aspects. The fourth part presents a wide spectrum of models in which some aspects of fuzziness and randomness co-occur. It includes papers on fuzzy statistical decision making, fuzzy stochastic and statistical dominance, probabilistic-set-based decision making, optimization under fuzziness and randomness and fuzzy dynamic programming with stochastic systems. The fifth and final part deals with applications in economy and finance, nuclear reactor protection, classification and pattern recognition, reliability and earthquake forecasting. The reader is provided with a set of tools which enable him to deal with diverse decision problems in which imprecision and uncertainty jointly occur.

---

This volume brings together for the first time articles by well-known experts focusing on the topic of the joint occurrence of imprecision, dealt with in terms of fuzzy sets and possibility theory, and randomness, dealt with in terms of probability theory, in a wide spectrum of decision making problems. In the introductory section, some basic issues related to decision making under uncertainty and fuzziness are discussed in some survey-type papers. The second part is devoted to basic theoretical issues, including uncertainty measures, fuzzy measures, fuzzy random variables, fuzzy statistics and evaluation and aggregation of imprecise and uncertain evidence. The third part presents the concepts of a stochastic fuzzy set and a probabilistic set which are basically some fuzzy sets involving random aspects. The fourth part presents a wide spectrum of models in which some aspects of fuzziness and randomness co-occur. It includes papers on fuzzy statistical decision making, fuzzy stochastic and statistical dominance, probabilistic-set-based decision making, optimization under fuzziness and randomness and fuzzy dynamic programming with stochastic systems. The fifth and final part deals with applications in economy and finance, nuclear reactor protection, classification and pattern recognition, reliability and earthquake forecasting. The reader is provided with a set of tools which enable him to deal with diverse decision problems in which imprecision and uncertainty jointly occur.
Content:
Front Matter....Pages I-IX
Essay on the History of the Development of Many-Valued Logics and Some Related Topics....Pages 1-9
Uncertainty Aversion and Separated Effects in Decision Making Under Uncertainty....Pages 10-25
Essentials of Decision Making Under Generalized Uncertainty....Pages 26-47
Decision Evaluation Methods Under Uncertainty and Imprecision....Pages 48-65
Fuzzy Random Variables....Pages 66-74
Fuzzy P-Measures and their Application in Decision Making....Pages 75-88
Theory and Applications of Fuzzy Statistics....Pages 89-112
Confidence Intervals for the Parameters of a Linguistic Random Variable....Pages 113-123
On Combining Uncertainty Measures....Pages 124-134
On the Combination of Vague Evidence of the Probabilistic Origin....Pages 135-144
Fuzzy Evaluation of Communicators....Pages 145-151
Uncertain Associational Relations: Compatibility and Transition Relations in Reasoning....Pages 152-167
Stochastic Fuzzy Sets: A Survey....Pages 168-183
Probabilistic Sets — A Survey....Pages 184-196
Decision Making Based on Fuzzy Stochastic and Statistical Dominance....Pages 197-214
Decision Making in a Probabilistic Fuzzy Environment....Pages 215-226
Randomness and Fuzziness in a Linear Programming Problem....Pages 227-239
Comparison of Methodologies for Multicriteria Feasibility — Constrained Fuzzy and Multiple-Objective Stochastic Linear Programming....Pages 240-265
Fuzzy Dynamic Programming with Stochastic Systems....Pages 266-285
Probabilistic-Possibilistic Approach to Some Statistical Problems with Fuzzy Experimental Observations....Pages 286-306
Estimation of Life-Time with Fuzzy Prior Information: Application in Reliability....Pages 307-321
Questionnaires with Fuzzy and Probabilistic Elements....Pages 322-330
From Fuzzy Data to a Single Action — A Simulation Approach....Pages 331-341
Probabilistic Sets in Classification and Pattern Recognition....Pages 342-352
Fuzzy Optimization of Radiation Protection and Nuclear Safety....Pages 353-373
Application of Fuzzy Statistical Decision Making in Countermeasures against Great Earthquakes....Pages 374-388
From an Oriental Market to the European Monetary System: Some Fuzzy-Sets-Related Ideas....Pages 389-399
Back Matter....Pages 400-401

---

This volume brings together for the first time articles by well-known experts focusing on the topic of the joint occurrence of imprecision, dealt with in terms of fuzzy sets and possibility theory, and randomness, dealt with in terms of probability theory, in a wide spectrum of decision making problems. In the introductory section, some basic issues related to decision making under uncertainty and fuzziness are discussed in some survey-type papers. The second part is devoted to basic theoretical issues, including uncertainty measures, fuzzy measures, fuzzy random variables, fuzzy statistics and evaluation and aggregation of imprecise and uncertain evidence. The third part presents the concepts of a stochastic fuzzy set and a probabilistic set which are basically some fuzzy sets involving random aspects. The fourth part presents a wide spectrum of models in which some aspects of fuzziness and randomness co-occur. It includes papers on fuzzy statistical decision making, fuzzy stochastic and statistical dominance, probabilistic-set-based decision making, optimization under fuzziness and randomness and fuzzy dynamic programming with stochastic systems. The fifth and final part deals with applications in economy and finance, nuclear reactor protection, classification and pattern recognition, reliability and earthquake forecasting. The reader is provided with a set of tools which enable him to deal with diverse decision problems in which imprecision and uncertainty jointly occur.
Content:
Front Matter....Pages I-IX
Essay on the History of the Development of Many-Valued Logics and Some Related Topics....Pages 1-9
Uncertainty Aversion and Separated Effects in Decision Making Under Uncertainty....Pages 10-25
Essentials of Decision Making Under Generalized Uncertainty....Pages 26-47
Decision Evaluation Methods Under Uncertainty and Imprecision....Pages 48-65
Fuzzy Random Variables....Pages 66-74
Fuzzy P-Measures and their Application in Decision Making....Pages 75-88
Theory and Applications of Fuzzy Statistics....Pages 89-112
Confidence Intervals for the Parameters of a Linguistic Random Variable....Pages 113-123
On Combining Uncertainty Measures....Pages 124-134
On the Combination of Vague Evidence of the Probabilistic Origin....Pages 135-144
Fuzzy Evaluation of Communicators....Pages 145-151
Uncertain Associational Relations: Compatibility and Transition Relations in Reasoning....Pages 152-167
Stochastic Fuzzy Sets: A Survey....Pages 168-183
Probabilistic Sets — A Survey....Pages 184-196
Decision Making Based on Fuzzy Stochastic and Statistical Dominance....Pages 197-214
Decision Making in a Probabilistic Fuzzy Environment....Pages 215-226
Randomness and Fuzziness in a Linear Programming Problem....Pages 227-239
Comparison of Methodologies for Multicriteria Feasibility — Constrained Fuzzy and Multiple-Objective Stochastic Linear Programming....Pages 240-265
Fuzzy Dynamic Programming with Stochastic Systems....Pages 266-285
Probabilistic-Possibilistic Approach to Some Statistical Problems with Fuzzy Experimental Observations....Pages 286-306
Estimation of Life-Time with Fuzzy Prior Information: Application in Reliability....Pages 307-321
Questionnaires with Fuzzy and Probabilistic Elements....Pages 322-330
From Fuzzy Data to a Single Action — A Simulation Approach....Pages 331-341
Probabilistic Sets in Classification and Pattern Recognition....Pages 342-352
Fuzzy Optimization of Radiation Protection and Nuclear Safety....Pages 353-373
Application of Fuzzy Statistical Decision Making in Countermeasures against Great Earthquakes....Pages 374-388
From an Oriental Market to the European Monetary System: Some Fuzzy-Sets-Related Ideas....Pages 389-399
Back Matter....Pages 400-401
....