A novel method for interval-value intuitionistic fuzzy multicriteria decision-making problems with immediate probabilities based on OWA distance operators

The goal of this work is to develop a novel decision-making method which can solve some complex decision problems that include the following three-aspect information: (1) information represented in the form of interval-valued intuitionistic fuzzy values (IVIFVs) not only intuitionistic fuzzy values (IFVs), (2) the probability information and the weighted information, and (3) the importance degree of each concept in the process of decision-making. Firstly, by integrating OWA operator, probabilistic weight (PW), and individual distance of two IVIFNs in the same formulation, we introduce two new distance operators named PIVIFOWAD operator and IPIVIFOWAD operator, respectively. Secondly, satisfaction degree of an alternative is proposed based on the positive ideal IVIFS and the negative ideal IVIFS and applied to MCDM. Finally, we use an illustrative example to show the feasibility and validity of the new method by comparing with the other existing methods

Decision making with Dempster-Shafer belief structure and the OWAWA operator

[EN] A new decision making model that uses the weighted average and the ordered weighted averaging (OWA) operator in the Dempster-Shafer belief structure is presented. Thus, we are able to represent the decision making problem considering objective and subjective information and the attitudinal character of the decision maker. For doing so, we use the ordered weighted averaging ¿ weighted average (OWAWA) operator. It is an aggregation operator that unifies the weighted average and the OWA in the same formulation. This approach is generalized by using quasi-arithmetic means and group decision making techniques. An application of the new approach in a group decision making problem concerning political management of a country is also developed.We would like to thank the anonymous reviewers for valuable comments that have improved the quality of the paper. Support from the Spanish Ministry of Education under project JC2009-00189 , the University of Barcelona (099311) and the European Commission (PIEFGA-2011-300062) is gratefully acknowledgedMerigó, JM.; Engemann, KJ.; Palacios Marqués, D. (2013). Decision making with Dempster-Shafer belief structure and the OWAWA operator. Technological and Economic Development of Economy. 19(sup 1):S100-S118. https://doi.org/10.3846/20294913.2013.869517SS100S11819sup 1Antuchevičienė, J., Zavadskas, E. K., & Zakarevičius, A. (2010). MULTIPLE CRITERIA CONSTRUCTION MANAGEMENT DECISIONS CONSIDERING RELATIONS BETWEEN CRITERIA / DAUGIATIKSLIAI STATYBOS VALDYMO SPRENDIMAI ATSIŽVELGIANT Į RODIKLIŲ TARPUSAVIO PRIKLAUSOMYBĘ. Technological and Economic Development of Economy, 16(1), 109-125. doi:10.3846/tede.2010.07Brauers, W. K. M., & Zavadskas, E. K. (2010). PROJECT MANAGEMENT BY MULTIMOORA AS AN INSTRUMENT FOR TRANSITION ECONOMIES / PROJEKTŲ VADYBA SU MULTIMOORA KAIP PRIEMONĖ PEREINAMOJO LAIKOTARPIO ŪKIAMS. 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A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Systems with Applications, 38(1), 1053-1060. doi:10.1016/j.eswa.2010.07.144Merigó, J. M. (2011). A unified model between the weighted average and the induced OWA operator. Expert Systems with Applications, 38(9), 11560-11572. doi:10.1016/j.eswa.2011.03.034Merigó, J. M. (2012). The probabilistic weighted average and its application in multiperson decision making. International Journal of Intelligent Systems, 27(5), 457-476. doi:10.1002/int.21531Merigó, J. M., & Casanovas, M. (2009). Induced aggregation operators in decision making with the Dempster-Shafer belief structure. International Journal of Intelligent Systems, 24(8), 934-954. doi:10.1002/int.20368Merigó, J. M., & Casanovas, M. (2010). The uncertain induced quasi-arithmetic OWA operator. International Journal of Intelligent Systems, 26(1), 1-24. doi:10.1002/int.20444MERIGÓ, J. 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Uncertain generalized aggregation operators. Expert Systems with Applications, 39(1), 1105-1117. doi:10.1016/j.eswa.2011.07.11

Proposition structure in framed decision problems: A formal representation.

Framing effects, which may induce decision-makers to demonstrate preference description invariance violation for logically equivalent options varying in semantic emphasis, are an economically significant decision bias and an active area of research. Framing is an issue inter alia for the way in which options are presented in stated-choice studies where (often inadvertent) semantic emphasis may impact on preference responses. While research into both espoused preference effects and its cognitive substrate is highly active, interpretation and explanation of preference anomalies is beset by variation in the underlying structure of problems and latitude for decision-maker elaboration. A formal, general scheme for making transparent the parameter and proposition structure of framed decision stimuli is described. Interpretive and cognitive explanations for framing effects are reviewed. The formalism’s potential for describing extant, generating new stimulus tasks, detailing decision-maker task elaboration. The approach also provides a means of formalising stated-choice response stimuli and provides a metric of decision stimuli complexity. An immediate application is in the structuring of stated-choice test instruments

How incidental values from the environment affect decisions about money, risk, and delay

How different are £0.50 and £1.50, or "a small chance" and "a good chance", or "three months" and "nine months"? Our experiments show that people behave as if these differences alter after incidental everyday experiences. Preference for a £1.50 lottery rather than a £0.50 lottery was stronger after exposure to intermediate supermarket prices. Preference for "a good chance" of winning rather than "a small chance" was stronger after predicting intermediate probabilities of rain. Preference for consumption in "three month" rather than "nine months" was stronger after planning for an intermediate birthday. These fluctuations offer a direct challenge to economic accounts which translate monies, risks, and delays into subjective equivalents by stable functions. The decision by sampling model, in which subjective values are rank positions constructed from comparisons with samples of monies, probabilities, or delays, predicts these effects and indicates a primary role for sampling in decision making

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Dominance of capacities by k-additive belief functions

In this paper we deal with the set of $k$-additive belieffunctions dominating a given capacity. We follow the lineintroduced by Chateauneuf and Jaffray for dominating probabilities and continued by Grabisch for general $k$-additive measures.First, we show that the conditions for the general $k$-additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid. On the other hand, we show that these conditions cannot be improved.We solve this situation by imposing additional constraints on the dominating functions. Then, we consider the more restrictive case of $k$-additive belief functions. In this case, a similar result with stronger conditions is proved. Although better, this result is not completely satisfactory and, as before, the conditionscannot be strengthened. However, when the initial capacity is a belief function, we find a subfamily of the set of dominating $k$-additive belief functions from which it is possible to derive any other dominant $k$-additive belief function, and such that theconditions are even more restrictive, obtaining the natural extension of the result for probabilities. Finally, we apply these results in the fields of Social Welfare Theory and Decision Under Risk.Linear programming, decision analysis, capacity,dominance, k-additivity, belief functions

Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance