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We develop in this paper a novel entropy-independent knowledge measure (KM), with which to reveal some significant aspects of psychological cognition hidden in the handling of intuitionistic fuzzy sets (IFSs). We briefly discuss the two facets of knowledge associated with an IFS, i.e., the information content and the information clarity. We then establish, based on the latest axiomatic definition of KM in the context of IFSs, a novel parameterized KM in which two significant aspects of psychological cognition are considered, personal attitude and preference to be exact. We believe that the KM provided in this manner could truly capture the unique features of an IFS, including the potential knowledge related to the specificity and non-specificity of an IFS, the amount of which depends actually on users' character traits. The developed KM is equipped with two parameters, one of which expresses the type of attitude towards the non-specificity of an IFS while the other indicates the degree of personal preference between those two facets of knowledge. We also show that some existing measures can be obtained as particular cases of this general model. Finally, we illustrate the application of this measure in decision making under uncertainty. [ABSTRACT FROM AUTHOR]

A novel model is presented in this article to derive the expected value from a ranking of alternatives, with which to tackle some uncertain problems, such as different types of att0itudes, in the creation of personalized quantifier caused by personal preference. There is no doubt that we consider here a reverse process of traditional ranking methods in decision making. More specifically, a representative sample of multi-attribute alternatives is prepared, and an involved person is asked to do nothing but provide, following personal preference or judgment on the whole, a ranking of alternatives of this sample. The relationship between the alternatives' importance weights and their ranking positions is investigated. A TOPSIS-based model can then be established to derive his/her personal expected value from this ranking. The idea of ordered weighted averaging (OWA) aggregations is fully taken into account in the modeling. We use this technique to create a personalized quantifier, thus making the creation much more efficient and safer compared with what we did before. Experimental results show that different rankings of alternatives may lead to different expected values that eventually determine different types of attitudes. Thus, the developed technique could be used as a tool for uncertainty modeling in more complex situations in which various personality traits have to be taken into account, especially for decision making under uncertainty. [ABSTRACT FROM AUTHOR]

A measure of knowledge should not be viewed simply as a dual measure of entropy in the context of intuitionistic fuzzy sets as there is no natural logic between these two kinds of measures with the introduction of hesitancy, nor in the context of interval-valued intuitionistic fuzzy sets (IVIFSs), for that matter. This work is devoted to the introduction of an axiomatic definition of knowledge measure for IVIFSs. In order to do that, a set of new axioms is presented with which knowledge measure should comply in the context of IVIFSs. A concrete model following these axioms is then developed to measure the amount of knowledge associated with an IVIFS. Two facets of knowledge associated with an IVIFS, i.e., the information content and the information clarity, are simultaneously taken into account in the construction of the model to truly reflect the nature of an IVIFS. In particular, the connection between knowledge measure and fuzzy entropy is investigated under this axiomatic framework. A series of tests is also provided to examine the performance of the developed measure. Finally, a concept of knowledge weight on attribute in multi-attribute decision making is presented and an illustrative example is used as a demonstration of the application of the developed technique to decision making under uncertainty. [ABSTRACT FROM AUTHOR]

A new form of personalized quantifier is developed in this paper, with which to investigate and formalize people's personalities or behavior intentions that have to be considered in increasingly complex situations. As we show in the article, the developed quantifier is realized by generalized Bernstein polynomials combined with interpolation spline, and finally expressed as a sequence of piecewise nonlinear polynomials with an adjustable degree. It is characterized by many excellent properties exemplified by such terms as sufficient smoothness, shape-preserving interpolation, and a high rate of convergence. In particular, the consistency of the ordered weighted averaging (OWA) aggregation under the guidance of the developed quantifier is addressed and proved. This actually provides a sound theoretical basis for practical use. We also experimentally show that the developed quantifier significantly outperforms, in all respects of geometrical characteristics, the other ones presented in previous work, whether from a viewpoint of global approximation of functions or local one. As such, the developed quantifier could be considered as an effective analytical tool for decision making under uncertainty in which different personality traits have to be taken into account. [ABSTRACT FROM AUTHOR]

Given the fact that totally unknown information cannot be expressed by Zadeh's fuzzy sets but can well be represented by Atanassov's intuitionistic fuzzy sets (A-IFSs), we provide in this paper a new idea, from the perspective of amount of knowledge, that the entropy for such information should be unique so that it may differ significantly from the entropy of a particular fuzzy element of which the membership and non-membership values are both equal to 0.5. Motivated by this idea, we present a more strict axiomatic definition of entropy on A-IFSs, and then develop a new entropy measure of A-IFSs that satisfies the refined axioms, with the aim of overcoming some drawbacks and ambiguities the existing entropy brings about and building a new entropy measurement model in the A-IFSs context to show some unique features of A-IFSs from the viewpoint of a specific purpose, notably those related to decision making. This allows us to capture the intrinsic amount of knowledge and the additional features that may be relevant when making decisions, and ultimately may be able to help us distinguish such particular cases in which the membership values are equal to the corresponding non-membership values in the A-IFSs context. Finally, a real-life example is provided for an in-depth discussion on the application of the developed models in decision making under uncertainty. [ABSTRACT FROM AUTHOR]

The ordered weighted averaging (OWA) operator provides a unified framework for multiattribute decision making (MADM) under uncertainty. In this paper, we attempt to tackle some issues arising from the quantifier guided aggregation using OWA operators. This allows us to consider a more general case involving the generation of quantifier targeted at the specified decision maker (DM) by using sample information. In order to do that, we first develop a repeatable interactive procedure in which with the given sample values, and the expected values the DM involved provides with personal preferences, we build nonlinear optimal models to extract from the DM information about his/her decision attitude in an OWA weighting vector form. After that, with the obtained attitudinal weighting vectors we suggest a suitable quantifier just for this DM by means of the piecewise linear interpolations. This obtained quantifier is totally derived from the behavior of the DM involved and thus inherently characterized by his/her own attitudinal character. Owing to the nature of this type of quantifier, we call it the subjective expected value of sample information-induced quantifier. We show some properties of the developed quantifier. We also prove the consistency of OWA aggregation guided by this type of quantifier. In contrast with parameterized quantifiers, our developed quantifiers are oriented toward the specified DMs with proper consideration of their decision attitudes or behavior characteristics, thus bringing about more intuitively appealing and convincing results in the quantifier guided OWA aggregation. [ABSTRACT FROM PUBLISHER]

The ranking of Atanassov's intuitionistic fuzzy values (A-IFVs) is nontrivial because there is no natural linear order among them, as opposed to fuzzy sets. In this paper, we tackle this difficult problem and develop a new novel technique for ranking A-IFVs based on amount of information using the geometrical representation of Atanassov's intuitionistic fuzzy sets (A-IFSs), with the aim of overcoming some drawbacks and ambiguities in existing methods and to build a new ranking model in the A-IFS context from the viewpoint of amount of information. We prove that the order on nonempty A-IFVs induced by our function is admissible in the A-IFS context. Thus, our developed method provides a total order that extends the usual partial order between A-IFVs. Moreover, we discuss the role that a decision maker's attitude can play in decision making under uncertainty. This allows us to introduce the idea of attitudinal-based extension of our developed technique, which is much more useful and flexible in real-world applications. By this, we also provide a new idea and explanation to evaluate two special A-IFVs: the completely known opposition (0,1,0) and the completely unknown information (0,0,1). Finally, an effort is made to extend the applicability of the developed methods by considering the situation in which Atanassov's interval-valued intuitionistic fuzzy sets are involved. Experimental studies show the good performance of the developed methods in the A-IF and A-IVIF situations, respectively. [ABSTRACT FROM AUTHOR]

Abstract: Recent studies on the combination rule of D–S evidence theory can be summarized as two categories, i.e. the methods based on modification for Dempster rule, and the methods based on correction to original evidence sources. However, both of them fail to deal with the role of cardinality of focal elements in process of combination, leading generally to the imperfect final results which are hard to show the inherent differences between different bodies of evidence. In this paper, we propose a combination rule based on the strategy of cross merging between evidences, a newly developed methodology which can better reflect the focusing degree of focal elements between bodies of evidence, and make final combination results more succinct, reasonable and valid. Throughout the process of combination, such global information as reliability, focusing weights, and expected support of evidences is thoroughly taken into account. In addition, an effort is made to allocate evidential conflict in proportion only among combination propositions in order to refine combination results and reduce their decision range. A numerical example and its modified version demonstrate that the presented approach has good adaptability to the evidences in accord or with high conflict, and significantly outperforms other combination methods of a similar kind. [Copyright &y& Elsevier]