Fuzzy Choice Research Articles

Degree of dominance and congruence axioms for fuzzy choice functions

In this paper we introduce the degree of dominance of an alternative x with respect to an available fuzzy set of alternatives. Interpreting an available fuzzy set of alternatives as a criterion in decision making the degree of dominance establishes a hierarchy of alternatives with respect to this criterion. With the degree of dominance new congruence axioms for fuzzy choice functions are formulated.

Revealed Preference, Congruence and Rationality: A Fuzzy Approach

In a previous paper connections between the congruence axioms WFCA, SFCA and the revealed preference axioms WAFRP, SAFRP for fuzzy choice functions whose domain contains the characteristic function...

A note on congruence conditions of fuzzy choice functions

In order to reflect the fuzziness existing in a choice problem, Banerjee introduces the concept of fuzzy choice function. Meanwhile, Banerjee proposes three congruence conditions in assessing the rationality of a fuzzy choice function. In this paper, we prove some dependencies among these conditions although Banerjee asserts that they are independent.

Estimation of a reduction in CO2 emissions by shifting commuters’ travel mode from the private car to public transport

A model for forecasting the amount of CO2 emissions due to urban commuter travel was developed. The model consisted of three submodels: a commuters’ number forecasting model, a fuzzy commute travel mode choice model and a CO2 emissions estimation. The model was tested using the real data of Osaka, Japan. Using this model, we also forecasted and analysed the efect of policy changes to shift commuters’ travel mode from private car to public transport in order to decrease the amount of CO2 emissions.

A CONTINGENCY APPROACH TO CHOICE

The moment of choice, when a decision option is identified as being preferred, is a key stage in a decision-making process. Some explicit or implicit mechanism, be it optimising, satisficing or a combination of the two, is required to make a choice. Dependable decision-making requires an appropriate choice mechanism, but the process and criteria by which a choice mechanism is selected are seldom addressed. A contingency approach to choice is proposed in which a choice mechanism is selected according to the characteristics of the information available and the meta-level constraints and objectives of the decision-maker. Information used in the choice is characterised according to the extent and type of uncertainty. The importance in effective decision-making of meta-level requirements, for example for inclusive and transparent mechanisms, is discussed. Normative and fuzzy choice mechanisms are cast within a generic framework of choice mechanisms. A new theory of choice based on interval probabilities is introduced for use in some situations where existing theories of choice are inappropriate.

VLSI implementation of fuzzy adaptive resonance and learning vector quantization

We present a mixed-mode VLSI chip performing unsupervised clustering and classification, implementing models of fuzzy adaptive resonance theory (ART) and learning vector quantization (LVQ), and extending to variants such as Kohonen self-organizing maps (SOM). The parallel processor classifies analog vectorial data into a digital code in a single clock, and implements on-line learning of the analog templates, stored locally and dynamically using the same adaptive circuits for on-chip quantization and refresh. The unit cell performing fuzzy choice and vigilance functions, adaptive resonance learning and long-term analog storage, measures 71 /spl mu/m/spl times/71 /spl mu/m in 2 /spl mu/m CMOS. Experimental learning results are included from a 16-input, 16-category prototype on a 2.2 mm/spl times/2.2 mm chip, operating at 10 ksample/s parallel data rate and 2 mW power dissipation.

Fuzzy route choice model for traffic assignment

In order to represent traffic assignment on a road network, we propose a new route choice model taking account of the imprecisions and the uncertainties lying in the dynamic choice process. This model makes possible a more accurate description of the process than those (deterministic or stochastic) used in the literature. We assume that drivers choose a path all the more than it is foreseen to have a lesser cost. The predicted cost for each path is modelled by a fuzzy subset which can represent imprecision on network knowledge (e.g. length of links) as well as uncertainty on traffic conditions (e.g. congested or uncongested network, incident … ). The costs of all possible paths are compared and result in an attractiveness degree for each path. Various comparison indices can be used to represent the different possible natures of drivers when making their decisions (pessimistic/optimistic, risk-taking/risk-averting). The fuzzy choice model was compared with the LOGIT model (a widely used stochastic discrete choice model) and has been proved to be able to find the same results. The effect of Advanced Travellers Information Systems (ATIS) on drivers is modeled as a modification of the imprecision or the uncertainty of the predicted cost of a route.

Interrelationships among fuzzy preference-based choice functions and significance of rationality conditions: A taxonomic and intuitive perspective

Classical choice theory deals with the issue of making a rational choice from a crisp preference relation. Arguing that human preferences are inherently imprecise, a lot of work has been done in the area of choice-making behavior using fuzzy preferences. This paper traces the evolution of research in the area of choice functions and related notions of rational choice, when fuzzy preferences are allowed. We have critically analyzed the work of various authors, especially with respect to intuitive underpinnings of introduced notions, by giving examples. We also present a unified picture of, and interrelationships between, choice functions and rationality conditions proposed by various authors. Based on these discussions, we suggest possible directions for future work.

Games decision makers play

This piece focuses on the microprocesses of decisions. It distills the complex cognitive processes inherent in decision making into pragmatic utility by articulating several “games”. These games, as they are described in the article, routinely undermine the best‐intentioned proposals, initiatives, strategies and good ideas as they are played in ways that elude most participants. The cognitive decision processes (dubbed “games” here) are described as: Framing; Criteria setting; Misuse of analogy; Misuse of rationality; and Commitment building. The key purpose of the article is to distill complex processes into manageable dialect to improve awareness. Argues that awareness and understanding of these processes is essential to achieve influence in decision making, to avoid the pitfalls of fuzzy choice, and to promote mastery over the decision‐making process.

Fuzzy choice functions, revealed preference and rationality

This paper investigates the conditions under which a fuzzy-set-valued choice function is rationalisable by a fuzzy revealed preference relation satisfying certain regularity conditions. Attention is confined to the case where the domain of the choice function consists of all (crisp) finite subsets of the universal set of alternatives. Two sets of weak and strong axioms of fuzzy revealed preference (WAFRP and SAFRP) are stated. In both cases it turns out that WAFRP is not equivalent to SAFRP and that SAFRP does not characterise rationality. In the special case where every set of avialable alternatives has at least one element which is unambiguously chosen, WAFRP is equivalent to SAFRP but SAFRP still does not characterise rationality. A fuzzy congruence condition, stronger than SAFRP, is proposed and is shown to be necessary and sufficient for rationality.

Expert assistant FICCKAS: Fuzzy information cluster, choice, and knowledge acquisition system

Abstract This paper contains a brief description of the data structures, functional structure, mathematical models and algorithms, and illustration of the user interface implemented in the Expert Assistant FICCKAS.

Fuzzy choice functions

The R-greatest and maximal sets of standard choice theory are extended to fuzzy R-greatest and fuzzy maximal sets. Unlike the precise counterparts of these concepts, these two sets do not in general coincide when preferences are reflexive and connected. A stronger than usual version of connectedness under which the two sets are equal is provided. The concept of a fuzzy choice function is introduced and conditions under which a fuzzy choice function may be rationalized as a fuzzy R-greatest or a fuzzy maximal set are discussed. Rationalizability with transitive and weakly transitive fuzzy preference relations is also considered.

Transitivity of fuzzy relations and rational choice

An attempt is made to explore the implications of weakening the transitivity condition used in defining a fuzzy preference ordering for various results established in the literature.

Fuzzy preferences and choice: A further progress report

Fuzzy preferences and choice: A further progress report

Rational choice function derived from a fuzzy preference

We shall prove that every fuzzy rational choice function is fuzzy regular (see Richter [6, p. 36] ), count the total number of the fuzzy rational choice ftmctions on a set of four elements and consider a semigroup of all fuzzy rational choice functions on a set.

Fuzzy Choice Functions

An approach to choice function theory based on fuzzy set theory is suggested. A number of necessary and sufficient conditions on a fuzzy choice function to be a fuzzy rational choice function of a certain type are established.

Fuzzy rational choice functions

We introduce a concept of fuzzy rationality of a choice function, characterize fuzzy rational choice functions and study the semigroup of all fuzzy rational choice functions on a finite set.

Structure of fuzzy binary relations

The structure of fuzzy binary relations of indifference and preference is studied. The full description of fuzzy equivalence relations in terms of fuzzy partitions is given. All possible logical relations between various transitivity properties of fuzzy preferences are established. These relations permit to choose the notion of a fuzzy quasi-order relation which is an analog of a corresponding crisp relation. The possible approaches to the fuzzy choice are outlined. Finally, the general notion of a relative ‘degree of fuzziness’ is defined in connection with a study of the quantitative description of preservation properties under fuzzy mappings.