scholarly journals FUZZY STRICT PREFERENCE RELATIONS COMPATIBLE WITH FUZZY ORDERINGS

2010 ◽  
Vol 18 (01) ◽  
pp. 13-24 ◽  
Author(s):  
BONIFACIO LLAMAZARES ◽  
BERNARD DE BAETS
Keyword(s):  
Equivalence Relation ◽  
Preference Relation ◽  
Strict Preference ◽  
Preference Modelling ◽  
Preference Relations ◽  
Weak Preference ◽  
Indifference Relation ◽  
Definition Of ◽  
Fuzzy Orderings ◽  
Fuzzy Preference

One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity.

An intuitionistic logic for preference relations

2019 ◽  
Vol 27 (4) ◽  
pp. 434-450 ◽  
Author(s):  
Paolo Maffezioli ◽  
Alberto Naibo
Keyword(s):  
Intuitionistic Logic ◽  
Preference Relation ◽  
Order Logic ◽  
First Order Logic ◽  
Strict Preference ◽  
Preference Relations ◽  
First Order ◽  
Weak Preference ◽  
The Way

AbstractWe investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely axiomatizable in first-order logic.

scholarly journals Additively Consistent Interval-Valued Intuitionistic Fuzzy Preference Relations and Their Application to Group Decision Making

Information ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 260 ◽  
Author(s):  
Hua Zhuang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Weighted Averaging ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Priority Weights ◽  
Interval Valued ◽  
Fuzzy Preference

This paper aims to propose an innovative approach to group decision making (GDM) with interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs). First, an IVIFPR is proposed based on the additive consistency of an interval-valued fuzzy preference relation (IVFPR). Then, two mathematical or adjusted programming models are established to extract two special consistent IVFPRs. In order to derive the priority weight of an IVIFPR, after taking the two special IVFPRs into consideration, a linear optimization model is constructed by minimizing the deviations between individual judgments and between the width degrees of the interval priority weights. For GDM with IVIFPRs, the decision makers’ weights are generated by combining the adjusted subjective weights with the objective weights. Subsequently, using an IVIF-weighted averaging operator, the collective IVIFPR is obtained and utilized to derive the IVIF priority weights. Finally, a practical example of a supplier selection is analyzed to demonstrate the application of the proposed method.

scholarly journals Decomposition and Arrow-Like Aggregation of Fuzzy Preferences

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 436 ◽  
Author(s):  
Armajac Raventós-Pujol ◽  
María J. Campión ◽  
Esteban Induráin
Keyword(s):  
Common Sense ◽  
New Technique ◽  
Impossibility Theorem ◽  
Binary Relations ◽  
Strict Preference ◽  
Weak Preference ◽  
Fuzzy Preferences ◽  
A New Technique ◽  
Fuzzy Setting ◽  
Fuzzy Preference

We analyze the concept of a fuzzy preference on a set of alternatives, and how it can be decomposed in a triplet of new fuzzy binary relations that represent strict preference, weak preference and indifference. In this setting, we analyze the problem of aggregation of individual fuzzy preferences in a society into a global one that represents the whole society and accomplishes a shortlist of common-sense properties in the spirit of the Arrovian model for crisp preferences. We introduce a new technique that allows us to control a fuzzy preference by means of five crisp binary relations. This leads to an Arrovian impossibility theorem in this particular fuzzy setting.

A CONSENSUS MODEL FOR GROUP DECISION-MAKING PROBLEMS WITH INTERVAL FUZZY PREFERENCE RELATIONS

2012 ◽  
Vol 11 (04) ◽  
pp. 709-725 ◽  
Author(s):  
J. M. TAPIA GARCÍA ◽  
M. J. DEL MORAL ◽  
M. A. MARTÍNEZ ◽  
E. HERRERA-VIEDMA
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Selection Process ◽  
Preference Relation ◽  
Feedback Mechanism ◽  
Consensus Model ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

Interval fuzzy preference relations can be useful to express decision makers' preferences in group decision-making problems. Usually, we apply a selection process and a consensus process to solve a group decision situation. In this paper, we present a consensus model for group decision-making problems with interval fuzzy preference relations. This model is based on two consensus criteria, a consensus measure and a proximity measure, and also on the concept of coincidence among preferences. We compute both consensus criteria in the three representation levels of a preference relation and design an automatic feedback mechanism to guide experts in the consensus reaching process. We show an application example in social work.

scholarly journals Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 185 ◽  
Author(s):  
Atiq-ur Rehman ◽  
Mustanser Hussain ◽  
Adeel Farooq ◽  
Muhammad Akram
Keyword(s):  
Decision Making ◽  
Preference Relation ◽  
Selection Procedure ◽  
Feedback Mechanism ◽  
Decision Makers ◽  
Consensus Process ◽  
Preference Relations ◽  
Priority Weights ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process.

ON ADDITIVE CONSISTENT PROPERTIES OF THE INTUITIONISTIC FUZZY PREFERENCE RELATION

2010 ◽  
Vol 09 (06) ◽  
pp. 1009-1025 ◽  
Author(s):  
ZAIWU GONG ◽  
LIANSHUI LI ◽  
JIE CAO ◽  
FEIXUE ZHOU
Keyword(s):  
Preference Relation ◽  
Fundamental Principle ◽  
Human Judgment ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Preference Relations ◽  
Weak Transitivity ◽  
Consistency Properties ◽  
Intuitionistic Fuzzy Preference Relation ◽  
Fuzzy Preference

We investigate the properties of additive consistent intuitionistic fuzzy preference relations (IFPR). Usually, consistency in fuzzy preference relations (FPR) is associated with transitivity such as general transitivity, weak transitivity, and restricted max–max transitivity. This paper extends the consistency properties of the FPR to those of the IFPR. Since weak transitivity is the minimal logical requirement and a fundamental principle of human judgment, this paper develops three determination theorems and the corresponding algorithms to judge the weak transitivity of an IFPR from different angles. Two numerical examples show that the three methods proposed are feasible and effective.

scholarly journals Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Zia Bashir ◽  
Tabasam Rashid ◽  
Mobashir Iqbal
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Decision Makers ◽  
Decision Support Model ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Hesitant Fuzzy Preference Relation ◽  
Fuzzy Preference

Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.

scholarly journals INCOMPLETE INTERVAL FUZZY PREFERENCE RELATIONS FOR SUPPLIER SELECTION IN SUPPLY CHAIN MANAGEMENT

2014 ◽  
Vol 21 (3) ◽  
pp. 379-404 ◽  
Author(s):  
Yejun XU ◽  
Ravi PATNAYAKUNI ◽  
Feifei TAO ◽  
Huimin WANG
Keyword(s):  
Supply Chain ◽  
Decision Maker ◽  
Supplier Selection ◽  
Preference Relation ◽  
Fuzzy Preference Relation ◽  
Chain Management ◽  
Preference Relations ◽  
Interval Fuzzy Preference Relation ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

In the analytical hierarchy process (AHP), it needs the decision maker to establish a pairwise comparison matrix requires n(n–1)/2 judgments for a level with n criteria (or alternatives). In some instances, the decision maker may have to deal with the problems in which only partial information and uncertain preference relation is available. Consequently, the decision maker may provide interval fuzzy preference relation with incomplete information. In this paper, we focus our attention on the investigation of incomplete interval fuzzy preference relation. We first extend a characterization to the interval fuzzy preference relation which is based on the additive transitivity property. Using the characterization, we propose a method to construct interval additive consistent fuzzy preference relations from a set of n–1 preference data. The study reveals that the proposed method can not only alleviate the comparisons, but also ensure interval preference relations with the additive consistent property. We also develop a novel procedure to deal with the analytic hierarchy problem for group decision making with incomplete interval fuzzy preference relations. Finally, a numerical example is illustrated and a supplier selection case in supply chain management is investigated using the proposed method.

scholarly journals Technology Selection For Construction Project, With The Use Of Fuzzy Preference Relation

2015 ◽  
Vol 61 (3) ◽  
pp. 105-118 ◽  
Author(s):  
N. Ibadov ◽  
J. Rosłon
Keyword(s):  
Preference Relation ◽  
Construction Project ◽  
Technology Selection ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Technological Complexity ◽  
Fuzzy Preference Relations ◽  
Criteria Weights ◽  
Selection For ◽  
Fuzzy Preference

AbstractArticle deals with the problem of technology selection for construction project. Three criteria were proposed: cost, time and technological complexity. To solve the problem, fuzzy preference relations were used. Authors present an algorithm supporting multi-criteria decision-making process. The algorithm creates fuzzy preference relations on the basis of the fuzzy comparison: “xi is better than xj”. Then, with the use of criteria weights it creates general fuzzy preference relation, finds all non-dominated (admissible) alternatives and the best one among them. The algorithm consists of 7 steps. Authors show application of the proposed algorithm - example calculations.

COMPUTING WITH WORDS IN DECISION MAKING THROUGH INDIVIDUAL AND COLLECTIVE LINGUISTIC CHOICE RULES

2001 ◽  
Vol 09 (supp01) ◽  
pp. 89-102 ◽  
Author(s):  
JANUSZ KACPRZYK ◽  
S£AWOMIR ZADROZNY
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Computing With Words ◽  
Final Solution ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Universal Representation ◽  
Fuzzy Preference

A fuzzy preference relation is a popular model to represent both individual and group preferences. However, what is often sought is a subset of alternatives that is an ultimate solution of a decision problem. In order to arrive at such a final solution individal and/or group choice rules may be employed. There is a wealth of such rules devised in the context of the classical, crisp preference relations. Originally, most of the popular group decision making rules were conceived for classical (crisp) preference relations (orderings), and then extended to the case of traditional fuzzy preference relations. Moreover, they often differ in their assumptions about the properties o the preference relations to be processed. In the paper we pursue the path towards a universal representation of such rules that provides an effective generalization of the classical rules for the fuzzy case. Moreover, it leads to a meaningful extension to the linguistic preferences, in the spirit of the computing with words paradigm.

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