A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets

Hesitant fuzzy sets, as an extension of fuzzy sets to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work is focused on the interval-valued hesitant fuzzy sets (IVHFSs) to manage additional uncertainty. Now that distance and similarity as a kind of information measures are essential and important numerical indexes in fuzzy set theory and all their extensions, the present work aims at investigating distance and similarity measures in the IVHFSs and then employing them into multiple attribute decision making application. To begin with, II-type generalized interval-valued hesitant fuzzy distance is firstly introduced in the IVHFS, along with its properties and its relationships with the traditional Hamming-Distance and the Euclidean distance. Afterwards, another interval-valued hesitant fuzzy Lp distance based on Lp metric is proposed and its relationship with the Hausdorff distance is discussed. In addition, different from most of similarity measures with dependent on the corresponding distances, a new similarity measure based on set-theoretic approach for IVHFSs is introduced and its properties are discussed; especially, a relative similarity measure is proposed based on the positive ideal IVHFS and the negative ideal IVHFS. Finally, we describe how the IVHFS and its relative similarity measure can be applied to multiple attribute decision making. A numerical example is then provided to illustrate the effectiveness of the proposed method

An effective similarity measurement under epistemic uncertainty

The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such inter-pretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets

Selecting target market by similar measures in interval intuitionistic fuzzy set

The selection of the target market plays vital role in promoting the marketing strategies of companies. We presented is a method for target market selection. We introduce some novel similarity measures between intuitionistic fuzzy sets and the novel similarity measures between interval-valued intuitionistic fuzzy sets. They are constructed by combining exponential and other functions. Finally, we introduce a multi-criteria decision making model to select target market by using the novel similarity measure of interval intuitionistic fuzzy sets

Multiaspect soft sets and its generalizations / Nor Hashimah Sulaiman

The theory of soft sets introduced in 1999 by Molodtsov is an alternative mathematical tool for dealing with uncertainties. It basically deals with information representations of objects characterized by parameters which are defined over a single common universal set. Combinations of the theory with fuzzy sets and interval-valued fuzzy sets have resulted in the so-called fuzzy soft sets and interval-valued fuzzy soft sets. Various theoretical studies on these theories and the variants have been made, and applications of the theories in various areas particularly in the area of decision making are continuously explored. Soft sets, fuzzy soft sets and interval-valued fuzzy soft sets have greater potential in information representation should the universe sets of elements not be restricted to only a common universal set. Real life situations may involve descriptions of objects, situations or entities based on certain characteristics or attributes which may be associated with different sets of elements of different types of universal sets. In this thesis, we introduce the concepts of multiaspect soft set (MASS), multiaspect fuzzy soft set (MAFSS) and multiaspect interval-valued fuzzy soft set (MAIVFSS) which are generalizations of soft sets, fuzzy soft sets and intervalvalued fuzzy soft sets, respectively. These concepts provide platforms for information representations that allow elements from different universal sets be taken into consideration in the description of a particular object, item or entity. MASS is defined for crisp data representation while MAFSS and MAIVFSS are respectively defined for fuzzy data representation with single and interval-valued membership degrees. For each concept, the set operations are established and the algebraic properties are studied. The concepts of mapping for multiaspect soft classes, multiaspect fuzzy soft classes and multiaspect interval-valued fuzzy soft classes are presented. In addition, we put forward the axiomatic definitions of distance, distance-based similarity measures and entropy for MAFSS and MAIVFSS. We introduce weighted and nonweighted distances and similarity measures based on the Hamming distance and the Euclidean distance. Relationships between the three measures are investigated. In the final part of the thesis, we highlight the applicability of some of the introduced concepts in solving group decision making problem under MAFSS and MAIVFSS environment

Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders

In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals

New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

In this paper we propose a new approach to construct similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop new approach for solving problems of pattern recognition and multi-criteria fuzzy decision making

Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential applications, that fuzzy logic programming frameworks enhanced with them can correctly work together with lexical resources and ontologies in order to improve their capabilities for knowledge representation and reasoning

Fuzzy Interval-Valued Multi Criteria Based Decision Making for Ranking Features in Multi-Modal 3D Face Recognition

Soodamani Ramalingam, 'Fuzzy interval-valued multi criteria based decision making for ranking features in multi-modal 3D face recognition', Fuzzy Sets and Systems, In Press version available online 13 June 2017. This is an Open Access paper, made available under the Creative Commons license CC BY 4.0 https://creativecommons.org/licenses/by/4.0/This paper describes an application of multi-criteria decision making (MCDM) for multi-modal fusion of features in a 3D face recognition system. A decision making process is outlined that is based on the performance of multi-modal features in a face recognition task involving a set of 3D face databases. In particular, the fuzzy interval valued MCDM technique called TOPSIS is applied for ranking and deciding on the best choice of multi-modal features at the decision stage. It provides a formal mechanism of benchmarking their performances against a set of criteria. The technique demonstrates its ability in scaling up the multi-modal features.Peer reviewedProo