Aggregation operators based on some extension of fuzzy sets.
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Date
2018-03-22
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UMT Lahore
Abstract
Bonferroni mean (BM) and heronian mean (HM) operators are useful tools for group decision making problems, when arguments are interrelated to each other.
In this thesis, we developed some BM and HM based aggregation operators.
We defined some aggregation operators for dual hesitant fuzzy (DHF) sets, for instance, we defined dual hesitant fuzzy geometric bonferroni mean (DHFGBM) and different properties of DHFGBM are discussed.
Some special cases are also studied in detail for DHFGBM.
In addition, dual hesitant fuzzy weighted geometric bonferroni mean (DHFWGBM) and dual hesitant fuzzy chouqet geometric bonferroni mean (DHFCGBM) proposed.
We also model a system of fuzzy soft differential equations (FSDEs) to analyze the behavior over the time of an individual depending on their companion’s actions under any particular situation against some decision by the help of BM.
Using the ability of BM to capture the interrelationship of arguments, we defined bonferroni fuzzy soft matrix (BFSM) and weighted bonferroni fuzzy soft matrix (WBFSM) for data representation.
WBFSM is a decision matrix and provide optimum fuzzy soft constant (OFSC), which is the key element of FSDEs.
By utilizing the OFSC, we developed a system of FSDEs to study a dynamical process with nonlinear uncertain and vague data.
We presented a novel efficient technique for analyzing the future attitude of people due to their present decisions.
To illustrate the practicality and feasibility of proposed technique, an example is also discussed with the help of phase portrait and line graphs.
With respect to multiple attribute group decision making problems, in which the value of the attributes are taken in the form of hesitant 2-tuple (H2T) or intuitionistic 2-tuple (I2T) linguistic information are called CW.
H2T linguistic arguments are used to evaluate the group decision making problems which have inter-dependent or interactive attributes.
Some operational laws are developed for H2T linguistic elements and based on these operational laws hesitant 2-tuple weighted averaging (H2TWA) operator and generalize hesitant 2-tuple averaging (GH2TA) operator are proposed.
Combining choquet integral (CI) with H2T linguistic information, defined hesitant 2-tuple correlated averaging (H2TCA) and generalize hesitant 2-tuple correlated averaging (GH2TCA) operators.
In the existing literature review, we observed that during aggregation procedure for H2T, more hesitation produces in the resultant element.
We targeted this issue and developed a diminishing hesitant 2-tuple averaging operator (DH2TA) operator for H2T linguistic arguments.
DH2TA operator work in the way that it’s aggregate all H2T linguistic elements and during the aggregation process it also controls the hesitation in the translation of the resulting aggregated xv xvi linguistic term.
We developed a scalar product for H2T linguistic elements and based on the scalar product, a diminishing weighted hesitant 2-tuple averaging operator (DWH2TA) is introduced.
Moreover, combining CI with H2T linguistic information, the diminishing choquet hesitant 2-tuple average operator (DCH2TA) operator is defined.
Most of existing operational laws in literature for handling the process for CW are not bounded and hence a logical problem comes.
We targeted this issue and developed closed operational laws based on Archimedean t-norm and t-conorm.
Some aggregation operators intuitionistic 2-tuple linguistic heronian mean (I2THM) and intuitionistic 2-tuple linguistic chouqet heronian mean (I2TCHM) based on these closed operational laws developed and discussed desired properties of the proposed operators.
Linkages between industry and university are the significant parts in the entire advancement of any country.
To assess university’s reputation for industry, we proposed a fusion approach by using heronian intuitionistic fuzzy analytic hierarchy process (HIF-AHP), fuzzy geometric bonferroni mean (FGHM) operator and 2-tuple fuzzy linguistic elements.
In each chapter, we developed some techniques based on proposed operators and demonstrated the validity and feasibility of these techniques by some examples.
Educational note: Sentence case formatting prioritizes readability by limiting capitalization to only the first word of each sentence, proper nouns/adjectives (e.g., "Archimedean," derived from the mathematician Archimedes), and acronyms (e.g., BM, DHF). This consistency avoids visual clutter, which is particularly useful for academic texts like the thesis excerpt provided—readers can quickly parse sentence boundaries without distraction from overcapitalized terms. Acronyms are retained in uppercase to preserve their symbolic meaning and avoid confusion with generic terms (e.g., "BM" remains distinct from the common noun "bm").